Viscosity measuring method and viscosity measuring apparatus

Abstract

A viscosity measuring method and apparatus including (1) a step in which a plunger having an outer radius R.sub.i is immersed into a sample in a container having an inner radius R.sub.0, by an initial depth L.sub.0; (2) a step in which the plunger is further immersed at a velocity v.sub.p1 by a distance ΔL.sub.1, and a force applied to the plunger is measured; (3) a step in which a peak value F.sub.T1 of the force is obtained; (4) a step in which the plunger is returned to the initial depth L.sub.0; (5) a step in which the plunger is further immersed at a velocity v.sub.p2 by a distance ΔL.sub.2, and a force applied to the plunger is measured; (6) a step in which a peak value F.sub.T2 of the force is obtained; (7) a step in which a flow behavior index n is obtained.

Claims

1. A method of measuring an apparent viscosity of a sample of non-Newtonian fluid comprising: (1) a step in which a plunger having an outer radius R.sub.i is immersed into a sample contained in a cylindrical container having an inner radius R.sub.0, coaxially with the cylindrical container by an initial depth L.sub.0 and stopped thereat, the outer radius R.sub.i of the plunger being smaller than the inner radius R.sub.0 of the cylindrical container; (2) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a first relative movement distance ΔL.sub.1, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time; (3) a step in which a first peak value F.sub.T1 of the force applied to the plunger from the sample is obtained, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; (4) a step in which the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat; (5) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by a second relative movement distance ΔL.sub.2, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time; (6) a step in which a second peak value F.sub.T2 of the force applied to the plunger from the sample is obtained, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; (7) a step in which a flow behavior index n of the sample is obtained, based on the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (1): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{\left(L_0+L_{2\_2}\right)}/\frac{F_{\mathrm{cb}1}}{\left(L_0+L_{2\_1}\right)}\right)}& \left(1\right)\end{array}$ in which $F_{\mathrm{cb}1}=F_{T1}-\rho {\mathrm{gL}}_{2\_1}\pi R_i^2,F_{\mathrm{cb}2}=F_{T2}-\rho {\mathrm{gL}}_{2\_2}\pi R_i^2,L_{2\_1}=\frac{\Delta L_1}{1-{\kappa }^2},L_{2\_2}=\frac{\Delta L_2}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration; (8) a step in which a dimensionless coordinate λ corresponding to the flow behavior index n is obtained, based on a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; and (9) a step in which an apparent viscosity μ.sub.a of the sample is calculated, based on the first relative movement distance ΔL.sub.1 or the second relative movement distance ΔL.sub.2 of the plunger at the first relative movement velocity v.sub.p1 or the second relative movement velocity v.sub.p2, the first peak value F.sub.T1 or the second peak value F.sub.T2, the dimensionless coordinate λ, and the following Expression (2): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(2\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb}}}{\pi \left(L_0+L_2\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb}}=F_T-\rho {\mathrm{gL}}_2\pi R_i^2,L_2=\frac{\Delta L}{1-{\kappa }^2},T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_p{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right]$ $\left(v_p=v_{p1}\mathrm{or}{v}_{p2},\Delta L_1\mathrm{or}\Delta L_2,F_T=F_{T1}\mathrm{or}{F}_{T2}\right).$

2. The viscosity measuring method according to claim 1, wherein the first and second relative movement distances ΔL.sub.1and ΔL.sub.2 are smaller than the initial depth L.sub.0.

3. The viscosity measuring method according to claim 1, wherein: the parameter κ is not less than 0.3 and not more than 0.98; the first and second relative movement velocities v.sub.p1 and v.sub.p2 are not less than 1 mm/min and not more than 1200 mm/min; and the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 are not more than 3 mm.

4. The viscosity measuring method according to claim 1, wherein: the parameter κ is not less than 0.3 and not more than 0.98; the first and second relative movement velocities v.sub.p1 and v.sub.p2 are not less than 1 mm/min and not more than 1200 mm/min; and a deformation ratio of the sample is not more than 10%.

5. The viscosity measuring method according to claim 1, wherein the predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ is described in the following Table (1) TABLE-US-00010 TABLE (1) (n, κ, λ) correspondence table (Values of λ for different values of κ and n) n 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 κ 0.1 0.4065 0.4889 0.5539 0.6009 0.6344 0.6586 0.6768 0.6907 0.7017 0.7106 0.2 0.5140 0.5680 0.6092 0.6398 0.6628 0.6803 0.6940 0.7049 0.7138 0.7211 0.3 0.5951 0.6313 0.6587 0.6794 0.6953 0.7078 0.7177 0.7259 0.7326 0.7382 0.4 0.6647 0.6887 0.7068 0.7206 0.7313 0.7399 0.7469 0.7527 0.7575 0.7616 0.5 0.7280 0.7433 0.7547 0.7636 0.7705 0.7761 0.7807 0.7846 0.7878 0.7906 0.6 0.7871 0.7962 0.8030 0.8082 0.8124 0.8158 0.8186 0.8209 0.8229 0.8246 0.7 0.8433 0.8480 0.8516 0.8544 0.8566 0.8584 0.8599 0.8611 0.8622 0.8631 0.8 0.8972 0.8992 0.9007 0.9019 0.9028 0.9035 0.9042 0.9047 0.9052 0.9055 0.9 0.9493 0.9498 0.9502 0.9504 0.9507 0.9508 0.9510 0.9511 0.9512 0.9513.

6. The viscosity measuring method according to claim 1, wherein the predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ is described in the following Expression (6a), Expression (6b) and Expression (6c) $\begin{array}{cc}{\varphi }_p={\int }_{\kappa }^{\lambda }{\left(\frac{{\lambda }^2}{x}-x\right)}^{s}dx-{\int }_{\lambda }^1{\left(x-\frac{{\lambda }^2}{x}\right)}^{s}dx& \left(6a\right)\\ \Phi =\frac{1}{s+3}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right]+{\varphi }_p\left(\frac{2\left(s+1\right)}{\left(s+3\right)}{\lambda }^2-\left({\lambda }^2-{\kappa }^2\right)\right)& \left(6b\right)\\ \Phi ={\varphi }_p{\kappa }^2.& \left(6c\right)\end{array}$

7. A method of measuring an apparent viscosity of a sample of non-Newtonian fluid comprising: (1) a step in which a plunger having an outer radius R.sub.i is immersed into a sample contained in a cylindrical container having an inner radius R.sub.0, coaxially with the cylindrical container by an initial depth L.sub.0 and stopped thereat, the outer radius R.sub.i of the plunger being smaller than the inner radius R.sub.0 of the cylindrical container; (2) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a relative movement distance ΔL, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time; (3) a step in which a first peak value F.sub.T1 of the force applied to the plunger from the sample is obtained, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; (4) a step in which the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat; (5) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by the relative movement distance ΔL, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time; (6) a step in which a second peak value F.sub.T2 of the force applied to the plunger from the sample is obtained, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; (7) a step in which a flow behavior index n of the sample is obtained, based on the relative movement distance ΔL at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (3): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{\left(F_{\mathrm{cb}1}\right)}\right)}& \left(3\right)\end{array}$ in which $F_{\mathrm{cb}1}=F_{T1}-\rho {\mathrm{gL}}_2\pi R_i^2,F_{\mathrm{cb}2}=F_{T2}-\rho {\mathrm{gL}}_2\pi R_i^2,L_2=\frac{\Delta L_1}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration; (8) a step in which a dimensionless coordinate λ corresponding to the flow behavior index n is obtained, based on a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; and (9) a step in which an apparent viscosity μ.sub.a of the sample is calculated, based on the relative movement distance ΔL of the plunger at the first relative movement velocity v.sub.p1 or the second relative movement velocity v.sub.p2, the first peak value F.sub.T1 or the second peak value F.sub.T2, the dimensionless coordinate λ, and the following Expression (4): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(4\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb}}}{\pi \left(L_0+L_2\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb}}=F_T-\rho {\mathrm{gL}}_2\pi R_i^2,T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_p{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right]$ $\left(v_p=v_{p1}\mathrm{or}{v}_{p2},F_T=F_{T1}\mathrm{or}{F}_{T2}\right).$

