JP7302867B2 - Method and apparatus for measuring viscosity coefficient - Google Patents

Description

TECHNICAL FIELD The present invention relates to a measuring method and a measuring device for measuring coefficients relating to viscosity of a sample.

Conventional methods for measuring the viscosity of a fluid sample include the capillary method, which measures the pressure loss of a fluid passing through a capillary tube, the falling body method, which measures the velocity of an object falling in a vertical tube, and the fluid that is passed between rotating discs. Four types are known: a rotary type that measures the required torque by injecting fluid, and a vibration type that measures damping vibration when fluid is injected between the inner and outer cylinders and the inner cylinder is vibrated (for example, Non-Patent Document 1 reference).

Hiroo Kawada, "Viscosity", Corona Publishing, 1958

However, in the conventional viscosity measurement method, high viscosity can be measured with high precision using a relatively large device, but there is a problem that it is difficult to measure a fluid with extremely low viscosity with high precision using a compact device. there were. In addition, when there is a spatial distribution of temperature and pressure inside the measuring device, there is also the problem that it is not possible to accurately determine at what temperature and pressure the measured viscosity is a value. Furthermore, non-Newtonian fluids whose viscosity depends on the shear rate (velocity gradient) cannot be measured under conditions where the shear rate is close to 0 in order to maintain measurement accuracy. This is because when the shear rate approaches 0, the shear stress becomes small and the viscosity cannot be measured with high accuracy. As a result, since the measurement is performed in a state where the spatial distribution of the shear rate occurs, there is also the problem that it is not possible to accurately determine what shear rate the measured viscosity corresponds to. become. Moreover, in the conventional viscosity measurement method, it was necessary to correct the measurement result.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-described problems, and provides a completely new method and apparatus for measuring a coefficient relating to viscosity that has never existed before.

In order to achieve the above object, the present invention provides a method for measuring a coefficient related to viscosity of a sample, which is a fluid, comprising the steps of: giving a disturbance to the sample in a container; measuring the damping rate of a given mode for the subsequent sample flow velocity; and calculating a coefficient for the viscosity of the sample based on the measured damping rate.
With such a configuration, it is possible to measure the viscosity coefficient of the sample, for example, the dynamic viscosity coefficient and the viscosity coefficient, by using the measurement result of the damping factor of the predetermined mode related to the flow velocity of the sample after the disturbance is applied. can. Such a method makes it possible to measure small viscous moduli even with a compact device. Also, for example, when the measurement is performed with a compact device, it is possible to suppress changes in the spatial distribution of temperature and pressure, and it becomes possible to measure the viscosity coefficient at a specific temperature and pressure. In addition, as will be described later, since the measurement is performed in a state close to a linearly stable steady state, the viscosity-related coefficient can be measured even if the shear rate is close to zero. Furthermore, there is also the advantage that there is no need to correct the measurement results as in the conventional method.

Further, in the method of measuring the coefficient related to viscosity according to the present invention, the predetermined mode may be the mode with the slowest attenuation.
With such a configuration, by measuring the attenuation rate of the flow velocity when a sufficient amount of time has passed since the disturbance was applied, the attenuation rate of the mode with the slowest attenuation can be measured. can be easily measured.

Further, in the method for measuring a coefficient related to viscosity according to the present invention, the container may be cylindrical, and in the step of imparting turbulence to the sample, the sample may be stirred so as to have an axially symmetrical flow velocity. It is desirable not to interfere with the flow after imparting the necessary disturbance.
With such a configuration, the eigen equation can be analytically solved, and the attenuation factor of the predetermined mode can be easily calculated.

Further, in the method for measuring a coefficient related to viscosity according to the present invention, the container may be open at the top.
With such a configuration, by putting a sample in a container that is open at the top and imparting disturbance, it is possible to measure the coefficient related to the viscosity of the sample, so that the coefficient related to viscosity can be easily measured. There is an advantage.

Moreover, in the method for measuring a coefficient related to viscosity according to the present invention, the container may be a closed container filled with a sample.
With such a configuration, it is possible to measure the viscosity-related coefficient of a sample that is difficult to put in a container whose top is open, such as a gaseous sample or a volatile sample.

In addition, in the method for measuring a coefficient related to viscosity according to the present invention, the coefficient related to viscosity may be a kinematic viscosity coefficient or a viscosity coefficient.

