Measurement of fluid flow

Abstract

A method for measuring a flow of a fluid in a tube includes heating the fluid in the tube with a heating element. A first signal is measured with a first temperature sensing element at a first location. A second signal is measured with a second temperature sensing element at a second location. At least one temperature signal is calculated based on the first signal and the second signal. The at least one temperature signal includes a difference temperature signal and a sum temperature signal. The difference temperature signal is calculated based on a difference between the second signal and the first signal. The sum temperature signal is calculated based on a sum of the second signal and the first signal. The flow is derived based on the difference temperature signal, the sum temperature signal, or a combination thereof.

Claims

1. A method for measuring a flow rate of a fluid in a tube, the method comprising: heating the fluid in the tube with a heating element; measuring a first signal with a first temperature sensing element of the fluid in the tube at a first location; measuring a second signal with a second temperature sensing element of the fluid in the tube at a second location, the second location being different from the first location; calculating at least one temperature signal based on the second signal and the first signal, in which the calculating the at least one temperature signal comprises: calculating a difference temperature signal based on a difference between the second signal and the first signal; and calculating a sum temperature signal based on a sum of the second signal and the first signal; and deriving the flow rate based on the at least one temperature signal, wherein the deriving the flow rate is based on a weighted combination of the sum temperature signal and the difference temperature signal, in which a sum temperature weight and a difference temperature weight is determined based on the sum temperature signal.

2. The method of claim 1, in which the method is performed in a flow measuring system, the flow measuring system comprising: the tube; the heating element; the first temperature sensing element; and the second temperature sensing element, the method further comprising: controlling a temperature of the flow measuring system and controlling a temperature of the fluid before the fluid enters the tube so that the temperature of the flow measuring system and the temperature of the fluid before the fluid enters the tube are equal.

3. The method of claim 2, in which the flow measuring system further comprises: a data processing apparatus, in which the deriving of the flow rate is performed by the data processing apparatus.

4. The method of claim 1 where the sum temperature signal is above a turning point threshold, the sum temperature weight is zero and the difference temperature weight is one.

5. The method of claim 4 where the sum temperature signal is between the turning point threshold and a second steep threshold, in which the turning point threshold is greater than the second steep threshold, the sum temperature weight is calculated with a first equation, the first equation comprising: $\mathrm{sum}\mathrm{temperature}\mathrm{weight}=\frac{\begin{array}{c}\mathrm{sum}\mathrm{temperature}\mathrm{signal}-\\ \mathrm{turning}\mathrm{point}\mathrm{threshold}\end{array}}{\begin{array}{c}\mathrm{second}\mathrm{steep}\mathrm{threshold}-\\ \mathrm{turning}\mathrm{point}\mathrm{threshold}\end{array}}$ in which the difference temperature weight is calculated with a second equation, the second equation comprising:
difference temperature weight=1sum temperature weight.

6. The method of claim 5, in which deriving the flow rate comprises: calculating a first product of the sum temperature weight and the sum temperature signal; calculating a second product of the difference temperature weight and the difference temperature signal; and calculating the weighted combination of the sum temperature signal and the difference temperature signal based on a sum of the first product and the second product.

7. The method of claim 4 where the sum temperature signal is between a second steep threshold and a first steep threshold, in which the turning point threshold is greater than the first steep threshold and the second steep threshold, and the second steep threshold is greater than the first steep threshold, the sum temperature weight is one and the difference temperature weight is zero.

8. The method of claim 7 where the sum temperature signal is between a first steep threshold and a flat threshold, in which the turning point threshold and the second steep threshold are both greater than the first steep threshold and the flat threshold, and the first steep threshold is greater than the flat threshold, the difference temperature weight is calculated with a third equation, the third equation comprising: $\mathrm{difference}\mathrm{temperature}\mathrm{weight}=\frac{\begin{array}{c}\mathrm{sum}\mathrm{temperature}\mathrm{signal}-\\ \mathrm{first}\mathrm{steep}\mathrm{threshold}\end{array}}{\begin{array}{c}\mathrm{flat}\mathrm{threshold}-\\ \mathrm{first}\mathrm{steep}\mathrm{threshold}\end{array}}$ in which the sum temperature weight is calculated with a fourth equation, the fourth equation comprising:
sum temperature weight=1difference temperature weight.

9. The method of claim 8, in which deriving the flow rate comprises: calculating a first product of the sum temperature weight and the sum temperature signal; calculating a second product of the difference temperature weight and the difference temperature signal; and calculating the weighted combination of the sum temperature signal and the difference temperature signal based on a sum of the first product and the second product.

10. The method of claim 7 where the sum temperature signal is less than the flat threshold, in which the flat threshold is less than each of the turning point threshold, first steep threshold and the second steep threshold, the sum temperature weight is zero and the difference temperature weight is one.

11. The method of claim 10, in which deriving the flow rate comprises: calculating a first product of the sum temperature weight and the sum temperature signal; First Inventor: Gervin Ruegenberg calculating a second product of the difference temperature weight and the difference temperature signal; and calculating the weighted combination of the sum temperature signal and the difference temperature signal based on a sum of the first product and the second product.

12. The method of claim 1, wherein the sum temperature weight corresponds to the sum temperature signal and the difference temperature weight corresponds to the difference temperature signal, and wherein a sum of the sum temperature weight and the difference temperature weight equals 1; wherein when the sum temperature is above a turning point threshold, the difference temperature weight is at least 0.7; when the sum temperature signal is in the range between a first steep threshold and a second steep threshold, the sum temperature weight is at least 0.7; and when the sum temperature signal is less than a flat threshold, the difference temperature weight is at least 0.7, wherein the turning point threshold is greater than the first steep threshold, the second steep threshold, and the flat threshold, the first steep threshold is greater than the second steep threshold and the flat threshold, the second steep threshold is greater than the flat threshold.

13. The method of claim 1, wherein the method further comprises linearizing a relationship between the flow rate and the difference temperature signal; and linearizing a relationship between the flow rate and the sum temperature signal.

14. The method of claim 1, in which the fluid is a liquid.

15. The method of claim 1, in which the first temperature sensing element and the second temperature sensing element are on opposite sides of the heating element.

16. The method of claim 1, in which the tube is a capillary having an inner diameter of 15 to 500 micrometers.

17. A flow measuring system for measuring a flow rate of a fluid in a tube, the system comprising: A) the tube; B) a heating element configured to heat the fluid in the tube; C) a first temperature sensing element configured to measure a first signal of the fluid in the tube at a first location; D) a second temperature sensing element configured to measure a second signal of the fluid in the tube at a second location, the second location being different from the first location; and E) a data processing apparatus, wherein the data processing apparatus is configured to i) calculate a difference temperature signal based on a difference between the second signal and the first signal; ii) calculate a sum temperature signal based on a sum of the second signal and the first signal; and ii) derive the flow rate based on at least one temperature signal, wherein the deriving the flow rate is based on a weighted combination of the sum temperature signal and the difference temperature signal, in which a sum temperature weight and a difference temperature weight is determined based on the sum temperature signal, wherein the system further comprises: F) at least one temperature control element configured to control a temperature of the flow measuring system, and a fluid temperature control element configured to control a temperature of the fluid.

18. The flow measuring system according to claim 17, wherein the at least one temperature control element is selected from a group consisting of a heating device and a peltier element.

19. The flow measuring system according to claim 17 further comprises: G) a heat transfer element configured to conduct heat between the at least one temperature control element and the flow measuring system.

20. The flow measuring system of claim 17, in which the first temperature sensing element and the second temperature sensing element are on opposite sides of the heating element.