8. A method of measuring an apparent viscosity of a sample of non-Newtonian fluid comprising: (1) a step in which a plunger having an outer radius R.sub.i is immersed into a sample contained in a cylindrical container having an inner radius R.sub.0, coaxially with the cylindrical container by an initial depth L.sub.0 and stopped thereat, the outer radius R.sub.i of the plunger being smaller than the inner radius R.sub.0 of the cylindrical container; (2) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a first relative movement distance ΔL.sub.1, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time; (3) a step in which a first peak value F.sub.T1 of the force applied to the plunger from the sample is obtained, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; (4) a step in which the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat; (5) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by a second relative movement distance ΔL.sub.2, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time; (6) a step in which a second peak value F.sub.T2 of the force applied to the plunger from the sample is obtained, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; (7) a step in which a flow behavior index n of the sample is obtained, based on the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (1): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{\left(L_0+L_{2\_2}\right)}/\frac{F_{\mathrm{cb}1}}{\left(L_0+L_{2\_1}\right)}\right)}& \left(1\right)\end{array}$ in which $F_{\mathrm{cb}1}=F_{T1}-\rho {\mathrm{gL}}_{2\_1}\pi R_i^2,F_{\mathrm{cb}2}=F_{T2}-\rho {\mathrm{gL}}_{2\_2}\pi R_i^2,L_{2\_1}=\frac{\Delta L_1}{1-{\kappa }^2},L_{2\_2}=\frac{\Delta L_2}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration; (8) a step in which a dimensionless coordinate λ corresponding to the flow behavior index n is obtained, based on a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; (9) a step in which the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat; (10) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a third relative movement velocity v.sub.p3 by a third relative movement distance ΔL.sub.3, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time; (11) a step in which a third peak value F.sub.T3 of the force applied to the plunger from the sample is obtained, based on measured values of the force caused by the relative movement of the plunger at the third relative movement velocity v.sub.p3; and (12) a step in which an apparent viscosity μ.sub.a of the sample is calculated, based on the third relative movement distance ΔL.sub.3 of the plunger at the third relative movement velocity v.sub.p3, the third peak value F.sub.T3, the dimensionless coordinate λ, and the following Expression (5): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(5\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb}\_3}}{\pi \left(L_0+L_{2\_3}\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb}\_3}=F_T-\rho {\mathrm{gL}}_{2\_3}\pi R_i^2,L_{2\_3}=\frac{\Delta L_3}{1-{\kappa }^2},T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_{p3}{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right].$

9. An apparatus for calculating an apparent viscosity μ.sub.a of a sample, the apparatus comprising: a cylindrical container having a predetermined inner radius R.sub.0, in which a sample is contained; a plunger having an outer radius R.sub.i that is smaller than the inner radius R.sub.0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable; a driving unit configured to relatively move the plunger coaxially with the cylindrical container; a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample; and a control unit configured to control the driving unit; wherein: the control unit is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a first relative movement distance ΔL.sub.1; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity v.sub.p1 and after the further immersing operation thereof; the control unit is configured to obtain a first peak value F.sub.T1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; the control unit is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by a second relative movement distance ΔL.sub.2; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity v.sub.p2 and after the further immersing operation thereof; the control unit is configured to obtain a second peak value F.sub.T2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; the control unit is further configured to obtain a flow behavior index n of the sample, based on the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (1): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{\left(L_0+L_{2\_2}\right)}/\frac{F_{\mathrm{cb}1}}{\left(L_0+L_{2\_1}\right)}\right)}& \left(1\right)\end{array}$ in which $F_{\mathrm{cb}1}=F_{T1}-\rho {\mathrm{gL}}_{2\_1}\pi R_i^2,F_{\mathrm{cb}2}=F_{T2}-\rho {\mathrm{gL}}_{2\_2}\pi R_i^2,L_{2\_1}=\frac{\Delta L_1}{1-{\kappa }^2},L_{2\_2}=\frac{\Delta L_2}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration so as to obtain a dimensionless coordinate λ corresponding to the flow behavior index n, based on the flow behavior index n and a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; and the control unit is further configured to calculate an apparent viscosity μ.sub.a of the sample, based on the first relative movement distance ΔL.sub.1 or the second relative movement distance ΔL.sub.2 of the plunger at the first relative movement velocity v.sub.p1 or the second relative movement velocity v.sub.p2, the first peak value F.sub.T1 or the second peak value F.sub.T2, the dimensionless coordinate λ, and the following Expression (2): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(2\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb}}}{\pi \left(L_0+L_2\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb}}=F_T-\rho {\mathrm{gL}}_2\pi R_i^2,L_2=\frac{\Delta L}{1-{\kappa }^2},T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_p{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right]$ $\left(v_p=v_{p1}\mathrm{or}{v}_{p2},\Delta L=\Delta L_1\mathrm{or}\Delta L_2,F_T=F_{T1}\mathrm{or}{F}_{T2}\right).$

10. The viscosity measuring apparatus according to claim 9, wherein the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 are smaller than the initial depth L.sub.0.

11. The viscosity measuring apparatus according to claim 9, wherein: the plunger ratio κ is not less than 0.3 and not more than 0.98; the first and second relative movement velocities v.sub.p1 and v.sub.p2 are not less than 1 mm/min and not more than 1200 mm/min; and the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 are not more than 3 mm.

12. The viscosity measuring apparatus according to claim 9, wherein: the plunger ratio κ is not less than 0.3 and not more than 0.98; the first and second relative movement velocities v.sub.p1 and v.sub.p2 are not less than 1 mm/min and not more than 1200 mm/min; and a deformation ratio of the sample is not more than 10%.

13. The viscosity measuring apparatus according to claim 9, wherein the predetermined relationship held among the flow behavior index n, the parameter κ is and the dimensionless coordinate λ is described in the following Table (1). TABLE-US-00011 TABLE (1) (n, κ, λ) correspondence table (Values of λ for different values of κ and n) n 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 κ 0.1 0.4065 0.4889 0.5539 0.6009 0.6344 0.6586 0.6768 0.6907 0.7017 0.7106 0.2 0.5140 0.5680 0.6092 0.6398 0.6628 0.6803 0.6940 0.7049 0.7138 0.7211 0.3 0.5951 0.6313 0.6587 0.6794 0.6953 0.7078 0.7177 0.7259 0.7326 0.7382 0.4 0.6647 0.6887 0.7068 0.7206 0.7313 0.7399 0.7469 0.7527 0.7575 0.7616 0.5 0.7280 0.7433 0.7547 0.7636 0.7705 0.7761 0.7807 0.7846 0.7878 0.7906 0.6 0.7871 0.7962 0.8030 0.8082 0.8124 0.8158 0.8186 0.8209 0.8229 0.8246 0.7 0.8433 0.8480 0.8516 0.8544 0.8566 0.8584 0.8599 0.8611 0.8622 0.8631 0.8 0.8972 0.8992 0.9007 0.9019 0.9028 0.9035 0.9042 0.9047 0.9052 0.9055 0.9 0.9493 0.9498 0.9502 0.9504 0.9507 0.9508 0.9510 0.9511 0.9512 0.9513.

14. The viscosity measuring apparatus according to claim 9, wherein the predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ is described in the following Expression (6a), Expression (6b) and Expression (6c). $\begin{array}{cc}{\varphi }_p={\int }_{\kappa }^{\lambda }{\left(\frac{{\lambda }^2}{x}-x\right)}^{s}dx-{\int }_{\lambda }^1{\left(x-\frac{{\lambda }^2}{x}\right)}^{s}dx& \left(6a\right)\\ \Phi =\frac{1}{s+3}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\lambda }^2\right)}^{\left(s+1\right)}\right)\right]+{\varphi }_p\left(\frac{2\left(s+1\right)}{\left(s+3\right)}{\lambda }^3-\left({\lambda }^2-{\kappa }^2\right)\right)& \left(6b\right)\\ \Phi ={\varphi }_p{\kappa }^2.& \left(6c\right)\end{array}$

