Bladeless mixer

Abstract

A bladeless mixer for mixing a liquid, includes a cylindrical or truncated cone-shaped receptacle having an axis A and a radius R, the radius R being the shortest distance between the axis A and a side wall of the receptacle, the liquid to be mixed being placed in the receptacle and having an exposed surface at a height H measured along axis A; a member for tilting the receptacle such that axis A forms a non-zero-degree angle of up to 30° relative to the vertical direction; a member for imparting a rotational movement to the receptacle along axis A at an angular speed of rotation Ω; wherein the aspect ratio H/R of the height H to the radius R and the angular speed of rotation Ω are selected such that an inherent mode of inertia of the liquid has an unstable resonance when the receptacle is tilted and rotates.

Claims

1. A method of mixing a liquid by means of a bladeless mixer containing a cylindrical or tapered container of axis A and radius R, wherein R is the smallest distance between axis A of the container and a side wall of the container, the container being tiltable such that axis A forms a non-zero angle α, chosen such that the angle is less than or equal to 30° relative to vertical, and the container being rotatable, the method comprising: a) placing the liquid in the container such that the liquid has a free surface at a height H measured along axis A when axis A is vertical, and b) applying a rotational motion to the container around axis A, with an angular speed of rotation Ω, and applying the non-zero angle α to tilt the container, wherein an aspect ratio H/R of height H over radius R and angular rotational speed Ω are chosen so as to observe an unstable resonance of an inertial eigenmode of the liquid wherein the inertial eigenmode of the liquid is the first mode with 1.79≤H/R≤2.19 and (Ω×R.sup.2×α)/v>1000, or the second mode with 0.86≤H/R≤1.06 and (Ω×R.sup.2×α)/v>15000 or the third mode with 0.56≤H/R≤0.68 and (Ω×R.sup.2×α)/v>50000 wherein Ω is the angular speed of rotation expressed in rad/s, R is the radius of the container expressed in m, H the height of the liquid in meter measured along axis A; α the angle of tilt between axis A and vertical, expressed in degrees °, and v the kinematic viscosity of the liquid to be mixed, expressed in m.sup.2/s.

2. The method according to claim 1, wherein the angular speed of rotation Ω is chosen such that: $\frac{\Omega \times R^2\times \alpha }{v}>3000$ and α is less than or equal to 2° or $\frac{\Omega \times R^2\times \alpha }{v}>5000$ and α is between 3° and 7°.

3. The method according to claim 1, wherein the angular speed of rotation Ω is chosen such that: $\frac{\Omega \times R^2\times \alpha }{v}>15000$ where α is between 5 and 10° or $\frac{\Omega \times R^2\times \alpha }{v}>30000$ where α is less than or equal to 5°.

4. The method according to claim 1, wherein: the angular speed of rotation Ω is variable, and the variation of angular speed of rotation Ω is less than or equal to 25% during a complete revolution of the container.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) The figures are given for information only, and are not restrictive of the invention in any manner.

(2) FIG. 1a shows diagrammatically a bladeless mixer according to an embodiment of the invention in an idle position.

(3) FIG. 1b shows diagrammatically the bladeless mixer of FIG. 1a in an operating position.

(4) FIG. 1c shows diagrammatically a system of cylindrical coordinates.

(5) FIG. 2a shows diagrammatically a section view of a first cylindrical container of a bladeless mixer according to one embodiment of the invention.

(6) FIG. 2b shows diagrammatically a section view of a second cylindrical container of a bladeless mixer according to one embodiment of the invention.

(7) FIG. 3a shows diagrammatically a section view of a third cylindrical container of a bladeless mixer according to one embodiment of the invention.

(8) FIG. 3b shows diagrammatically a section view of a fourth cylindrical container of a bladeless mixer according to one embodiment of the invention.

(9) FIG. 4a shows diagrammatically a first perspective view of a roughly cylindrical container of a bladeless mixer according to one embodiment of the invention.

(10) FIG. 4b shows diagrammatically a second perspective view of a roughly cylindrical container of a bladeless mixer according to one embodiment of the invention.

(11) FIG. 4c shows diagrammatically a third perspective view of a roughly cylindrical container of a bladeless mixer according to one embodiment of the invention.

DETAILED DESCRIPTION OF AT LEAST ONE EMBODIMENT OF THE INVENTION

(12) Unless otherwise stipulated, a given element shown in different figures has a single reference.

(13) FIG. 1a shows diagrammatically a bladeless mixer 10 according to an embodiment of the invention in an idle position. FIG. 1b shows diagrammatically bladeless mixer 10 in an operating position. FIGS. 1a and 1b are described jointly.