21. A pump system comprising: A) a first pump configured to pump a first fluid to a mixer via a first tube; B) a second pump configured to pump a second fluid to the mixer via a second tube; C) a first flow measuring system configured to measure a first flow rate of the first fluid in the first tube, the first flow measuring system comprising: i) the first tube; ii) a first heating element configured to heat the first fluid in the first tube; iii) a first temperature sensing element configured to measure a first signal of the first fluid in the first tube at a first location; iv) a second temperature sensing element configured to measure a second signal of the first fluid in the first tube at a second location, the second location being different from the first location; and v) a data processing apparatus, wherein the data processing apparatus is configured to a) calculate a first difference temperature signal based on a difference between the second signal and the first signal; b) calculate a first sum temperature signal based on a sum of the second signal and the first signal; and c) derive the first flow rate based on at least one temperature signal, wherein the deriving the first flow rate is based on a weighted combination of the sum temperature signal and the difference temperature signal, in which a sum temperature weight and a difference temperature weight is determined based on the sum temperature signal, wherein the first flow measuring system further comprises: vi) at least one first temperature control element configured to control a temperature of the first flow measuring system, and a first fluid temperature control element configured to control a temperature of the first fluid; and D) a pump control unit configured to i) receive a first flow signal corresponding to the first flow rate from the first flow measuring system; and ii) adjust a first setting of the first pump.

22. The pump system of claim 21 further comprising E) a second flow measuring system configured to measure a second flow rate of the second fluid in the second tube, the second flow measuring system comprising: i) the second tube; ii) a second heating element configured to heat the second fluid in the second tube; iii) a third temperature sensing element configured to measure a third signal of the second fluid in the second tube at a third location; iv) a fourth temperature sensing element configured to measure a fourth signal of the second fluid in the second tube at a fourth location, the third location being different from the fourth location; and v) the data processing apparatus is further configured to a) calculate a second difference temperature signal based on a difference between the third signal and the fourth signal; b) calculate a second sum temperature signal based on a sum of the third signal and the fourth signal; and c) derive the second flow rate based on at least one temperature signal, wherein the deriving the second flow rate is based on a weighted combination of the sum temperature signal and the difference temperature signal, in which a sum temperature weight and a difference temperature weight is determined based on the sum temperature signal, wherein the second flow measuring system further comprises: vi) at least one second temperature control element configured to control a temperature of the second flow measuring system, and a second fluid temperature control element configured to control a temperature of the second fluid; and F) the pump control unit is further configured to i) receive a second flow signal corresponding to the second flow rate from the second flow measuring system; and ii) adjust a second setting of the second pump.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the present invention will now be described with reference to the accompanying drawings. It should be understood that these embodiments are meant to exemplify, and not to limit, the scope of the present invention.

(2) FIG. 1 depicts a prior art system for measuring and controlling flow;

(3) FIG. 2 depicts another prior art system for measuring and controlling flow;

(4) FIG. 3 depicts a further prior art system for measuring flow;

(5) FIG. 4 depicts an exemplary system for measuring the flow in a configuration where the flow is zero;

(6) FIG. 5 depicts the system of FIG. 4 in a configuration having a low non-zero flow;

(7) FIG. 6 depicts the system of FIG. 4 in a configuration having a flow higher than the flow in FIG. 5;

(8) FIG. 7 depicts the system of FIG. 4 in a configuration having a very high flow;

(9) FIG. 8 depicts curves of the sum and differential temperatures against the flow;

(10) FIG. 9 depicts a preheater to be employed in embodiments of the present invention;

(11) FIG. 10 depicts a flow sensor system according to embodiments of the present invention;

(12) FIG. 11 depicts curves corresponding to the sum and differential temperatures against the flow, where different sections of flow are identified;

(13) FIG. 12 depicts linearized correlations between the flow and linearized temperature signals;

(14) FIG. 13 illustrates how a transition curve may be employed to connect different linearized temperature signals having an overlapping flow range, according to embodiments of the present invention;

(15) FIG. 14 depicts curves corresponding to the sum temperature signal and the differential temperature signal, used to define different sections of the flow signal;

(16) FIG. 15 corresponds to FIG. 14 and also depicts a graph with weights for the usage of a difference temperature signal and a sum temperature signal, according to an embodiment of the present invention;

(17) FIG. 16 corresponds to FIG. 14 and also depicts a graph with weights for the usage of a difference temperature signal and a sum temperature signal, according to another embodiment of the present invention;

(18) FIG. 17 depicts an HPLC system according to embodiments of the present invention;

(19) FIG. 18 illustrates the transformation of a sum temperature signal;

(20) FIG. 19 depicts a transformed sum temperature signal and a transformed difference temperature signal

(21) FIG. 20 depicts the signals of FIG. 19, together with an exemplary weighting function; and

(22) FIG. 21 depicts a composed signal.

DETAILED DESCRIPTION OF EMBODIMENTS

(23) In the following, the functional principle and behavior of thermal flow sensors will be explained in detail, based on an example. Some components of the actual sensor element (also referred to as flow measuring system) of such a thermal flow sensor are shown in FIG. 4. FIG. 4 depicts a thermal flow sensor at zero flow.

(24) The sensor element comprises a tube 1, which in the depicted embodiment is an elongated capillary 1. The capillary 1 has a wall 2 that is formed by (e.g., consists of) a sufficiently pressure-resistant material, preferably glass, ceramic or metal. The fluid or liquid of which the flow is to be measured is located inside the capillary.

(25) At the outer end of the wall 2 of the capillary 1, a heating element 10 is attached, and two temperature sensing elements 11a and 11b (also referred to as temperature sensors 11a, 11b) are arranged to the left and right of it, preferably at the same distance.

(26) As an example, temperature sensors 11a, 11b on the basis of thermal elements (i.e., thermocouples) are used, as they provide an approximately linear signal and do not measure an absolute temperature but the difference between the temperature at the capillary wall 2 and reference junction that has approximately the same temperature as the housing of the sensor. In this manner, changes in the ambient temperature are automatically compensated for.

(27) If the fluid/liquid stagnates inside the capillary 1, i.e. if the flow inside the capillary 1 equals zero, the heat of the heating element 10 spreads evenly in all directions. What is thus created is a substantially rotationally symmetrical temperature profile, which is represented by isotherms 20a. The temperature profile is particularly symmetrical with respect to the heating element 10 and the two temperature sensors 11a and 11b. Thus, the temperatures of both temperature sensors 11a, 11b are the same, or the differential temperature between them is zero.

(28) The differential temperature signal is usually linearized in an evaluation circuit. At that, the differential temperature is converted into a flow rate based on a recorded calibration curve or look up table, for example in nanoliter per minute (nL/min).

(29) In an analysis of the sum temperature that is suitable for the measurement of higher flow rates, instead of the difference between the temperatures, the sum of the two temperatures is analyzed. It reaches its maximum if the liquid stagnates, as the heat dissipation is at its lowest in that case.

(30) FIG. 5 depicts the case that the fluid/liquid moves in the capillary 1 from left to right, which will be referred to as a positive flow (that is, flow>0) in the following.

(31) The internal diameter of the capillary 1 is so large that a laminar flow is created inside the capillary 1. In a straight elongated capillary 1, a parabolic velocity profile is created in that case, which is indicated by the arrows (velocity vectors) 3b.

(32) This parabolic velocity profile distorts the temperature profile generated by the heating element 10 in flow direction. This can be seen from the changed shape of the isotherms 20b. The flow transports the liquid heated by the heating element 10 in flow direction, leading to a rise of the temperature of the temperature sensor 11b that is arranged downstream. On the other hand, the liquid that is heated at the temperature sensor 11a is constantly replaced by new liquid, so that its temperature drops. Thus, a differential temperature results between the temperature sensors 11a and 11b, which is a measure for the flow through the sensor, and is provided as a flow rate signal after linearization in the evaluation circuit. At a low flow, the sum temperature is influenced by the flow rate only to a small degree and cannot be analyzed in any useful manner in this range.

(33) At a higher flow, which is indicated in FIG. 6 by longer velocity vectors 3c, the flow profile becomes yet more unsymmetrical. As can be seen from the shape of the isotherms 20c, the upstream temperature sensor 11a is now barely heated by the heating element 10. As a result of that, the differential temperature between the sensors 11a and 11b keeps increasing. It is again linearized and provided as the flow rate signal.