15. An apparatus for calculating an apparent viscosity μ.sub.a of a sample, the apparatus comprising: a cylindrical container having a predetermined inner radius R.sub.0, in which a sample is contained; a plunger having an outer radius R.sub.i that is smaller than the inner radius R.sub.0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable; a driving unit configured to relatively move the plunger coaxially with the cylindrical container; a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample; and a control unit configured to control the driving unit; wherein: the control unit is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a relative movement distance ΔL; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity v.sub.p1 and after the further immersing operation thereof; the control unit is configured to obtain a first peak value F.sub.T1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; the control unit is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by the relative movement distance ΔL; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity v.sub.p2 and after the further immersing operation thereof; the control unit is configured to obtain a second peak value F.sub.T2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; the control unit is further configured to obtain a flow behavior index n of the sample, based on the relative movement distances ΔL at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (3): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{F_{\mathrm{cb}1}}\right)}& \left(3\right)\end{array}$ in which $F_{{\mathrm{cb}}_1}=F_{T1}-\rho {\mathrm{gL}}_2\pi R_i^2,F_{{\mathrm{cb}}_2}=F_{T2}-\rho {\mathrm{gL}}_2\pi R_i^2,L_2=\frac{\Delta L}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration so as to obtain a dimensionless coordinate λ corresponding to the flow behavior index n, based on the flow behavior index n and a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; and the control unit is further configured to calculate an apparent viscosity μ.sub.a of the sample, based on the relative movement distance ΔL of the plunger at the first relative movement velocity v.sub.p1 or the second relative movement velocity v.sub.p2, the first peak value F.sub.T1 or the second peak value F.sub.T2, the dimensionless coordinate λ, and the following Expression (4): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(4\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb}}}{\pi \left(L_0+L_2\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb}}=F_T-\rho {\mathrm{gL}}_2\pi R_i^2,T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_p{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right]$ $\left(v_p=v_{p1}\mathrm{or}{v}_{p2},F_T=F_{T1}\mathrm{or}{F}_{T2}\right).$

16. An apparatus for calculating an apparent viscosity μ.sub.a of a sample, the apparatus comprising: a cylindrical container having a predetermined inner radius R.sub.0, in which a sample is contained; a plunger having an outer radius R.sub.i that is smaller than the inner radius R.sub.0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable; a driving unit configured to relatively move the plunger coaxially with the cylindrical container; a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample; and a control unit configured to control the driving unit; wherein: the control unit is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a first relative movement distance ΔL.sub.1; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity v.sub.p1 and after the further immersing operation thereof; the control unit is configured to obtain a first peak value F.sub.T1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; the control unit is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by a second relative movement distance ΔL.sub.2; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity v.sub.p2 and after the further immersing operation thereof; the control unit is configured to obtain a second peak value F.sub.T2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; the control unit is further configured to obtain a flow behavior index n of the sample, based on the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (1): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{\left(L_0+L_{2\_2}\right)}/\frac{F_{\mathrm{cb}1}}{\left(L_0+L_{2\_1}\right)}\right)}& \left(1\right)\end{array}$ in which $F_{{\mathrm{cb}}_1}=F_{T1}-\rho {\mathrm{gL}}_{2\_1}\pi R_i^2,F_{{\mathrm{cb}}_2}=F_{T2}-\rho {\mathrm{gL}}_{2\_2}\pi R_i^2,L_{2\_1}=\frac{\Delta L_1}{1-{\kappa }^2},L_{2\_2}=\frac{\Delta L_2}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration so as to obtain a dimensionless coordinate λ corresponding to the flow behavior index n, based on the flow behavior index n and a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; the control unit is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a third relative movement velocity v.sub.p3 by a third relative movement distance ΔL.sub.3; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the third relative movement velocity v.sub.p3 and after the further immersing operation thereof; the control unit is configured to obtain a third peak value F.sub.T3 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the third relative movement velocity v.sub.p3; and the control unit is further configured to calculate an apparent viscosity μ.sub.a of the sample, based on the third relative movement distance ΔL.sub.3 of the plunger at the third relative movement velocity v.sub.p3, the third peak value F.sub.T3, the dimensionless coordinate λ, and the following Expression (5): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(5\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb\_}3}}{\pi \left(L_0+L_{2\_3}\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb\_}3}=F_T-\rho {\mathrm{gL}}_{2\_3}\pi R_i^2,L_{2\_3}=\frac{\Delta L_3}{1-{\kappa }^2},T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_{p3}{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right].$

17. A control apparatus for controlling a viscosity measuring apparatus including: a cylindrical container having a predetermined inner radius R.sub.0, in which a sample is contained; a plunger having an outer radius R.sub.i that is smaller than the inner radius R.sub.0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable; a driving unit configured to relatively move the plunger coaxially with the cylindrical container; and a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample; wherein: the control apparatus is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a first relative movement distance ΔL.sub.1; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity v.sub.p1 and after the further immersing operation thereof; the control apparatus is configured to obtain a first peak value F.sub.T1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; the control apparatus is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by a second relative movement distance ΔL.sub.2; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity v.sub.p2 and after the further immersing operation thereof; the control apparatus is configured to obtain a second peak value F.sub.T2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; the control apparatus is further configured to obtain a flow behavior index n of the sample, based on the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (1): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{\left(L_0+L_{2\_2}\right)}/\frac{F_{\mathrm{cb}1}}{\left(L_0+L_{2\_1}\right)}\right)}& \left(1\right)\end{array}$ in which $F_{\mathrm{cb}1}=F_{T1}-\rho {\mathrm{gL}}_{2\_1}\pi R_i^2,F_{\mathrm{cb}2}=F_{T2}-\rho {\mathrm{gL}}_{2\_2}\pi R_i^2,L_{2\_1}=\frac{\Delta L_1}{1-{\kappa }^2},L_{2\_2}=\frac{\Delta L_2}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration so as to obtain a dimensionless coordinate λ corresponding to the flow behavior index n, based on the flow behavior index n and a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; and the control apparatus is further configured to calculate an apparent viscosity μ.sub.a of the sample, based on the first relative movement distance ΔL.sub.1 or the second relative movement distance ΔL.sub.2 of the plunger at the first relative movement velocity v.sub.p1 or the second relative movement velocity v.sub.p2, the first peak value F.sub.T1 or the second peak value F.sub.T2, the dimensionless coordinate λ, and the following Expression (2): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(2\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb}}}{\pi \left(L_0+L_2\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb}}=F_T-\rho {\mathrm{gL}}_2\pi R_i^2,L_2=\frac{\Delta L}{1-{\kappa }^2},T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_{p3}{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right]$ $\left(v_p=v_{p1}\mathrm{or}{v}_{p2},\Delta L=\Delta L_1\mathrm{or}\Delta L_2,F_T=F_{T1}\mathrm{or}{F}_{T2}\right).$

18. The control apparatus according to claim 17, wherein the predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ is described in the following Table (1). TABLE-US-00012 TABLE (1) (n, κ, λ) correspondence table (Values of λ for different values of κ and n) n 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 κ 0.1 0.4065 0.4889 0.5539 0.6009 0.6344 0.6586 0.6768 0.6907 0.7017 0.7106 0.2 0.5140 0.5680 0.6092 0.6398 0.6628 0.6803 0.6940 0.7049 0.7138 0.7211 0.3 0.5951 0.6313 0.6587 0.6794 0.6953 0.7078 0.7177 0.7259 0.7326 0.7382 0.4 0.6647 0.6887 0.7068 0.7206 0.7313 0.7399 0.7469 0.7527 0.7575 0.7616 0.5 0.7280 0.7433 0.7547 0.7636 0.7705 0.7761 0.7807 0.7846 0.7878 0.7906 0.6 0.7871 0.7962 0.8030 0.8082 0.8124 0.8158 0.8186 0.8209 0.8229 0.8246 0.7 0.8433 0.8480 0.8516 0.8544 0.8566 0.8584 0.8599 0.8611 0.8622 0.8631 0.8 0.8972 0.8992 0.9007 0.9019 0.9028 0.9035 0.9042 0.9047 0.9052 0.9055 0.9 0.9493 0.9498 0.9502 0.9504 0.9507 0.9508 0.9510 0.9511 0.9512 0.9513.