(14) Mixer 10 contains a roughly cylindrical container 1, of axis A and of radius R. A liquid to be mixed 2 is placed in container 1. Liquid to be mixed 2 is characterised by a kinematic viscosity v, typically expressed in m.sup.2/s. Liquid to be mixed 2 has a free surface 3 at a height H measured along axis A. Free surface 3 is, by definition, the surface of the liquid to be mixed 2 which is not in contact with the walls of container 1. Height H can be defined as the length of axis A which is immersed in liquid 2. Height H is typically measured in the idle position of FIG. 1a. Height H and radius R are typically expressed in m.

(15) In the idle position of FIG. 1a axis A of container 1 has a vertical direction, and container 1 is stationary. The expression “vertical direction” is understood to mean a direction parallel to the direction of force of gravity g.

(16) In the operating position of FIG. 1b container 1 is tilted and rotating around axis A. Container 1 is tilted by means of a tilting device 51. The tilt is chosen such that axis A of container 1 forms a non-zero angle α which is less than or equal to 30° relative to the vertical direction, angle α is preferentially less than or equal to 15°, and more preferentially less than or equal to 5°. Angle α can, for example, be equal to 0.5°, or to 1°, or to 5°, or to 15°. With an angle α higher than 30°, the flow on the free surface may produce shear. Container 1 is rotated around axis A by a drive device 50. Container 1 is made to rotate around axis A with an angular speed of rotation Ω typically expressed in rad/s.

(17) Aspect ratio H/R of height H over radius R is advantageously chosen such that a resonance of an inertial eigenmode of liquid to be mixed 2 is achieved. A first inertial eigenmode can be defined as a global and periodic or stationary disrupting motion, which disturbs liquid to be mixed 2 placed in container 1 which is tilted and rotating. The tilt of axis A relative to vertical enables rotating liquid 2 to be forced into an inertial eigenmode. For each inertial eigenmode there is a plurality of resonances.

(18) For the first inertial eigenmode of liquid 2 placed in container 1 which is tilted and rotating, aspect ratio H/R is chosen such that:

(19) $1,79\times k\le \frac{H}{R}\le 2,19\times k$
where k is a non-zero natural integer, and k is preferentially equal to 1. Aspect ratio H/R is preferentially chosen such that it is roughly equal to 1.99. This helps facilitate the appearance of a resonance of the first inertial eigenmode.

(20) For the second inertial eigenmode of liquid 2 placed in container 1 which is tilted and rotating, aspect ratio H/R is advantageously chosen such that:

(21) $0,86\times k\le \frac{H}{R}\le 1,06\times k$
where k is a non-zero natural integer, and k is preferentially equal to 1. Preferentially, aspect ratio H/R is chosen to be roughly equal to 0.96. This helps facilitate the appearance of a resonance of the second inertial eigenmode.

(22) For the third inertial eigenmode of liquid 2 placed in container 1 which is tilted and rotating, aspect ratio H/R is advantageously chosen such that:

(23) $0,56\times k\le \frac{H}{R}\le 0,68\times k$
where k is a non-zero natural integer, and k is preferentially equal to 1. Aspect ratio H/R is preferentially chosen to be roughly equal to 0.62. This helps facilitate the appearance of a resonance of the third inertial eigenmode.

(24) Angular speed of rotation Ω of container 1 is advantageously chosen such that an unstable resonance of the inertial eigenmode of liquid 2 placed in tilted, rotating container 1 is achieved. The expression “unstable” is understood to mean that other motions, different from the motion of the inertial eigenmode, appear within liquid 2, without any additional external constraint. Mixing within liquid 2 is indeed better when the resonance is unstable.

(25) For the first inertial eigenmode, where k=1, and for a constant angular speed of rotation Ω, an unstable resonance of the inertial eigenmode of liquid 2 placed in container 1 which is tilted and rotating is typically observed, on the following condition:

(26) $\frac{\Omega \times R^2\times \alpha }{v}>1000$
where: Ω is the angular speed of rotation expressed in rad/s, R is the radius of container 1 expressed in m, α is the angle of tilt between axis A and the vertical direction expressed in degrees v is the kinematic viscosity of liquid to be mixed 2, expressed in m.sup.2/s in the case of miscible liquids; kinematic viscosity is the average viscosity of the liquids.

(27) For the second inertial eigenmode, where k=1, and for a constant angular speed of rotation Ω, an unstable resonance of the inertial eigenmode of liquid 2 placed in container 1 which is tilted and rotating is typically observed, on the following condition:

(28) $\frac{\Omega \times R^2\times \alpha }{v}>15000$

(29) For the third inertial eigenmode, where k=1, and for a constant angular speed of rotation Ω, an unstable resonance of the inertial eigenmode of liquid 2 placed in container 1 which is tilted and rotating is typically observed, on the following condition:

(30) $\frac{\Omega \times R^2\times \alpha }{v}>50000$

(31) Where radius R, angle of tilt α and kinematic viscosity v are fixed, the previous inequalities enable an assessment to be made of minimum angular speed of rotation Ω which must be applied to container 1 to create an unstable resonance, in each of the first, second and third inertial eigenmodes. In general terms, the greater angular speed of rotation Ω, the higher the rate of shear within liquid to be mixed 2, and the greater the quantity of energy required to rotate container 1. It is therefore typically sought to create an unstable resonance, whilst choosing the lowest possible angular speed of rotation Ω.