(34) At an even higher flow, more and more heat is dissipated through the liquid, so that the differential temperature reaches a maximum and subsequently decreases again. In this range, a meaningful analysis of the differential temperature is no longer possible. Instead, the sum temperature of the sensors 11a and 11b may be analyzed. Since more heat is dissipated at a higher flow, the heat strongly decreases with an increasing flow rate and can already be linearized and then used as a measure for the flow.

(35) At a very high flow, even more heat is dissipated through the liquid, so that generally lower temperatures are achieved. This is indicated in FIG. 7 by a lower number of isotherms as compared to FIG. 6.

(36) Already in FIG. 6, the temperature sensor 11a was barely heated, and this is also not changed by the further increased flow. However, due to the increased heat removal, the temperature sensor 11b is at even higher flow rates (see FIG. 7) also heated to a lesser degree, so that the differential temperature is similarly low as when the flow is low.

(37) Thus, a very low differential temperature can occur either as a result of a very low or an extremely high flow. Therefore the relation between the differential temperature and the flow is now ambiguous. At medium to high flow, the sum temperature shows an unambiguous and clear connection to the flow rate. Therefore, this signal can be used as a good measure for the flow.

(38) The dependencies between flow and differential temperature as well as sum temperature are plotted in FIG. 8. The horizontal axis corresponds to the flow rate, the Y-axis corresponds to the measured differential temperature or sum temperature.

(39) The dashed curve 110 shows the sum temperature. The curve extends symmetrically to the X-axis, i.e. negative flows result in the same sum temperature as positive flows of the same value. The curve has its maximum 110a at flow=zero, as in this case no heat is dissipated through the liquid. At low positive or negative flows, the heat removal through the liquid is negligible, therefore the shape of the curve remains almost horizontal at first, so that in this range no accurate analysis is possible. With slightly higher flows, the curve rapidly begins to fall steeply, so that it can be analyzed very well in this range. At very high flows, the curve becomes more and more flat.

(40) The solid line 100 shows the differential temperature. To make the rendering more clear, the curve has been scaled in such a manner that its maximum is as high as in the curve 110. In actuality, the differential temperatures are substantially lower than the sum temperatures, therefore the curve would actually be substantially smaller in the vertical direction. The differential temperature extends in a point-symmetric manner with respect to the origin, i.e. negative flows result in a differential temperature that is as high as with positive flows, only with the reversed algebraic sign. At low flows, the curve initially has an approximately linear and very steep shape in the range 100a. At higher flows, the curve becomes increasingly non-linear and finally reaches a saturation point 100b. Here, the effect of the heat removal starts becoming dominant. At even higher flows, the curve keeps dropping in the range 100c, and ultimately becomes more flat.

(41) A general challenge with thermal measuring principles is the influence of the ambient temperature or the sensor temperature, as well as of the temperature of the inflowing liquid. Since these influences act in the same way on both temperature sensors 11a and 11b in the flow sensor, the differential temperature does not change as a result of this, i.e. the curve 100 is almost not influenced by the changes in the ambient temperature or in the inflowing liquid.

(42) In contrast to that, changes in ambient temperature have a direct effect on the temperature sum signal. Consequently, the entire curve 110 is displaced in the vertical direction. For example, if the ambient temperature is lowered, the result is a curve (curve 111) that is displaced downwards.

(43) Since the curve has a very flat shape when the flow is high, such a vertical displacement corresponds to an extremely large error of the measured flow.

(44) Thermal elements (thermocouples) may be used for the temperature sensors 11a and 11b. Due to their functional principle, thermocouples always measure the difference of the temperatures between a measurement site and a reference site. The reference site is arranged inside the sensor 11a, 11b in such a manner that it substantially measures the temperature of the sensor housing, and the measurement site measures the temperature at the capillary wall 2. Since both temperatures change equally when the ambient temperature changes, the influence of the ambient temperature on the sensor signal is largely eliminated in this manner. However, the temperature at the measurement site, i.e. the capillary wall 2, is also significantly influenced by the temperature of the inflowing fluid/liquid or of the medium, which will be referred to as the medium temperature in the following. This influence cannot be eliminated by using thermocouples. Due to the flat shape of the curve 110, already small changes in the medium temperature result in big changes of the sensor signal.

(45) Due to these reasons, the precision of flow sensors according to the state of the art is considerably inferior in the analysis of the sum temperature, in particular at very high flow rates, than at low flow rates and in the analysis of the differential temperature. Measuring errors of 10% and more may easily occur in prior art systems, which is useless for common HPLC applications.

(46) E.g., to create a wide range flow sensor that facilitates an accurate flow measurement in the entire range that is covered by the curves, the influence of the ambient temperature or the medium temperature on the temperature sum signal is advantageously eliminated.

(47) According to embodiments of the present invention, the influence of the ambient temperature and the medium temperature can be eliminated by keeping the temperature of the flow sensor and the medium temperature constant. In the following, this is referred to as temperature control.

(48) In flow sensors that have a housing with good thermal conductivity, for example a metal housing, the temperature control of the sensor can be effected by connecting the housing to a temperature-controlled surface, for example a metal plate, in a way that enables good thermal conductivity. The temperature-controlled surface can be maintained at a constant temperature. One solution is the use of heating elements that are in thermal contact with the temperature-controlled surface, and one or multiple temperature sensors that are likewise in thermal contact with the temperature-controlled surface, wherein the heating power is set by a control circuit in such a manner that the temperature corresponds to a given set value. Here, the temperature-controlled surface can also be the sensor housing itself, or the control can be integrated partially or entirely into the sensor.

(49) In such a temperature control by means of simple heating elements no active cooling is possible. Therefore, in this case, the set value of the temperature must be chosen to be higher than the expected highest ambient temperature of the arrangement. If instead of the heating elements, Peltier coolers are used, for example, they can be used to provide active heating as well as active cooling, as long as a sufficient heat supply or heat removal is ensured at the other side of the Peltier cooler. In that case, temperature control to normal ambient temperature or even below that is possible, as well. However, this solution entails considerably more effort than a temperature control by means of heating elements.

(50) According to embodiments of the invention, the medium temperature is also kept constant. E.g., for this purpose, an eluent preheater may be arranged in flow direction directly in front of the flow sensor, with the eluent preheater bringing the medium to the desired temperature. There are active and passive eluent preheaters available in different designs.

(51) FIG. 9 shows, by way of example, a simple eluent preheater 220, which may be a passive preheater 220, in an opened state. It comprises a continuous capillary 223, which in the assembled state is fitted in such a manner between the housing halves 221 and 222 that a good heat transfer is ensured between the capillary 223 and the housing halves 221, 222.

(52) The area 224 of the capillary, which is located in the interior of the housing, is bent in a meandering shape. As a result, the flow conditions in the capillary are changed in such a way that a particularly good heat exchange results between the medium and the capillary. In addition, this makes it possible to accommodate a greater capillary length inside the housing.

(53) E.g., in order to achieve a constant medium temperature, the housing of the eluent preheater is maintained at a constant temperature. Since the two housing halves 221 and 222 are connected so as to have a good thermal coupling in the assembled state, it is sufficient if one of the housing halves is in good heat contact with a temperature-controlled surface. In that case, the thermal resistance between the liquid and the temperature-controlled surface is very small, so that the medium temperature at the exit of the eluent preheater is practically equal to the temperature of the temperature-controlled surface.

(54) Here, it may be advantageous to use a common temperature-controlled surface that is in thermal contact with the flow sensor as well as with the eluent preheater 220. In this case, the liquid is brought to practically the same temperature as the sensor, i.e. the liquid that flows from the eluent preheater 220 into the sensor has the same temperature as the sensor itself. In this way, a heat exchange between the liquid and the sensor housing, which would falsify the sensor signal, is avoided.