19. The control apparatus according to claim 17, wherein the predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ is described in the following Expression (6a), Expression (6b) and Expression (6c). $\begin{array}{cc}{\varphi }_p={\int }_{\kappa }^{\lambda }{\left(\frac{{\lambda }^2}{x}-x\right)}^{s}dx-{\int }_{\lambda }^1{\left(x-\frac{{\lambda }^2}{x}\right)}^{s}dx& \left(6a\right)\\ \Phi =\frac{1}{s+3}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\lambda }^2\right)}^{\left(s+1\right)}\right)\right]+{\varphi }_p\left(\frac{2\left(s+1\right)}{\left(s+3\right)}{\lambda }^3-\left({\lambda }^2-{\kappa }^2\right)\right)& \left(6b\right)\\ \Phi ={\varphi }_p{\kappa }^2.& \left(6c\right)\end{array}$

20. A control apparatus for controlling a viscosity measuring apparatus including: a cylindrical container having a predetermined inner radius R.sub.0, in which a sample is contained; a plunger having an outer radius R.sub.i that is smaller than the inner radius R.sub.0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable; a driving unit configured to relatively move the plunger coaxially with the cylindrical container; and a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample; wherein: the control apparatus is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a relative movement distance ΔL; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity v.sub.p1 and after the further immersing operation thereof; the control apparatus is configured to obtain a first peak value F.sub.T1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; the control apparatus is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by the relative movement distance ΔL; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity v.sub.p2 and after the further immersing operation thereof; the control apparatus is configured to obtain a second peak value F.sub.T2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; the control apparatus is further configured to obtain a flow behavior index n of the sample, based on the relative movement distance ΔL at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (3): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{F_{\mathrm{cb}1}}\right)}& \left(3\right)\end{array}$ in which $F_{\mathrm{cb}1}=F_{T1}-\rho {\mathrm{gL}}_2\pi R_i^2,F_{\mathrm{cb}2}=F_{T2}-\rho {\mathrm{gL}}_2\pi R_i^2,L_2=\frac{\Delta L}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration so as to obtain a dimensionless coordinate λ corresponding to the flow behavior index n, based on the flow behavior index n and a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; and the control apparatus is further configured to calculate an apparent viscosity μ.sub.a of the sample, based on the relative movement distance ΔL of the plunger at the first relative movement velocity v.sub.p1 or the second relative movement velocity v.sub.p2, the first peak value F.sub.T1 or the second peak value F.sub.T2, the dimensionless coordinate λ, and the following Expression (4): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(4\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb}}}{\pi \left(L_0+L_2\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb}}=F_T-\rho {\mathrm{gL}}_2\pi R_i^2,T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_p{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right]$ $\left(v_p=v_{p1}\mathrm{or}{v}_{p2},F_T=F_{T1}\mathrm{or}{F}_{T2}\right).$

21. A control apparatus for controlling a viscosity measuring apparatus including: a cylindrical container having a predetermined inner radius R.sub.0, in which a sample is contained; a plunger having an outer radius R.sub.i that is smaller than the inner radius R.sub.0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable; a driving unit configured to relatively move the plunger coaxially with the cylindrical container; and a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample; wherein: the control apparatus is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity v.sub.p1 by a first relative movement distance ΔL.sub.1; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity v.sub.p1 and after the further immersing operation thereof; the control apparatus is configured to obtain a first peak value F.sub.T1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity v.sub.p1; the control apparatus is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity v.sub.p2 by a second relative movement distance ΔL.sub.2; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity v.sub.p2 and after the further immersing operation thereof; the control apparatus is configured to obtain a second peak value F.sub.T2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity v.sub.p2; the control apparatus is further configured to obtain a flow behavior index n of the sample, based on the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 at the first and second relative movement velocities v.sub.p1 and v.sub.p2, the first and second peak values F.sub.T1 and F.sub.T2, and the following Expression (1): $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{\left(L_0+L_{2\_2}\right)}/\frac{F_{\mathrm{cb}1}}{\left(L_0+L_{2\_1}\right)}\right)}& \left(1\right)\end{array}$ in which $F_{\mathrm{cb}1}=F_{T1}-\rho {\mathrm{gL}}_{2\_1}\pi R_i^2,F_{\mathrm{cb}2}=F_{T2}-\rho {\mathrm{gL}}_{2\_2}\pi R_i^2,L_{2\_1}=\frac{\Delta L_1}{1-{\kappa }^2},L_{2\_2}=\frac{\Delta L_2}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$ ρ represents density of sample, and g represents gravitational acceleration so as to obtain a dimensionless coordinate λ corresponding to the flow behavior index n, based on the flow behavior index n and a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ; the control apparatus is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L.sub.0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a third relative movement velocity v.sub.p3 by a third relative movement distance ΔL.sub.3; the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the third relative movement velocity v.sub.p3 and after the further immersing operation thereof; the control apparatus is configured to obtain a third peak value F.sub.T3 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the third relative movement velocity v.sub.p3; and the control apparatus is further configured to calculate an apparent viscosity μ.sub.a of the sample, based on the third relative movement distance ΔL.sub.3 of the plunger at the third relative movement velocity v.sub.p3, the third peak value F.sub.T3, the dimensionless coordinate λ, and the following Expression (5): $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(5\right)\end{array}$ in which ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb\_}3}}{\pi \left(L_0+L_{2\_3}\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb\_}3}=F_T-\rho {\mathrm{gL}}_{2\_3}\pi R_i^2,L_{2\_3}=\frac{\Delta L_3}{1-{\kappa }^2},T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_{p3}{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right].$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic view of a viscosity measuring apparatus in one embodiment of the present invention.

(2) FIG. 2 is a schematic diagram for explaining a function of the viscosity measuring apparatus in one embodiment of the present invention.

(3) FIG. 3 is a graph showing an example of a force-time curve created in one embodiment of the present invention.

(4) FIG. 4 is a schematic view of a cone-and-plate type viscometer.

(5) FIG. 5 is a graph showing a relationship between a shear rate and an apparent viscosity of a 1.5% solution of locust bean gum, obtained by the cone-and-plate type viscometer shown in FIG. 4.

(6) FIG. 6 is a graph showing a relationship between a shear rate and an apparent viscosity of a 2% solution of LM pectin, obtained by the cone-and-plate type viscometer shown in FIG. 4.

(7) FIG. 7 is a graph created for obtaining a flow behavior index n of a sample, in a measurement example according to one embodiment of the present invention.

(8) FIG. 8 is a graph showing a measurement result of a measurement example according to one embodiment of the present invention, in which a 1.5% solution of locust bean gum is used as a sample, and a κ0.9 acrylic plunger is used as a plunger.

(9) FIG. 9 is a graph showing a measurement result of a measurement example according to one embodiment of the present invention, in which a 1.5% solution of locust bean gum is used as a sample, and a κ0.8 acrylic plunger is used as a plunger.

(10) FIG. 10 is a graph showing a measurement result of a measurement example according to one embodiment of the present invention, in which a 1.5% solution of locust bean gum is used as a sample, and a κ0.7 acrylic plunger is used as a plunger.

(11) FIG. 11 is a graph showing a measurement result of a measurement example according to one embodiment of the present invention, in which a 1.5% solution of locust bean gum is used as a sample, and a κ0.5 acrylic plunger is used as a plunger.

(12) FIG. 12 is a graph showing a measurement result of a measurement example according to one embodiment of the present invention, in which a 2% solution of LM pectin is used as a sample, and a κ0.9 acrylic plunger is used as a plunger.

(13) FIG. 13 is a graph showing a measurement result of a measurement example according to one embodiment of the present invention, in which a 2% solution of LM pectin is used as a sample, and a κ0.8 acrylic plunger is used as a plunger.

(14) FIG. 14 is a graph showing a measurement result of a measurement example according to one embodiment of the present invention, in which a 2% solution of LM pectin is used as a sample, and a κ0.7 acrylic plunger is used as a plunger.

(15) FIG. 15 is a graph showing a measurement result of a measurement example according to one embodiment of the present invention, in which a 2% solution of LM pectin is used as a sample, and a κ0.5 acrylic plunger is used as a plunger.

(16) FIG. 16 is a graph showing a measurement result of a comparative measurement example, in which a 1.5% solution of locust bean gum is used as a sample, and a κ0.9 acrylic plunger is used as a plunger.

(17) FIG. 17 is a graph showing a measurement result of a comparative measurement example, in which a 1.5% solution of locust bean gum is used as a sample, and a κ0.8 acrylic plunger is used as a plunger.

(18) FIG. 18 is a graph showing a measurement result of a comparative measurement example, in which a 1.5% solution of locust bean gum is used as a sample, and a κ0.7 acrylic plunger is used as a plunger.

(19) FIG. 19 is a graph showing a measurement result of a comparative measurement example, in which a 1.5% solution of locust bean gum is used as a sample, and a κ0.5 acrylic plunger is used as a plunger.

(20) FIG. 20 is a graph showing a measurement result of a comparative measurement example, in which a 2% solution of LM pectin is used as a sample, and a κ0.9 acrylic plunger is used as a plunger.