(32) Alternatively, angular speed of rotation Ω can be variable. A variation of angular speed of rotation Ω of less than or equal to 25% during a complete revolution of container 1 is preferred.

(33) In the present document the expression “cylindrical container” is understood to mean a container having a side wall defined by a straight line called the generator, passing through a variable point describing a curve, called the guide curve, and maintaining a constant direction. The guide curve is preferentially a circle. This container shape is preferred, since it facilitates forecasting of the flow of a liquid placed in the said container, where the container is tilted and rotating, and the definition of aspect ratio H/R, enabling a resonance of a first inertial eigenmode of the said liquid to be obtained.

(34) Alternatively, the guide curve can be: an ellipse, or a convex polygon contained in a circle, or a convex polygon contained in an ellipse, or

(35) However, when a liquid is placed in a tilted, rotating container, where the container has a polygonal section, the liquid generally has a flow including vortices in the corners, which is undesirable, since a vortex dissipates large amounts of energy.

(36) In general terms, the expression “radius of the cylindrical container of axis A” is understood to mean the smallest distance between axis A of the container and a side wall of the recipient.

(37) FIG. 2a shows a section view of a first cylindrical container according to one aspect of the invention, having a guide curve in the shape of a circle. The cross-section is made using a plane perpendicular to the axis of rotation of the first cylindrical container.

(38) FIG. 2b shows a section view of a second cylindrical container according to one aspect of the invention, having a guide curve in the shape of a convex N-sided polygon contained in a circle. The cross-section is made using a plane perpendicular to the axis of rotation of the second cylindrical container. In the particular example of FIG. 2b the guide curve is a regular convex octagon and N=8. Other values of N could of course be chosen, such as N=4 or N=16. The largest possible value of N is chosen in preference, in order that the guide curve approaches the circle containing the N-sided convex polygon.

(39) FIG. 3a shows a section view of a third cylindrical container according to one aspect of the invention, having a guide curve in the shape of an ellipse. The cross-section is made using a plane perpendicular to the axis of rotation of the third cylindrical container. An ellipse in which the foci are as close to one another as possible is preferentially chosen, in order that the guide curve approaches a circle.

(40) FIG. 3b shows a section view of a fourth cylindrical container according to one aspect of the invention, having a guide curve in the shape of a convex N-sided polygon contained in an ellipse. The foci of the ellipse containing the N-sided convex polygon are preferentially as close as possible to one another. The cross-section is made using a plane perpendicular to the axis of rotation of the fourth cylindrical container. In the particular example of FIG. 3b the guide curve is a regular convex octagon contained within an ellipse and N=8. Other values of N could of course be chosen, such as N=4 or N=16. The largest possible value of N is chosen in preference, in order that the guide curve approaches the ellipse containing the N-sided convex polygon.

(41) The expression “roughly cylindrical container” is understood to mean a cylindrical or tapered container. Indeed, the diametrical variations of the container's section do not disrupt the mixer's operation if they are kept small, i.e. less than or equal to 20%, and preferentially less than or equal to 10%.

(42) It will be understood that the manufacture of the container can lead to shapes which are not perfectly cylindrical, in particular tapered shapes.

(43) FIG. 4a shows diagrammatically a first perspective view of a roughly cylindrical container according to one aspect of the invention: the dimensions of the section of the container in a plane perpendicular to its axis of rotation are constant, and the container is perfectly cylindrical.

(44) FIG. 4b shows diagrammatically a second perspective view of a roughly cylindrical container according to one aspect of the invention: the dimensions of the section of the container in a plane perpendicular to its axis of rotation vary continuously; the container is tapered. The container of FIG. 4b has a base and an aperture, and the radius of the base is higher than the radius of the aperture.

(45) FIG. 4c shows diagrammatically a third perspective view of a roughly cylindrical container according to one aspect of the invention: the dimensions of the section of the container in a plane perpendicular to its axis of rotation vary continuously; the container is tapered. The container of FIG. 4c has a base and an aperture, and the radius of the base is lower than the radius of the aperture.

(46) FIGS. 4a to 4c show three examples of roughly cylindrical containers according to one aspect of the invention, where each container has a circular guide curve. In accordance with the description given above in connection with FIGS. 2a, 2b, 3a and 3b, it will be understood that the examples of FIGS. 4a to 4c can be extended to containers with elliptical guide curves, or guide curves with the shape of a convex polygon contained in a circle, or with the shape of a convex polygon contained in an ellipse.