(55) Such an arrangement according to an embodiment of the invention is shown in FIG. 10. The flow sensor 5 and the eluent preheater 220 (which may also be generally referred to as fluid temperature control element) are mounted onto a common temperature-controlled surface 212 (which may also be referred to as heat transfer element 212) having a good thermal conductivity. The temperature control is effected via two heating elements 210a and 210b as well as the temperature sensor 211. The electrical connections of these components are not shown with a view to rendering the illustration more clear. During operation, the temperature of the temperature-controlled surface 212 is detected by the temperature sensor 211, and the heating power of the heating elements 210a and 210b is controlled in such a manner by the electronic control circuit that the temperature corresponds to the set value. This control circuit can be realized as a separate circuit, or can be integrated into the control of the complete device, and is also not shown with a view to rendering the illustration more clear.

(56) Temperature differences may still occur even with such a temperature control, since even materials having a good thermal conductivity, such as for example aluminum, have only a limited thermal conductivity. Hence, changes in ambient temperature can influence the local temperature distribution inside the arrangement and thereby impair the reproducibility of the flow measurement. In order to avoid this, it may be advantageous to surround the entire arrangement shown in FIG. 10 with heat-insulating material (e.g. with such a housing) so as to reduce heat flows between the arrangement and the environment, or the temperature differences within the arrangement resulting there from. This heat insulation is not shown in FIG. 10, so that the inner components of the structure may be seen. Alternatively, it is also possible to install the entire arrangement inside a housing, which in turn is also temperature-controlled. This solution is space-saving and very effective, but requires additional technical effort.

(57) Since all components shown in FIG. 10 are connected to each other in a manner that ensures good thermal conductivity, they have almost exactly the same temperature during operation. This temperature will be referred to as the target temperature in the following.

(58) The medium or the liquid reaches via an inlet capillary 223a first the eluent preheater 220, where it is brought to target temperature. The connecting capillary 223b guides the medium into the flow sensor 5. Even at very low flow rates, there is no significant change in temperature inside the capillary 223b, since the capillary is kept at target temperature by means of heat conduction from the eluent preheater 220 on the one hand and from the flow sensor 5 on the other. The flow sensor 5 itself is also mounted on the temperature-controlled surface 212, and is thus likewise maintained at target temperature.

(59) In this manner, the influences of the ambient temperature and the medium temperature are eliminated to a great extent.

(60) Instead of bringing the flow sensor 5 and the eluent preheater 220 to the target temperature through a common temperature-controlled surface, this can also be effected by means of separate temperature control devices for both components. In this case, different target temperatures for the eluent preheater 220 and the flow sensor 5 would also be possible. However, there is no relevant advantage to be expected from that, so that the common temperature control is the preferred embodiment.

(61) The arrangement of the components shown in FIG. 10 is to be understood as merely an exemplary embodiment. Depending on the overall structure, the components can also be arranged in a different manner.

(62) For example, if a sufficiently good thermal insulation is provided, only one single heating element 210 may be sufficient. Conversely, it is also possible to arrange more than two heating elements 210a, 210b in a distributed manner in order to achieve a more uniform temperature distribution. Likewise, multiple temperature sensors 211 may also be used.

(63) According to embodiments of the invention, the measuring accuracy of the flow sensor 5 can be improved by temperature-controlling the flow sensor 5 and the medium that enters the flow sensor 5 in such a manner that a reproducibility sufficient for HPLC applications is achieved in differential temperature analysis as well as in sum temperature analysis.

(64) The entire arrangement 200 including all components shown in FIG. 10 as well as the thermal insulation that is not shown will be referred to as temperature-controlled flow sensor in the following.

(65) Furthermore, in embodiments of the present invention, different measuring ranges may be combined, as described below.

(66) In flow sensors that are currently available, differential temperature analysis and sum temperature analysis represent two different operating modes, if these possibilities are even offered at all. Such sensors can work only in one or the other operating mode.

(67) As will be explained in the following, according to embodiments of the invention, a single continuous measuring range including the entire low flow range is created by combining both operating modes. For this purpose, the differential temperature signal as well as the sum temperature signal are analyzed, i.e. both signals are available in parallel or quasi simultaneously, i.e., by reading both signals in quick succession in an alternating manner. However, it will be understood that flow sensors may also be equipped with appropriate hardware so as to make both signals available at the same time.

(68) In typical HPLC applications, the total flow is constant in most cases, and is comprised of two or more partial flows with a variable mixing ratio. Here, the mixing ratio, and thus the partial flows, are varied during the usual gradients in the range of 0 to 100% of the total flow. Each flow sensor is responsible for one of these partial flows. For regulating the partial flows, the flow sensors should ideally provide an interruption-free and exact flow signal in the entire range between 0 and 100% of the total flow.

(69) E.g., to create a flow sensor according to embodiments of the invention with a continuous, interruption-free and exact measuring range that covers the entire low flow range, it will first be considered what kind of information is yielded by the differential temperature and the sum temperature signals in which flow range.

(70) FIG. 11 again shows the differential temperature signal (curve 100) and the sum temperature signal (curve 110) of the flow sensor. In addition, a number of ranges I to VI is mapped above and below the X-axis.

(71) The differential temperature, i.e. the curve 100, provides a signal with the right algebraic sign in the entire positive and negative flow range. In section I, the shape of the curve is very steep, so that a very exact analysis is possible here. In the sections II, the curve passes the maximum 101 or the minimum 102, where the slope of the curve has a zero-crossing. Thus, no analysis or only an inaccurate analysis is possible in the sections II. In the sections III, the differential temperature has a sufficiently high slope again, so that analysis is possible.

(72) The sum temperature, i.e. the curve 110, runs symmetrically with respect to the Y-axis, and is monotonically increasing for negative flow rates and monotonically decreasing for positive flow rates. Therefore, in the sections V and VI, the curve provides a signal that is a measure for the value of the flow rate. Here, a differentiation between positive and negative flow is not possible. In the neighborhood of the maximum 111, the shape of the curve is very flat or even horizontal at flow rate zero. Therefore, only a rough statement about the flow rate is possible in section IV. In the sections V, the curve 110 has a very steep shape, so that a relatively exact analysis is possible here. In the sections VI, the curve 110 becomes increasingly flat, so that the analysis becomes increasingly inaccurate at higher positive or negative flow rates. In this range, the curve 100 provides a more accurate flow signal, especially since the differential temperature is largely unsusceptible to changes in ambient and medium temperature.

(73) Thus, the differential temperature 100 provides a signal with the right algebraic sign in the entire range, while the sum temperature 110 reflects the value of the flow rate at least approximately in the entire range. By analyzing these two signals, it can already be determined whether the flow is positive or negative, and in which of the ranges I to III or IV to VI it is. Depending on the respective range, the flow rate is then determined either based on the differential temperature 100, on the sum temperature 110 or on a combination of the two.

(74) At a low flow rate, i.e. in the range I, the curve 100 is used. In the range II, the curve 100 does not provide an accurate signal, instead the curve 110 or the range V can be used here for this purpose. If the flow rate is even higher, the precision of the curve 110 decreases, so that here the curve 100 or the range III is used once more.

(75) Since all the defined ranges for curve 100 and curve 110 overlap, an accurate analysis is possible for the entire positive and negative flow range.

(76) The correlations between the difference or sum temperatures (curve 100 or 110, referred to as temperature signals in the following) and the flow rate are both nonlinear, as can be seen in FIG. 11. Thus, linearization is required in order to obtain a linear signal that reflects the measured flow rate. Numerous methods for linearization of signals are known. In the simplest case, a look up table is recorded that gives the correlation between the temperature signal and the flow rate for a number of sampling points. If the temperature signal does not fall exactly on one of the sampling points, the flow rate is calculated by interpolation between neighboring sampling points. Alternatively, it is also possible to map the functional correlation between the temperature signals and the flow rate by suitable mathematic functions, for example polynomials, exponential functions, or splines. If these functions are calculated in such a manner that the X-values correspond to the temperature signal and the Y-axis corresponds to the flow rate, the temperature signal must merely be inserted into the function to obtain the flow signal. Due to mathematical reasons, in that case the function must be calculated sectionwise, if necessary.