(21) FIG. 21 is a graph showing a measurement result of a comparative measurement example, in which a 2% solution of LM pectin is used as a sample, and a κ0.8 acrylic plunger is used as a plunger.

(22) FIG. 22 is a graph showing a measurement result of a comparative measurement example, in which a 2% solution of LM pectin is used as a sample, and a κ0.7 acrylic plunger is used as a plunger.

(23) FIG. 23 is a graph showing a measurement result of a comparative measurement example, in which a 2% solution of LM pectin is used as a sample, and a κ0.5 acrylic plunger is used as a plunger.

(24) FIG. 24 is a view used for explaining a measuring theory of a viscosity measuring method according to one embodiment of the present invention.

(25) FIG. 25 is a schematic diagram for explaining an operation of a plunger in a viscosity measuring method of JP3446117B.

(26) FIG. 26 is a graph for explaining how to obtain an initial value F.sub.v0 of a force in the viscosity measuring method of JP3446117B.

MODE FOR CARRYING OUT THE INVENTION

(27) An embodiment of the present invention will be described in detail below, with reference to the accompanying drawings.

(28) FIG. 1 is a schematic view of a viscosity measuring apparatus in one embodiment of the present invention, and FIG. 2 is a schematic diagram for explaining a function of the viscosity measuring apparatus.

(29) As shown in FIGS. 1 and 2, a viscosity measuring apparatus 10 in this embodiment includes: a cylindrical container 11 having a predetermined inner radius R.sub.0, in which a sample is contained; a plunger 12 having an outer radius R.sub.i that is smaller than the inner radius R.sub.0 of the cylindrical container 11, the plunger 12 being arranged inside the cylindrical container 11 coaxially therewith so as to be relatively movable; a driving unit 13 configured to relatively move the plunger 12 coaxially with the cylindrical container 11; a measuring unit 14 configured to measure a force applied to the plunger 12 from the sample; and a control unit (control apparatus) 15 configured to control the driving unit 13.

(30) The driving unit 13 in this embodiment includes: a base seat 13a on which surface the cylindrical container 11 is placed; a support member 13b supporting the base seat 13a; and a ball screw (not shown) configured to linearly move the support member 13b in the vertical direction; and a motor (not shown) connected to the ball screw.

(31) The ball screw and the motor are arranged inside a housing 16 of the viscosity measuring apparatus 10, and illustration of them is omitted. A screw shaft of the ball screw vertically stands in the housing 16.

(32) A vertically extending slit 18 is formed in a front surface of the housing 16. The support member 13b has a horizontally extending elongate shape. One end side of the support member 13b is fixed on a nut portion of the ball screw through the slit 18.

(33) The base seat 13a is fixed on the other end side of the support member 13b, with the surface thereof being oriented vertically upward. The cylindrical container 11 is placed on the surface of the base seat 13a, such that a central axis of the cylindrical container 11 is in parallel with the vertical direction.

(34) The motor (not shown) is configured to transmit a rotating power to the ball screw (not shown). The rotating power transmitted to the ball screw is converted to a vertical linear power, so that the support member 13b is linearly moved in the vertical direction together with the base seat 13a and the cylindrical container 11 on the base seat 13a.

(35) The measuring unit 14 in this embodiment is a load sensor (load cell). The measuring unit 14 is arranged vertically above the base seat 13a, and is supported fixedly to the housing 16. A measuring surface of the measuring unit 14 is oriented vertically downward.

(36) A plunger attachment 17 is fixed on the measuring surface of the measuring unit 14, and the plunger 12 is attached to the plunger attachment 17. Thus, a vertically upward force applied to the plunger 12 is transmitted to the measuring unit 14 through the plunger attachment 17. The measuring unit 14 is configured to measure a value of the force with a passage of time.

(37) The cylindrical container 11 is arranged coaxially with the plunger 12. The outer radius R.sub.i of the plunger 12 is smaller than the inner radius R.sub.0 of the cylindrical container 11. Thus, when the cylindrical container 11 is linearly moved vertically upward by the driving unit 13, the plunger 12 is relatively inserted from above into the cylindrical container 11 coaxially therewith in a noncontact manner.

(38) The control unit 15 in this embodiment is connected to the measuring unit 14, and is configured to read out a measurement value of the force measured by the measuring unit 14 and to store the measurement value in a storage unit. The control unit 15 is formed of a computer system including the storage unit storing a control program and so on.

(39) In addition, the control unit 15 is connected to the driving unit 13 so as to control an operation of the driving unit 13. To be specific, the control unit 15 is connected to the motor of the driving unit 13 so as to control a direction and a value of a current to be supplied to the motor, whereby a rotating direction and a rotating amount of the motor are controlled. As a result, the cylindrical container 11 on the base seat 13a is linearly moved vertically upward at a desired velocity, and is located (stopped) at a desired position in the vertical direction.

(40) Further, the control unit 15 in this embodiment is configured to control the driving unit 13 such that the plunger 12 is immersed into the sample 20 contained in the cylindrical container 11 coaxially with the cylindrical container 11 by a predetermined initial depth L.sub.0 and stopped thereat, and that the plunger 12 is then further immersed into the sample 20 coaxially with the cylindrical container 13 at a first relative movement velocity v.sub.p1 by a first relative movement distance ΔL.sub.1. During the further immersing operation of the plunger 12 at the first relative movement velocity v.sub.p1 and after the further immersing operation thereof, the measurement unit 14 in this embodiment is configured to measure a force applied to the plunger 12 from the sample 20 with a passage of time. The control unit 15 in this embodiment is configured to obtain a first peak value F.sub.T1 of the force applied to the plunger 12 from the sample 20, based on measurement values of the force caused by the relative movement of the plunger 12 at the first relative movement velocity v.sub.p1.

(41) Further, the control unit 15 in this embodiment is configured to control the driving unit 13 such that the plunger 12 is returned coaxially with the cylindrical container 11 to the initial depth L.sub.0 and stopped thereat, and that the plunger 12 is then further immersed into the sample 20 at a second relative movement velocity v.sub.p2 by a predetermined movement distance ΔL.sub.2. During the further immersing operation of the plunger 12 at the second relative movement velocity v.sub.p2 and after the further immersing operation thereof, the measurement unit 14 in this embodiment is configured to measure a force applied to the plunger 12 from the sample 20 with a passage of time. Then, the control unit 15 in this embodiment is configured to obtain a second peak value F.sub.T2 of the force applied to the plunger 12 from the sample 20, based on measurement values of the force caused by the relative movement of the plunger 12 at the second relative movement velocity v.sub.p2.

(42) Although not necessary, the control unit 15 in this embodiment is configured to control the driving unit 13 such that the plunger 12 is returned coaxially with the cylindrical container 11 to the initial depth L.sub.0 and stopped thereat, and that the plunger 12 is then further immersed into the sample 20 at an m.sup.th relative movement velocity v.sub.pm (m=3, 4, 5, . . . ) by an m.sup.th relative movement distance ΔL.sub.m. During the further immersing operation of the plunger 12 at the m.sup.th relative movement velocity v.sub.pm and after the further immersing operation thereof, the measurement unit 14 in this embodiment is configured to measure a force applied to the plunger 12 from the sample 20 with a passage of time. Then, the control unit 15 in this embodiment is configured to obtain an m.sup.th peak value F.sub.Tm of the force applied to the plunger 12 from the sample 20, based on measurement values of the force caused by the relative movement of the plunger 12 at the m.sup.th relative movement velocity v.sub.pm.

(43) Further, the control unit 15 in this embodiment is configured to obtain a flow behavior index n of the sample 20, based on the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 (and the m.sup.th relative movement distance ΔL.sub.m) at the first and second relative movement velocities v.sub.p1 and v.sub.p2 (and the m.sup.th relative movement velocity v.sub.pm), the first and second peak values F.sub.T1 and F.sub.T2 (and the m.sup.th peak value F.sub.Tm), and the following Expression (1):

(44) $\begin{array}{cc}s=\frac{1}{n}=\frac{\ln \left(\frac{v_{p2}}{v_{p1}}\right)}{\ln \left(\frac{F_{\mathrm{cb}2}}{\left(L_0+L_{2\_2}\right)}/\frac{F_{\mathrm{cb}1}}{\left(L_0+L_{2\_1}\right)}\right)}& \left(1\right)\end{array}$
in which

(45) $F_{\mathrm{cb}1}=F_{T1}-\rho {\mathrm{gL}}_{2\_1}\pi R_i^2,F_{\mathrm{cb}2}=F_{T2}-\rho {\mathrm{gL}}_{2\_2}\pi R_i^2,L_{2\_1}=\frac{\Delta L}{1-{\kappa }^2},L_{2\_2}=\frac{\Delta L}{1-{\kappa }^2},\kappa =\frac{R_i}{R_0},$

(46) ρ represents density of sample, and g represents gravitational acceleration

(47) so as to obtain a dimensionless coordinate λ corresponding to the flow behavior index n, based on the flow behavior index n and a predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ.

(48) Further, the control unit 15 in this embodiment is configured to calculate an apparent viscosity μ.sub.a of the sample 20, based on the first relative movement distance ΔL.sub.1 or the second relative movement distance ΔL.sub.2 (or the m.sup.th relative movement distance ΔL.sub.m) of the plunger 12 at the first relative movement velocity v.sub.p1 or the second relative movement velocity v.sub.p2 (or the m.sup.th relative movement velocity v.sub.pm), the first peak value F.sub.T1 or the second peak value F.sub.T2 (or the m.sup.th peak value F.sub.Tm), the dimensionless coordinate λ, and the following Expression (2):

(49) $\begin{array}{cc}{\mu }_a=\frac{{\sigma }_w}{\frac{d\gamma }{dt}}& \left(2\right)\end{array}$
in which

(50) ${\sigma }_w=\frac{{\mathrm{PR}}_0{T}_w}{2},\frac{d\gamma }{dt}={\left(\frac{{\mathrm{PR}}_0}{2K}\right)}^s{\left(\frac{{\lambda }^2}{\kappa }-\kappa \right)}^s,P=\frac{F_{\mathrm{cb}}}{\pi \left(L_0+L_2\right)R_0{R}_i\left(T_w+\kappa \right)},F_{\mathrm{cb}}=F_T-\rho {\mathrm{gL}}_2\pi R_i^2,L_2=\frac{\Delta L}{1-{\kappa }^2},T_w=\frac{{\lambda }^2}{\kappa }-\kappa ,K=\frac{{\mathrm{PR}}_0}{2}{\left(\frac{\Phi R_0}{v_{p3}{\kappa }^2}\right)}^n,\Phi =\frac{{\kappa }^2}{{\lambda }^2\left(1-s\right)}\left[{\left(1-{\lambda }^2\right)}^{\left(s+1\right)}-\left({{\kappa }^{\left(1-s\right)}\left({\lambda }^2-{\kappa }^2\right)}^{\left(s+1\right)}\right)\right]$$\left(v_p=v_{p1}\mathrm{or}{v}_{p2},\Delta L=\Delta L_1\mathrm{or}\Delta L_2,F_T=F_{T1}\mathrm{or}{F}_{T2}\right).$

(51) To be specific, for example, the predetermined relationship held among the flow behavior index n, the parameter κ and the dimensionless coordinate λ is shown in the following Table (1).

(52) TABLE-US-00004 TABLE (1) (n, κ, λ) correspondence table (Values of λ for different values of κ and n) n 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 κ 0.1 0.4065 0.4889 0.5539 0.6009 0.6344 0.6586 0.6768 0.6907 0.7017 0.7106 0.2 0.5140 0.5680 0.6092 0.6398 0.6628 0.6803 0.6940 0.7049 0.7138 0.7211 0.3 0.5951 0.6313 0.6587 0.6794 0.6953 0.7078 0.7177 0.7259 0.7326 0.7382 0.4 0.6647 0.6887 0.7068 0.7206 0.7313 0.7399 0.7469 0.7527 0.7575 0.7616 0.5 0.7280 0.7433 0.7547 0.7636 0.7705 0.7761 0.7807 0.7846 0.7878 0.7906 0.6 0.7871 0.7962 0.8030 0.8082 0.8124 0.8158 0.8186 0.8209 0.8229 0.8246 0.7 0.8433 0.8480 0.8516 0.8544 0.8566 0.8584 0.8599 0.8611 0.8622 0.8631 0.8 0.8972 0.8992 0.9007 0.9019 0.9028 0.9035 0.9042 0.9047 0.9052 0.9055 0.9 0.9493 0.9498 0.9502 0.9504 0.9507 0.9508 0.9510 0.9511 0.9512 0.9513

(53) Next, an operation of the above embodiment is described.

(54) Firstly, the cylindrical container 11 in which the sample 20 of non-Newtonian fluid is contained is placed on the surface of the base seat 13a, with the cylindrical container 11 being positioned coaxially with the plunger 12. (1) Then, the driving unit 13 is controlled by the control unit 15 such that the cylindrical container 11 is linearly moved vertically upward, and that a lower end part of the plunger 12 is immersed into the sample 20 in the cylindrical container 11 by a predetermined initial depth L.sub.0 and stopped thereat. At this time, a measurement value of a force measured by the measuring unit 14 is initialized to zero. (2) Then, the driving unit 13 is controlled by the control unit 15 such that the cylindrical container 11 is further linearly moved vertically upward at a first relative movement velocity v.sub.p1 by a first relative movement distance ΔL.sub.1. Namely, the plunger 12 is further immersed into the sample 20 in the cylindrical container 11 at the first relative movement velocity v.sub.p1 by the first relative movement distance ΔL.sub.1.

(55) During the further immersing operation of the plunger 12 at the first relative movement velocity v.sub.p1 and after the further immersing operation thereof, a vertically upward force applied to the plunger 12 from the sample 20 is measured by the measuring unit 14 with a passage of time. Measured values of the force measured by the measuring unit 14 are read out by the control unit 15 and stored. (3) The control unit 15 in this embodiment is configured to obtain a first peak value F.sub.T1 of the force applied to the plunger 12 from the sample 20, based on the measurement values of the force caused by the relative movement of the plunger 12 at the first relative movement velocity v.sub.p1. To be specific, a force-time curve as shown in FIG. 3 is created based on the measured values of the measuring unit 14, and a maximum value of the force-time curve is taken as the first peak value F.sub.T1.

(56) According to a result of the experiment conducted by the inventor, a time corresponding to the maximum valve (peak value) of the force-time curve is often in conformity to a moment at which the further immersing operation is stopped, but is sometimes before the moment at which the further immersing operation is stopped. (4) Then, the driving unit 13 is controlled by the control unit 15 such that the cylindrical container 11 is linearly moved vertically downward whereby the plunger 12 is returned coaxially with the cylindrical container 11 to the initial depth L.sub.0 and stopped thereat. (5) Then, the driving unit 13 is controlled by the control unit 15 such that the cylindrical container 11 is linearly moved vertically upward at a second relative movement velocity v.sub.p2 by a second relative movement distance ΔL.sub.2. Namely, the plunger 12 is further immersed into the sample 20 in the cylindrical container 11 at the second relative movement velocity v.sub.p2 by the second relative movement distance ΔL.sub.2.

(57) During the further immersing operation of the plunger 12 at the second relative movement velocity v.sub.p2 and after the further immersing operation thereof, a vertically upward force applied to the plunger 12 from the sample 20 is measured by the measuring unit 14 with a passage of time. Measured values of the force measured by the measuring unit 14 are read out by the control unit 15 and stored. (6) The control unit 15 in this embodiment is configured to obtain a second peak value F.sub.T2 of the force applied to the plunger 12 from the sample 20, based on the measurement values of the force caused by the relative movement of the plunger 12 at the second relative movement velocity v.sub.p2. To be specific, a force-time curve is created based on the measured values of the measuring unit 14, and a maximum value of the force-time curve is taken as the second peak value F.sub.T2.

(58) Both of the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 of the plunger 12 are values at which a steady flow can be obtained in an annulus between the plunger 12 and the cylindrical container 11. In this embodiment, since the annulus is filled with the sample 20 before the plunger 12 is relatively moved, a steady flow can be generated in the annulus even when the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 of the plunger 12 are short. Thus, an amount of the sample 20 adhering to the plunger 12 and to the cylindrical container 11 is small, whereby continuous measurements (e.g., measurements at 60 to 120 second intervals) can be carried out without increasing a measurement error.