(77) Independently of the kind of the function used, the look up table or function must be determined by calibrating the sensor. Here, a known flow rate is for example guided through the sensor for each sampling point, and the associated temperature signal is analyzed. The sampling points or the parameters of the used functions are stored. Depending on the production tolerances of the sensor, it may be sufficient to perform this calibration just once and then use it for all sensors of the respective type, or it may be necessary to calibrate every single sensor individually. The linearization can be performed in the sensor itself or in the further signal path, respectively.

(78) As has already been described above, the differential temperature as well as the sum temperature can be analyzed only in certain sections. For this reason, a linearization is only necessary in these sections. Such a linearization by section is significantly easier from the mathematical point of view and in addition more accurate than a linearization of the entire curve 100 or 110.

(79) The differential temperature (curve 100) is only linearized in the analyzable sections I and III, the sum temperature (curve 110) is linearized only in the sections V.

(80) Here, the sum temperature is multiplied by the algebraic sign of the differential temperature signal to obtain a sum temperature signal with the correct algebraic sign.

(81) Regarding the linearization of the different sections of the temperature signals, reference is made to FIG. 12. FIG. 12 shows the shape of the analyzable linearized curve sections I and III of the differential temperature (curve 100) as a double line, and shows the shape of the curve sections V of the sum temperature (curve 110), which is corrected with respect to its algebraic sign, as a simple bold line. The linearized curves 100 or 110 all lie on the same straight line having the slope 1.

(82) The sections I and V overlap in a relatively small area. There is a (substantially larger) overlapping between the sections V and III. As will be explained in the following, these overlappings may be used to avoid any signal jumps due to possible inaccuracies.

(83) A general challenge when switching measuring ranges or the operational modes of sensors and measuring devices is that, as a result of unavoidable inaccuracies and drift effects, measuring errors occur that have different effects in the individual measuring ranges or operational modes. This challenge is particularly pronounced in the flow sensors that are discussed herein, since the analysis of the sum temperature represents a different measuring principle than the analysis of the differential temperature.

(84) As a consequence of the inaccuracies, the linearized curve sections are overlapped by artefacts such as noise, non-linearities and zero point errors, which in addition have different impacts in the individual sections. In this case, given the same real flow rate, an analysis of the differential temperature would lead to a slightly different flow signal than an analysis of the sum temperature. If one simply switched between the analysis of the differential temperature and the analysis of the sum temperature at a certain point, a signal jump would occur.

(85) In a closed control circuit that is designed to regulate the flow rate to a predefined value, such signal jumps lead to an instability of the controller, as the latter tries to counteract the ostensive change of the flow rate. As a result, the actual flow rate is changed into the reverse direction, which in turn causes a new signal jump in the reverse direction. Such undesired behavior is advantageously avoided.

(86) According to embodiments of the invention, this is done by utilizing the overlapping areas between the sections I and V, or V and III in FIG. 12. In these overlapping areas, a linearized differential temperature signal as well as a linearized sum temperature signal are simultaneously present. Based on the two signals, an overall signal is calculated which comprises the two individual signals with different weightings.

(87) This will be explained in the following based on FIG. 13.

(88) FIG. 13 shows, by way of example, a linearized differential temperature signal 100 that covers the flow range up to 5 L/min and includes typical errors like offset shift and noise. Due to the inaccuracies the signal does not have a straight shape and does not run exactly through the origin of the coordinate system. Further, a similar inaccurate sum temperature signal 110 is shown covering the flow range from 3 L/min upwards. In the overlapping area between 3 and 5 L/min, both signals are available. However, they do not coincide as a result of the inaccuracies. At a low flow rate, only the differential temperature signal can be used. If the flow rate increases, the differential temperature signal is no longer available from 5 L/min on, so that at that point at the latest the sum temperature signal must be switched to. The result in this case is a signal jump from approximately 4.2 L/min to approximately 5.0 L/min.

(89) In this example, an overlapping area of 3 L/min to 5 L/min is present in which the differential temperature signal as well as the sum temperature signal are available. According to the invention, a transition curve 120 is calculated in this overlapping area, with this transition curve 120 representing a continuous transition from curve 100 to curve 110. Thus, the linearized curve 100 is used in the flow range of up to 3 L/min, the transition curve 120 is used between 3 and 5 L/min, and the linearized curve 110 is used above 5 L/min.

(90) According to the invention, the calculation of the transition curve is carried out by means of a variable weighting of the linearized curves 100 and 110. Different weighting functions may be used. Usually a simple linear weighting is sufficient, which will be explained based on the following example. By using more complicated weighting functions, it may be achieved that the transition curve starts and ends with even the same slopes as the adjoining linearized curves. However, in practice the theoretic advantage is of minor relevance.

(91) As an example, a weighting function is used that has the value zero at 3 L/min and increases in a linear manner until reaching the value 1 at 5 L/min. This corresponds to the following linear equation, wherein FI indicates the flow rate in L/min:
g=(FI3 L/min)/(5 L/min3 L/min)

(92) The curve 110 is weighted with the factor g, and the curve 110 is weighted with 1g. At 3 L/min, the curve 110 is thus weighted with the factor 0, and the curve 100 is weighted with the factor 1. It is the other way around at 5 L/min: The curve 110 is weight with the factor 1, and the curve 100 is weighted with the factor 0. In the range in between, the weighting function varies in a linear manner with the flow rate. Thus, for example at 3.5 L/min, the curve 110 is weighted with the factor 0.25, and the curve 100 is weighted with the factor 0.75. The function values of the transition curve 120 are obtained by multiplying the function value of the curves 100 and 110 by the weightings, and by subsequently adding the results.

(93) The transition curve 120 appears not smooth as the noise floor from the sensor signals is still included.

(94) Transition curves can also be calculated for all other overlappings in the same manner.

(95) The overlapping between the ranges V and III is very large, i.e. the differential temperature as well as the sum temperature can be analyzed in a very large flow range. Although it would be easily possible to calculate the transition curve in this entire range, it should be taken into consideration that the differential temperature yields more accurate results in this range than the sum temperature. Therefore, it is more expedient to analyze only the differential temperature in a relatively large part of this range, and to choose the transitional area to be correspondingly smaller.

(96) In keeping with the above considerations, determining the analyzable sections and also calculating the transition curves is always carried out based on the flow rate. However, the actual flow rate is not yet known at this point, as it is precisely what is supposed to be determined by means of these analyses.

(97) Thus, for determining the ranges and for calculating the transition curves, the non-linearized sum signal is used. FIG. 13 shows the same signals and sections as FIG. 11. Since the curve 110 is symmetrical to the X-axis, it is sufficient to look at the 1.sup.st quadrant.

(98) The sum temperature signal (curve 110) is monotonically decreasing in the entire 1.sup.st quadrant. For this reason, each of the transitions between the sections I/II, II/III, IV/IV and V/VI can be assigned in an unambiguous manner to a corresponding sum temperature signal or to a point on the Y-axis, respectively. Here, point I corresponds to the transition I/II, point II corresponds to the transition II/III, point IV corresponds to the transition IV/V, and point V corresponds to the transition IV/V. It will be understood that these points denote certain values of thresholds of the sum temperature signal 110. The sum temperature signal at point IV will also be referred to as the turning point threshold IV (as it is the point closest to the turning point); point II will also be referred to as first steep threshold II; point I will also be referred to as second steep threshold I (as these threshold lie on the section of the sum temperature vs. flow curve that is relatively steep); and point V will also be referred to as flat threshold V (as this threshold lies on the section of the sum temperature vs. flow curve that is relatively flat).