(59) Further, by sequentially repeating the step (4), the step (5) in which the relative movement velocity and the relative movement distance of the plunger 12 are changed and the step (6), peak values of forces at three kinds or more relative movement velocities may be respectively obtained. Namely, the driving unit 13 is controlled by the control unit 15 such that the cylindrical container 11 is linearly moved vertically downward, whereby the plunger 12 is returned coaxially with the cylindrical container 11 to the initial depth L.sub.0 and stopped thereat. Then, the driving unit 13 is controlled by the control unit 15 such that the cylindrical container 11 is further linearly moved vertically upward at a different m.sup.th relative movement velocity v.sub.pm (m=3, 4, 5, . . . ) by an m.sup.th relative movement distance ΔL.sub.m. Namely, the plunger 12 is further immersed into the sample 20 in the cylindrical container 11 at the m.sup.th relative movement velocity v.sub.pm by the m.sup.th relative movement distance ΔL.sub.m. During the further immersing operation of the plunger 12 at the m.sup.th relative movement velocity v.sub.pm and after the further immersing operation thereof, a vertically upward force applied to the plunger 12 from the sample 20 is measured by the measuring unit 14 with a passage of time. Measurement values of the force measured by the measuring unit 14 are read out by the control unit 15 and stored. The control unit 15 in this embodiment is configured to obtain an m.sup.th peak value F.sub.Tm of the force applied to the plunger 12 from the sample 20, based on the measurement values of the force caused by the relative movement of the plunger 12 at the m.sup.th relative movement velocity v.sub.pm. To be specific, a force-time curve is created based on the measured values of the measuring unit 14, and a maximum value of the force-time curve is taken as the m.sup.th peak value F.sub.Tm. (7) Thereafter, the control unit 15 in this embodiment is configured to obtain a flow behavior index n of the sample 20, based on the first and second relative movement distances ΔL.sub.1 and ΔL.sub.2 (and the m.sup.th relative movement distance ΔL.sub.m) at the first and second relative movement velocities v.sub.p1 and v.sub.p2 (and the m.sup.th relative movement velocity v.sub.pm), the first and second peak values F.sub.T1 and F.sub.T2 (and the m.sup.th peak value F.sub.Tm), and the above Expression (1). When the peak values of the forces at the three kinds or more relative movement velocities have been already obtained, a value shown by the expression “v.sub.pj/v.sub.pi” and a value shown by the expression “(F.sub.cb.sub._.sub.j/(L.sub.0+L.sub.2.sub._.sub.j)/ (F.sub.cb.sub._.sub.i/(L.sub.0+L.sub.2.sub._.sub.j)” are respectively calculated for each pair (v.sub.pi, v.sub.pj) of two kinds of relative movement velocities, with reference to the above Expression (1). In a logarithmic axial graph, the former value is plotted as a vertical axis value and the latter value is plotted as a horizontal axis value. From an inclination thereof, an inverse s (=1/n) of the flow behavior index n of the sample 20 is obtained. (8) Following thereto, the control unit 15 is configured to obtain a dimensionless coordinate λ corresponding to the flow behavior index n, based on a predetermined relationship held among the flow behavior index n, a parameter κ and the dimensionless coordinate λ. (9) Then, the control unit 15 is configured to calculate an apparent viscosity μ.sub.a of the sample 20, based on the first relative movement distance ΔL.sub.1 or the second relative movement distance ΔL.sub.2 (or the m.sup.th relative movement distance ΔL.sub.m) of the plunger 12 at the first relative movement velocity v.sub.p1 or the second relative movement velocity v.sub.p2 (or the m.sup.th relative movement velocity v.sub.pm), the first peak value F.sub.T1 or the second peak value F.sub.T2 (or the m.sup.th peak value F.sub.Tm), the dimensionless coordinate λ, and the above Expression (2).

(60) Next, a concrete example is described.

(61) As an apparatus including the driving unit 13, the measuring unit 14 and the control unit 15 of the viscosity measuring apparatus 10, there was used a rheometer CR-3000EX-S manufactured by Sun Scientific Co., Ltd. (sample stage velocity: 0.5 to 1200 mm/min, distance resolution: 0.01 mm, measurement load: ±20 N, load resolution: 10.sup.−4 N, maximum data fetch interval: 2000 points/sec). As the cylindrical container 11, there was used a stainless cup through which thermostatic water is circulated (internal diameter: 50.04 mm, depth: 66.60 mm). As the plunger 12, there was used a κ0.9 acrylic plunger (external diameter: 45.03 mm, length: 61.5 mm, parameter κ=0.900), a κ0.8 acrylic plunger (external diameter: 40.04 mm, length: 61.5 mm, parameter κ=0.800), a κ0.7 acrylic plunger (external diameter: 35.01 mm, length: 61.5 mm, parameter κ=0.700) or a κ0.5 acrylic plunger (external diameter: 25.03 mm, length: 61.5 mm, parameter κ=0.500).

(62) On the other hand, a substance showing a standard viscosity of non-Newtonian fluid is not commercially available. Thus, as the sample 20 of non-Newtonian fluid, there were prepared a 1.5% solution of locust bean gum and a 2% solution of low methoxyl pectin (hereinafter LM pectin).

(63) The 1.5% solution of locust bean gum was a solution in which purified locust bean gum (CP Kelco Aps, GENU GUM type RL-200-J) and potassium sorbate (Taito Co. Ltd., food additive) were blended with one another as shown in the Table (2) below.

(64) TABLE-US-00005 TABLE (2) Composition of 1.5% solution of locust bean gum Material Locust bean gum 13.5 g Potassium Sorbate 0.45 g Demineralized water 886.5 ml Total 900.0 g
To be specific, 886.5 ml of boiled demineralized water was put into a mixer, and 13.5 g of locust bean gum and 0.45 g of potassium sorbate were added thereto. They were dissolved by stirring and deaerated. The solution was filled into a sealed container up to a final weight of 900 g. The sealed container containing the solution was left in a thermostatic chamber at 25° C. for 16 to 24 hours. A specific gravity of the 1.5% solution of locust bean gum at 25° C., which was obtained by using a Hubbard pycnometer, was 1007.1 kg/m.sup.3.

(65) In addition, the 2% solution of LM pectin was a solution in which LM pectin (DuPont Nutrition & Health, Grindsted pectin LC 810), citric acid monohydrate (Wako Co., special grade reagent), calcium citrate (Katayama Chemical Ltd., first grade reagent), calcium chloride (dehydrate) (Wako Co., special grade reagent), sucrose (granulated sugar) (Mitsui Sugar Co., Ltd.), potassium sorbate (Taito Co., Ltd., food additive) were blended with one another as shown in the Table (3) below.

(66) TABLE-US-00006 TABLE (3) Composition of 2% solution of LM pectin Material Table 3a Buffer solution Citric Acid, monohydrate 28.000 g Tri-Calcium, di-citrate, tetra hydrate 0.808 g Demineralized water 171.192 ml Dissolved and fill up to 200 ml Table 3b Calcium chloride solution Calcium chloride, dehydrate 6.600 g Demineralized water 193.4 ml Dissolved and fill up to 200 ml Table 3c LM Pectin solution Demineralized water 456.0 ml Table 3a Buffer solution 30.00 ml Table 3b Calcium chloride solution 3.00 ml Pectin LC 810 18.00 g Sucrose 390.10 g Potassium Sorbate 0.90 g Final weight 900 g pH = 3.1
To be specific, a buffer solution was made by dissolving by stirring 28.000 g of citric acid monohydrate and 0.808 g of calcium citrate in 171.192 ml of demineralized water, and by filling the solution into a sealed container up to a final weight of 200 ml. In addition, a calcium chloride solution was made by dissolving by stirring 6.600 g of calcium chloride (dehydrate) in 193.4 ml of demineralized water, and by filling the solution into a sealed container up to a final weight of 200 ml. 30 ml of the buffer solution and 10 ml of the calcium chloride solution were put into 458 ml of demineralized water. While they were heated and boiled, mixture of 390 g of sucrose (granulated sugar) and 18 g of LM pectin were put thereinto little by little, and they were dissolved by stirring. After boiled, 0.90 g of potassium sorbate was put thereinto and dissolved by stirring. The solution was filled into a sealed container up to a final weight of 900 g, and thereafter cooled and left in a thermostatic chamber at 25° C. for 16 to 24 hours. A specific gravity of the 2% solution of LM pectin at 25° C., which was obtained by using a Hubbard pycnometer, was 1212.3 kg/m.sup.3.