(99) Based on the sum temperature signal it can thus be unambiguously determined whether the sum temperature signal, the differential temperature signal, or a transition curve is to be used for determining the flow rate. The weight function for the transition curve can also be calculated directly from the sum temperature signal. In that case, it will be non-linear with respect to the flow rate, but that is of no relevant difference.

(100) Table 1 shows an example of such an analysis.

(101) TABLE-US-00001 TABLE 1 measured weighting sum explanation of sum differential temperature the analysis temperature temperature >IV section IV 0 1 I . . . IV transition I/V (ST IV)/(I IV) 1 (ST IV)/ (I IV) II . . . I section II 1 0 V . . . II transition V/III 1 (ST II)/ (ST II)/(V II) (V II) <V section III 0 1

(102) In order to obtain the overall signal of the flow sensor according to the invention, at first the non-linearized sum temperature ST is determined. Subsequently it is verified based on the first table column in which of the indicated ranges the value ST is located. The weighting factors for the sum temperature and the differential temperature are determined in correspondence to the two right columns in the respective table row.

(103) Then, the linearized sum and differential temperatures are multiplied by the corresponding weighting factors, and the two products are added.

(104) This yields the measurement signal of the flow sensor according to embodiments of the invention.

(105) The above described switching between the measurement modes and the weighting factors according to Table 1 can also be considered as the usage of a single weighting function for the complete measurement range, as is exemplarily depicted in FIG. 15.

(106) FIG. 15 depicts a global or complete measurement function as line 150. The X-values of this function are the sum temperatures, which is why the X-axis is depicted vertically in FIG. 15. In accordance with Table 1, the weighting function has the value 1 for sum temperatures >IV and <V. I.e., here, only the difference temperature is used. For sum temperatures between II and I, the weighting function has the value 0, i.e., only the sum temperature is used. In the ranges lying in between, i.e., I to IV and V to II, the weighting function, which may also be referred to as complete or global weighting function, corresponds to the above described transitioning functions. The complete weighting function (line 150) comprises the straight segments and is continuous, but not continuous differentiable.

(107) As described, the weighting function determines whether the linearized difference temperature signal, the linearized sum temperature signal, or a combination/mixture of these is utilized for the assessment. Herein, the present technology usually utilizes the signal that can be analyzed better. The analyzability of the signals does not change abruptly, but gradually. For example, the sum temperature (curve 110) is also substantially analyzable and usable at small flows, i.e., in region IV. Only when the flow approaches 0, the signal can no longer be analyzed, as the slope of the curve 100 approaches 0.

(108) That means that the global or complete weighting function is not limited to line 150 depicted in FIG. 15. Instead, the global weighing function may also be realized differently. Thus, the weighting function can be defined in a manner being optional when regarding all technical considerations.

(109) In particular, a smooth weighting function can be used, which does not comprise sudden or abrupt changes in the slope and is thus continuous differentiable. Such a weighting function is exemplarily depicted as curve 151 in FIG. 16. The curve is similar to curve 150 in FIG. 15. However, the curve 160 comprises curved transitioning functions and smooth transitions between the different regions. Furthermore, also the sections depicted as straight sections in curve 151 do not necessarily have to be straight, as it is not required that the weighting function is exactly 0 or 1.

(110) As for the weighting function in FIG. 15, also for the weighting function in FIG. 16, the weighting of the linearized sum temperature signal and difference temperature signal is typically complementary, i.e., the weighing function is in the range 0 to 1 and the sum of the weighting function is 1. I.e., when the sum temperature is weighted with the function w, the difference temperature is weighted with the function 1w.

(111) While the above described method may be suitable to arrive at the flow, the skilled person will understand that other methods may also be employed.

(112) In the above, signals received from the flow sensor have been linearized for both measuring areas (i.e., sum temperature signal and difference temperature signal) by using calibration curves. The calibration curves have been determined by corresponding measurements and a comparison with the actual flow rate. Then, the linearized measurements signals were combined to a single measurement signal covering the complete flow area.

(113) In the below method that will now be described the sensor signals of both measurement areas will first be transformed by applying (different) mathematical functions, to correspond to one another to some extent in an overlap section. In the overlap sections, transformation functions between the transformed sensor signals (transformed difference temperature signal and transformed sum temperature signal) are calculated to arrive at a single, continuous signal. The linearization of this signal is again performed by means of a calibration measurement.

(114) The now described method again originates at the sensor signals 100 (difference temperature) and 110 (sum temperature) depicted in FIG. 11. These signals are transformed such that they can be put together to a continuous signal in a simple manner.

(115) This will be further illustrated by means of a simple example:

(116) The sum temperature signal 100 is first vertically offset and re-scaled. Furthermore, the resulting signal is multiplied by the sign of the difference temperature signal, so that a negative flow rate result in a negative signal.

(117) This transformation follows the following equation:
s.sub.1(f)=(s(f)shift.sub.s).Math.scale.sub.s.Math.sign(d(f))

(118) where

(119) s(f) sum signal of the sensor depending on the flow rate f;

(120) s.sub.1(f) transformation of the function s(f);

(121) shift.sub.s vertical offset;

(122) scale.sub.s factor;

(123) sign(x) function for the sign (1 for x<0, 0 for x=0, 1 for x>0);

(124) d(f) difference temperature signal of the sensor depending on the flow rate f.

(125) Curve 113 in FIG. 18 depicts the resulting function s.sub.1(f). Due to the multiplication with the sign of the difference temperature signal, the signal 113 increases for every flow. At flow rate 0, there is a discontinuity (a signal step). This is not problematic, as this area will not be used in the following.

(126) The parameter shift.sub.s=80 was selected such that the negative and the positive portion of the curve almost go through the origin, when disregarding the section generated by the flattening of the signal at very low flows. This value can be determined by applying a tangent to the curve 110 at the steepest sections of curve 110. The tangents of the negative and positive section intersect at this value.

(127) The parameter scale.sub.s=1 is negative so that the signal increases with increasing flow rate. The absolute value can be determined discretionary so that the values of s.sub.1(f) are in a reasonable range.

(128) Analogously to the sum temperature signal s(f), also the difference temperature signal d(f) is transformed. As the sign of this signal is already the same as the sign of the flow, no correction of the sign is necessary:
d.sub.1(f)=(d(f)shift.sub.D).Math.scale.sub.D,

(129) where

(130) d(f) difference temperature signal of the sensor depending on the flow rate f;

(131) d.sub.1(f) transformation of the function d(f);

(132) shift.sub.D vertical offset;

(133) scale.sub.D factor.

(134) Curve 103 in FIG. 19 depicts the resulting function d.sub.1(f). In addition, the transformed sum temperature function (curve 113) is depicted. The value shift.sub.D may be used to balance potential zero-point-errors of the difference temperature signal. As no such errors were present in the present setup, shift.sub.D=0 was used. The value scale.sub.D=0.22 was selected so that the slopes of the approximately linear sections of curves 103 and 113 are approximately equal, at least for some overlap sections 115. Thus, overlap sections 115 as great as possible are generated, in which the transformed difference temperature signal 103 and the transformed sum temperature signal 113 correspond to one another well.

(135) As depicted in FIG. 19, the transformed functions (curves 103 and 113) correspond very well to one another in the overlap sections 115. This is not by accident, but has been achieved by transforming the sum temperature signal so that it is approximately proportional to the flow rate in the overlap sections 115. At low flow rates, the difference temperature signal is almost linear to the flow rate anyway. This signal has been transformed so that its slope corresponds to the sum temperature signal in these sections.

(136) For the parameters scales, shifts, scale), and shift), no generally applicable ranges can be provided. It depends on the signal scaling and the signal shape, as well as on manufacturing tolerances of the flow sensor used, which values are expedient. The parameters are therefore determined in a suitable manner as described above.

(137) To obtain a composite sensor signal which is relevant in the whole flow area, a weighting function is desirable having smooth transitions between the curves in the overlap sections 115, even when both curves do not perfectly conform in the overlap sections 115. This weighting function is calculated in a similar manner as discussed above by starting with the transformed sum temperature signal 113.

(138) In the discussed example, very simple transformations were used for the sensor signals for reasons of comprehensibility. This way the transition from a transformed difference temperature signal 103 to a transformed sum temperature signal 113 is only possible in the discussed overlap sections 115. At higher flow rates, there is no further overlap, such that a transition back to the difference temperature signal is not possible. Further, the difference temperature signal decreases at higher flow rates, while the transformed sum temperature signal 113 increases, so that the slope of a combined signal would change its sign. Thus, the relation between the signal and the flow rate would not be unambiguous.

(139) To avoid these problems and to simplify the following description, in the present embodiment, the transformed sum temperature signal 113 is still analyzed at higher flow rates, i.e., in comparison to FIG. 15, the weight of the transformed difference temperature signal remains 0 at higher flow rates. Practical tests have shown that this is completely sufficient. Thus, a weighting function is needed resulting in the transformed difference temperature signal 103 for small positive of negative flow rates, and resulting in the transformed sum temperature signal 113 for high positive or negative flow rates, and resulting in a smooth transition for the overlap sections.

(140) FIG. 20 depicts the transformed sum temperature signal 113, the transformed difference temperature signal 103 and the weighting function w. Different to the previous Figures, the scaling has been adapted so that the section surrounding the origin is enlarged.

(141) For determining the weighting function w, two switching thresholds th.sub.H and th.sub.L are defined to correspond to the transformed sum temperature signal at the start and the end of the desired transition section. In FIG. 20, they are depicted as the lines identified as th.sub.H and th.sub.L.

(142) As long as the transformed sum temperature 113 is below th.sub.L, only the difference temperature should be taken into account, the weighting function is thus 1. If the transformed sum temperature 113 is above th.sub.H and th.sub.L, only the sum temperature should be taken into account, the weighting function is then 0. It will be understood that the threshold th.sub.L may correspond to the turning point threshold discussed above, and that the threshold th.sub.H may correspond to the second steep threshold discussed above, though the threshold values may be different because of the transformation.

(143) Between th.sub.H and th.sub.L, the weighting function could simply progress linearly (as also discussed above). As a further example for a continuous differentiable function, a cosine-shaped transition is used.

(144) The weighting function is thus defined in sections as followed:

(145) $\begin{array}{cc}\mathrm{for}{s}_1\left(f\right)<{\mathrm{th}}_L\text{:}& w=1\\ \mathrm{for}{\mathrm{th}}_L{s}_1\left(f\right){\mathrm{th}}_H\text{:}& w=\frac{1}{2}.Math.\left(\cos \left(\frac{{\mathrm{th}}_L-s_1\left(f\right)}{{\mathrm{th}}_H-{\mathrm{th}}_L}.Math.\right)+1\right)\\ \mathrm{for}{s}_1\left(f\right)>{\mathrm{th}}_H\text{:}& w=0\end{array}$

(146) The weighting function is depicted as curve 130 in FIG. 20.

(147) The calculated weighting function w is now applied to the transformed temperature signals d.sub.1(f) and s.sub.1(f) to obtain a combined sensor signal c(f):
c(f)=w.Math.d(f)+(1w).Math.s(f)

(148) This combined sensor signal is depicted as curve 140 in FIG. 21. The signal is continuously rising over the complete measuring section so that the signal values can always be assigned unambiguously to a flow rate.

(149) However, the relation between the combined sensor signal 140 and the flow is not linear, as no linearization has been performed hitherto.

(150) To obtain the measured flow rate based on the combined sensor signal, the inverse function of c(f) is needed.

(151) This function is determined by a calibration. Here, different known flow rates are guided through the sensor, wherein the actual flow is checked, e.g., by means of a calibrated flow sensor or by means of a scale. For each flow rate, the combined sensor signal is determined so that the individual measurement points are located on curve 140. The inverse function is obtained by switching x- and y-axes. This function may be stored, e.g., by means of a lookup table. Another option is to approximate the values of the inverse function by means of a suitable mathematical function, e.g., a polynomial function.

(152) This function can be stored in the analysis control of the sensor. During operation, only the combined sensor signal needs to be inserted to arrive at the measured flow rate.

(153) The calibration is desirable due to the non-linear behavior of the sensor. Depending on how great the exemplary variation of the sensors caused by manufacturing tolerances are, individual sensors may behave differently. In such a case, it may be advantageous to calibrate each sensor individually.

(154) In case the sensor is used with different solvents, it may be advantageous to perform a calibration with every individual solvent.

(155) Still further embodiments of the present invention will now be described.

(156) As described, at high flow rates, the difference temperature signal may be used instead of the sum temperature signal. Depending on the behavior of the flow sensor, this may be advantageous.

(157) In the embodiment that has just been described, such a usage of the difference temperature signal at high flow rates has been omitted for sake of simplicity of description. However, it will be understood that such a usage of the difference temperature signal is also possible for the just described embodiment.

(158) In such a case it may be advantageous that the transformation of the difference temperature signal is done so that the slope at high flows has the same sign as the transformed sum temperature signal and so that overlap sections result in which both signals are approximately the same.

(159) This may be done by transforming the difference temperature signal stepwise, i.e., the transformation is done in a different manner for high flow rates than for low flow rates. The change of the section is done in a section where the sum temperature signal is well analyzable, i.e., in a section where the usage of the difference temperature signal is not necessary.

(160) The discussed transformation of the signals were very simple (but still functional). This has been done to facilitate an easy understanding. As the transformation is only a mathematical mapping, completely different transformations may be used, too. For example, for the transformation of the sum temperature function, an exponential part of the sum temperature function may be added, to obtain a better linearity at high flow rates.

(161) In such a case, the transformed sum temperature function would be as follows:
s.sub.2(f)=(c.sub.1.Math.e.sup.(s(f)-c.sup.2.sup.).Math.c.sup.3+(s(f)c.sub.2).Math.c.sub.4+c.sub.5).Math.sign(d(f))

(162) Here, c.sub.1 to c.sub.5 are constants, which may be determined so that the resulting sum temperature signal s.sub.2 is monotonously increasing and so that the signals can be well combined.

(163) It may be surprising that the transformation may be performed in almost any manner. The reason is that the usage of another transformation process results in another combined sensor signal; however, this is reversed again by means of the calibration.

(164) For any combined sensor signal, it is desirable that it exhibits a relevant and monotonously increasing or decreasing relation to the actual flow. If this is met, the combination of different transformation functions are mathematically equivalent if they are combined with the appropriate calibration functions.

(165) Also completely different mathematical procedures, such as two-dimensional transformation functions, may be used. However, it is generally desirable that they yield a combined function meeting the above discussed characteristics.

(166) It is also possible to already take the weighting function into account when transforming the signals. In the sections where one of the signals is not relevant, it has been multiplied by the weighting function 0, in accordance with the above discussed rationales. If, e.g., using a transformation so that the transformed signal is approximately constant in these sections, changes of the sensor signal in these sections also have no impact on the combined signal. This way weighting functions may be integrated into the transformation.

(167) By using a two-dimensional transformation, the sum temperature signal and the difference temperature signal can be taken into account simultaneously, and thus generate a combined signal without explicitly using a weighting function.

(168) All these combinations of sum and difference temperature signals are possible, according to embodiments of the present invention.

(169) The described embodiments may be used in an HPLC pump. In that regard, reference is made to FIG. 17. FIG. 17 shows, in an exemplary manner, the use of the described embodiment in a binary HPLC pump that has two solvent channels.