(67) For the sample 20 of non-Newtonian fluid, an apparent viscosity μ.sub.a0 as a reference was measured beforehand by using a conical plunger having a diameter of 40 mm and a conical angle of 4 degrees of a cone-and-plate type viscometer (Viscoanalyser RA-100 manufactured by Rheologica Instrument AB Company). To be specific, as shown in FIG. 4, the sample 20 was sandwiched between the conical plunger and a flat plate, and a torque M applied to the conical plunger by rotation was measured. A shear rate dγ/dt and an apparent viscosity μ.sub.a0 were calculated, based on the torque M and the following Expression (8):

(68) $\begin{array}{cc}\frac{d\gamma }{dt}=\frac{\Omega }{\theta },{\mu }_{a0}=\frac{3M}{2\pi R^3}\frac{\theta }{\Omega }& \left(8\right)\end{array}$
in which a cone angle is represented as θ, an angular velocity is represented as Ω and a plunger diameter is represented as R.

(69) FIG. 5 shows a relationship between a shear rate dγ/dt and an apparent viscosity μ.sub.a0 of the 1.5% solution of locust bean gum at 25° C., which was obtained by the cone-and-plate type viscometer, and FIG. 6 shows a relationship between a shear rate dγ/dt and an apparent viscosity μ.sub.a0 of the 2% solution of LM pectin at 25° C., which was obtained by the cone-and-plate type viscometer. Based on FIG. 5, the following Expression (9) was obtained as a shear rate-apparent viscosity curve (reference line) of the 1.5% solution of locust bean gum.

(70) $\begin{array}{cc}\mathrm{Viscosity}\mathrm{curve}{\mu }_{a0}=6.725\times {\left(\frac{d\gamma }{dt}\right)}^{-0.2417}& \left(9\right)\end{array}$

(71) Coefficient of determination R.sup.2=0.9971

(72) Based on FIG. 6, the following Expression (10) was obtained as a shear rate-apparent viscosity curve (reference line) of the 2% solution of LM pectin.

(73) $\begin{array}{cc}\mathrm{Viscosity}\mathrm{curve}{\mu }_{a0}=6.420\times {\left(\frac{d\gamma }{dt}\right)}^{-0.4160}& \left(10\right)\end{array}$

(74) Coefficient of determination R.sup.2=0.0.9942

(75) The 1.5% solution of locust bean gum and 2% solution of LM pectin belong to a category of a power low fluid of non-Newtonian fluid. The power low fluid is a non-Newtonian fluid whose minimum value (referred to as yield value) of a shear stress required for starting fluidity is zero.

(76) Next, a measurement example according to this embodiment is described. (1) The sample 20 was firstly put into the cylindrical container 11, and the plunger 12 was immersed into the sample 20 to an initial depth L.sub.0=41.6 mm from a liquid level and stopped thereat. Thereafter, by adjusting a temperature of the water circulated through the cylindrical container 11, an actual temperature of the sample 20 being measured was controlled to be 25±0.3° C. (2) Then, under a condition in which a first relative movement distance ΔL.sub.1 of the plunger 12 was set at 2 mm in the driving unit 13, the plunger 12 was further immersed into the sample 20 at a first relative movement velocity v.sub.p1=2.45 mm/s. (3) During the further immersing operation and after the further immersing operation, a force applied to the plunger 12 from the sample 20 was measured. Based on the measurement result, a force-time curve was created so as to obtain a first peak value F.sub.T1 of the force applied to the plunger 12 from the sample 20. Note that, when the plunger 12 was moved at a high velocity, since a stopping distance was elongated by inertia, an actual first relative movement distance ΔL.sub.1 was calculated based on a time corresponding to the first peak value F.sub.T1 shown by the force-time curve and the first relative movement velocity v.sub.p1.

(77) In the measurement example according to this embodiment, by sequentially (twice) repeating a step in which the plunger 12 was returned to the initial depth L.sub.0=41.6 mm and stopped thereat, the step (2) and the step (3), the first peak value F.sub.T1 corresponding to the first relative movement velocity v.sub.p1 was measured three times in total. (4) Then, the plunger 12 was returned to the initial depth L.sub.0=41.6 mm and stopped thereat. (5) Thereafter, under a condition in which a second relative movement distance ΔL.sub.2 of the plunger 12 was set at 2 mm in the driving unit 13, the plunger 12 was further immersed into the sample 20 at a second relative movement velocity v.sub.p2=4.90 mm/s. (6) During the further immersing operation and after the further immersing operation, a force applied to the plunger 12 from the sample 20 was measured. Based on the measurement result, a force-time curve was created so as to obtain a second peak value F.sub.T2 of the force applied to the plunger 12 from the sample 20. An actual second relative movement distance ΔL.sub.2 was calculated also based on a time corresponding to the second peak value F.sub.T2 shown by the force-time curve and the second relative movement velocity v.sub.p2.

(78) In the measurement example according to this embodiment, by sequentially (twice) repeating the step (4) to the step (6), the second peak value F.sub.T2 corresponding to the second relative movement velocity v.sub.p2 was measured three times in total.

(79) In the measurement example according to this embodiment, the step (4), the step (5) in which the relative movement velocity of the plunger 12 was changed to one of a third relative movement velocity v.sub.p3=7.35 mm/s, a fourth relative movement velocity v.sub.p4=9.80 mm/s, a fifth relative movement velocity v.sub.p5=12.25 mm/s, a sixth relative movement velocity v.sub.p6=14.70 mm/s, a seventh relative movement velocity v.sub.p7=17.15 mm/s and an eighth relative movement velocity v.sub.p8=19.60 mm/s, and the step (6) were repeated at 60 to 120 second intervals.

(80) Namely, the plunger 12 was returned to the initial depth L.sub.0=41.6 mm and stopped thereat. Under a condition in which a third relative movement distance ΔL.sub.3 of the plunger 12 was set at 2 mm in the driving unit 13, the plunger 12 was further immersed into the sample 20 at the third relative movement velocity v.sub.p3=7.35 mm/s. During the further immersing operation and after the further immersing operation, a force applied to the plunger 12 from the sample 20 was measured. Based on the measurement result, a force-time curve was created so as to obtain a third peak value F.sub.T3 of the force applied to the plunger 12 from the sample 20. An actual third relative movement distance ΔL.sub.3 was calculated also based on a time corresponding to the third peak value F.sub.T3 shown by the force-time curve and the third relative movement velocity v.sub.p3. By repeating the above steps, the third peak value F.sub.T3 corresponding to the third relative movement velocity v.sub.p3 was measured three times in total.

(81) Then, the plunger 12 was returned to the initial depth L.sub.0=41.6 mm and stopped thereat. Under a condition in which a fourth relative movement distance ΔL.sub.4 of the plunger 12 was set at 2 mm in the driving unit 13, the plunger 12 was further immersed into the sample 20 at the fourth relative movement velocity v.sub.p4=9.80 mm/s. During the further immersing operation and after the further immersing operation, a force applied to the plunger 12 from the sample 20 was measured. Based on the measurement result, a force-time curve was created so as to obtain a fourth peak value F.sub.T4 of the force applied to the plunger 12 from the sample 20. An actual fourth relative movement distance ΔL.sub.4 was calculated also based on a time corresponding to the fourth peak value F.sub.T4 shown by the force-time curve and the fourth relative movement velocity v.sub.p4. By repeating the above steps, the fourth peak value F.sub.T4 corresponding to the fourth relative movement velocity v.sub.p4 was measured three times in total.

(82) Then, the plunger 12 was returned to the initial depth L.sub.0=41.6 mm and stopped thereat. Under a condition in which a fifth relative movement distance ΔL.sub.5 of the plunger 12 was set at 2 mm in the driving unit 13, the plunger 12 was further immersed into the sample 20 at the fifth relative movement velocity v.sub.p5=12.25 mm/s. During the further immersing operation and after the further immersing operation, a force applied to the plunger 12 from the sample 20 was measured. Based on the measurement result, a force-time curve was created so as to obtain a fifth peak value F.sub.T5 of the force applied to the plunger 12 from the sample 20. An actual fifth relative movement distance ΔL.sub.5 was calculated also based on a time corresponding to the fifth peak value F.sub.T5 shown by the force-time curve and the fifth relative movement velocity v.sub.p5. By repeating the above steps, the fifth peak value F.sub.T5 corresponding to the fifth relative movement velocity v.sub.p5 was measured three times in total.