(170) Via the intake pipes 300a and 300b, two pump blocks 302a and 302b aspirate the solvent from solvent containers 301a and 301b. Pressure sensors 303a and 302b detect the pressures at the outlets of the pump blocks 302a, 302b. Via connection lines 310a and 310b, the solvents reach temperature-controlled flow sensors 200a and 200b according to embodiments of the invention, and from there are transported through connection capillaries 311a and 311b to a mixer 305. The latter combines the two partial flows and makes them available for the rest of the HPLC system at outlet 306 of the pump.

(171) The temperature-controlled flow sensors 200a and 200b according to embodiments of the invention constantly measure the two partial flows and forward the measurement values to a control unit 320, which is indicated by the two effect arrows. The control unit 320 compares the measured partial flows to the corresponding reference values, which result from the solvent composition that is desired at a given point in time and the desired total flow rate. The control unit 320 is designed to keep the deviations between the reference and actual values as small as possible by controlling the operating speeds of the two pump blocks 302a and 302b accordingly. This is indicated by the effect arrows between the control unit 320 and the pump blocks 302a, 302b. At least one of the two connections 311a or 311b advantageously has a certain minimum flow resistance in order to decouple the two solvent channels from each other under cybernetic aspects and to dampen the control loop. The required height of this flow resistance depends on the realization of the total system and especially on the set control parameters. A higher flow resistance facilitates faster and more accurate controlling, but on the other hand it creates a relevant pressure loss at high flow rates, whereby the maximal pressure available at the exit is correspondingly reduced.

(172) For measuring the pressures at the exit outlet, a system pressure sensor 304 is provided. In principle, it is not a necessary feature for the functionality of the system, and neither are the pressure sensors 303a and 303b, so they are to be regarded as optional features.

(173) The described embodiments expand the usable measuring range so strongly by the thermal flow sensors that the entire low flow range is covered.

(174) The expansion is achieved, inter alia, by combining different measuring modes into a single continuous measuring range. At that, at least in the overlapping areas, the signals of the different measuring modes are recorded at the same time or quasi at the same time, and are combined into a single continuous signal.

(175) E.g., in order to meet the extremely high requirements with respect to precision and reproducibility as they apply in the application of the invention in HPLC, the thermal flow sensor itself as well as the solvent that enters the sensor may also be temperature-controlled.

(176) As a result of these measures, a substantially larger measuring range is covered than the conventional thermal flow sensors, while at the same time offering a higher degree of precision.

(177) In particular, flow sensors according to embodiments of the invention may facilitate high-precision measurement of flow rates between just a few nL/min up to at least 100 L/min within a single continuous measuring range.

(178) Thanks to the application of the flow sensor according to embodiments of the invention in an HPLC pump having an active flow control, the dynamic range or the range of usable flow rates can be expanded to cover the entire low flow range between just a few nL/min up to approximately 100 L/min.

(179) In the entire mentioned range, a precision and reproducibility satisfying HPLC requirements may be obtained. This is achieved in a single continuous operating range without any exchange or switching of components.

(180) Another advantage of the invention may be that, as compared to a flow control according to the state of the art that works with conventional thermal flow sensors, it requires only very little additional effort.

(181) While certain preferred embodiments have been described with reference to the Figures, it will be understood that these embodiments are not intended to limit the scope of the present invention. What has been explained in this document is the basic principle of embodiments of the invention with readily available components. The most expedient embodiment from the current technical perspective has been described. Apart from that, various other embodiments are conceivable. Such other embodiments may possibly be more expedient depending on the overall technical concept and the characteristics of the used components.

(182) When discussing the structure and the functional principle of the flow sensor (see the flow sensor depicted in FIG. 10, for example), an embodiment was chosen in which the heating element and the temperature sensors are all positioned at the same side of the capillary. Numerous other embodiments are conceivable, in particular such embodiments in which the heating element and/or the temperature sensors enclose the sensor capillary, such as for example a heating coating that is applied to the outer wall of the capillary. In that case, temperature profiles would result that are rotationally symmetrical with respect to the capillary axis, for example. However, this would not have any influence on the basic functionality of the flow sensor and the realization according to the invention.

(183) It has been described that the differential temperature signal is analyzed at low flow rates, the sum temperature signal is analyzed at slightly higher flow rates, and the differential temperature signal is analyzed again at high flow rates, as the latter provides a higher precision in this range. Depending on the specific technical realization or the characteristics of the sensor, the sum temperature signal can also reach a good precision at high flow rates. In that case, the differential temperature signal could only be analyzed at low flow rates.

(184) Current flow sensors analyze the sum temperature signal at higher flow rates, as far as they have different analyzing modes at all. The sum temperature signal reflects the amount of heat that is dissipated from the sensor element through the liquid, and namely independently of the direction of the flow. Alternatively, it would also be possible to obtain the sum temperature signal only from one of the two temperature sensors that are present in the sensor, even though this has various disadvantages, such as that the signal becomes direction-dependent, for example.

(185) The shown embodiment of the eluent preheater is to be understood merely as an exemplary embodiment. When using a passive eluent preheater without its own active temperature control, it is not the type of construction that is relevant, but rather it is only important that a sufficiently small thermal resistance is reached between the temperature-controlled surface and the medium.

(186) Instead of using a passive eluent preheater, the temperature control of the medium can also be performed by means of active heating of a component through which the medium flows by using a controlled heating element. In that case, a temperature sensor measures the actual temperature of the liquid preferably downstream from the heating element and a control circuit controls the heating power so that the temperature is equal to a set value. In this solution the thermal resistance between the temperature control and the medium is not critical.

(187) It is also possible to detect the influence of the temperature on the signal of the flow sensor in the entire operating range of the sensor and across the expected temperature range, and to perform a mathematical correction. In this way, there would no longer be the necessity to temperature-control the sensor and/or the medium itself.

(188) In the described embodiment for temperature control, the entire housing of the sensor and of the eluent preheater is temperature-controlled. In this manner, the invention can be realized with commercially available components. Instead, it is also possible to have a sensor in which the temperature control is already integrated. The eluent preheater can also be integrated into the housing of the sensor. In this manner, a smaller type of construction is facilitated so that also less power is needed for temperature control. This in turn facilitates a temperature control via Peltier elements that can also provide active cooling, so that it is no longer necessary to temperature-control to a value that is higher than the highest operating temperature that is to be expected.

(189) The flow sensor can be designed in such a way that the sum temperature as well as the differential temperature can be read simultaneously. It is also possible to integrate the linearization and combination of modes into the sensor, so that the sensor itself is rendered capable of providing a correct signal in the entire range.

(190) As far as the application of the invention in HPLC is concerned, the description was implicitly based on pump blocks that can generate a continuous solvent flow. However, especially in the low flow range, sometimes so-called syringe pumps are used, which have to be refilled either at predetermined intervals or at the latest at the point when the syringe is empty. The invention can be used in the same manner in that case, as well.

(191) Whenever a relative term, such as about, substantially or approximately is used in this specification, such a term should also be construed to also include the exact term. That is, e.g., substantially straight should be construed to also include (exactly) straight.

(192) Whenever steps were recited in the above or also in the appended claims, it should be noted that the order in which the steps are recited in this text may be accidental. That is, unless otherwise specified or unless clear to the skilled person, the order in which steps are recited may be accidental. That is, when the present document states, e.g., that a method comprises steps (A) and (B), this does not necessarily mean that step (A) precedes step (B), but it is also possible that step (A) is performed (at least partly) simultaneously with step (B) or that step (B) precedes step (A). Furthermore, when a step (X) is said to precede another step (Z), this does not imply that there is no step between steps (X) and (Z). That is, step (X) preceding step (Z) encompasses the situation that step (X) is performed directly before step (Z), but also the situation that (X) is performed before one or more steps (Y1), . . . , followed by step (Z). Corresponding considerations apply when terms like after or before are used.

(193) While in the above, preferred embodiments have been described with reference to the accompanying drawings, the skilled person will understand that this embodiment was provided for illustrative purpose only and should by no means be construed to limit the scope of the present invention, which is defined by the claims.