Further, the viscosity-related coefficient measuring device according to the present invention is a device for measuring the viscosity-related coefficient of a sample, which is a fluid, and comprises a container in which the sample is placed, a disturbance imparting means for imparting disturbance to the sample in the container, measuring means for measuring the attenuation rate of a predetermined mode relating to the flow velocity of the sample after being disturbed by the disturbance imparting means; calculating means for calculating a coefficient relating to the viscosity of the sample based on the measured attenuation rate; and calculating means and an output means for outputting the coefficient related to the viscosity calculated by.
With such a configuration, it is possible to measure the viscosity coefficient of the sample, for example, the dynamic viscosity coefficient and the viscosity coefficient, by using the measurement result of the damping factor of the predetermined mode related to the flow velocity of the sample after the disturbance is applied. can. With such a device, it is possible to measure small viscous coefficients even with a compact device. Also, for example, when the measurement is performed with a compact device, it is possible to suppress changes in the spatial distribution of temperature and pressure, and it becomes possible to measure the viscosity coefficient at a specific temperature and pressure. Further, as will be described later, since the measurement is possible only in a state close to a linearly stable steady state, for example, even if the shear rate is close to 0 in the vicinity of a stable stationary state, the coefficient related to viscosity can be measured. Furthermore, there is also the advantage that there is no need to correct the measurement results as in the conventional method. By predetermining the shape and size of the container and the mode corresponding to the attenuation factor of the object to be measured, the same calculation formula can be used each time as the calculation formula for calculating the viscosity-related coefficient. Therefore, there is no need to change the calculation formula each time the viscosity-related coefficient is measured, and the viscosity-related coefficient can be measured more easily.

INDUSTRIAL APPLICABILITY According to the method and apparatus for measuring a coefficient related to viscosity according to the present invention, even a compact device can measure a small coefficient related to viscosity with high accuracy. Further, for example, when the viscosity coefficient is measured using a compact device, changes in the spatial distribution of temperature and pressure can be suppressed, and the viscosity coefficient at a specific temperature and pressure can be measured. In addition, even under conditions where the shear rate is close to zero, the viscosity coefficient can be measured. Furthermore, there is no need to correct the measurement results.

Schematic diagram showing the configuration of a kinematic viscosity measuring device according to an embodiment of the present invention. 3 is a flow chart showing a method for measuring a kinematic viscosity coefficient according to the same embodiment; FIG. 4 is a diagram showing an example of time change of the flow velocity of the sample in the same embodiment; FIG. 4 is a partially enlarged view showing an example of the time change of the sample flow velocity in the same embodiment;

Hereinafter, the method and apparatus for measuring a coefficient related to viscosity according to the present invention will be described using embodiments. In the following embodiments, constituent elements and steps with the same reference numerals are the same or correspond to each other, and repetitive description may be omitted. The method and apparatus for measuring the viscosity-related coefficient of the present embodiment measure the viscosity-related coefficient of the sample using the measurement result and the calculation result of the damping factor of a predetermined mode related to the flow velocity of the fluid sample. . In this embodiment, the case where the coefficient related to viscosity is the kinematic viscosity coefficient will be mainly described, and the case where the coefficient related to viscosity is other than the kinematic viscosity coefficient will be described later.

FIG. 1 is a schematic diagram showing the configuration of a kinematic viscosity coefficient measuring device 1 according to the present embodiment. A kinematic viscosity measuring device 1 according to the present embodiment includes a container 11, a disturbance imparting means 12, a measuring means 13, a storage means 14, a calculating means 15, an output means 16, and a control means 17. .

A container 11 contains a fluid sample 5 whose kinematic viscosity is to be measured. The sample 5 may be, for example, a liquid, a gas, or a supercritical fluid. The container 11 may be, for example, a container with an open top, as shown in FIG. 1, or a closed container. When the top of the container 11 is open, it is preferable that the container 11 is arranged so that the bottom surface is horizontal. Moreover, when the sample is gaseous or volatile, for example, the container 11 is preferably a closed container. If the container 11 is a closed container, the container 11 is preferably filled with the sample 5 . That is, it is preferable that substantially only the sample 5 is contained in the container 11, which is a closed container. Even when the sample 5 is filled in the container 11, which is a closed container, the container 11 may contain a tracer, as will be described later.

Although the shape of the container 11 does not matter, the shape having rotational symmetry with respect to an arbitrary integer N with respect to the stirring axis when stirring the sample 5 placed in the container 11 for imparting disturbance, that is, It may be in the shape of a body of revolution. The shape of the container 11 may be, for example, a cylindrical shape, a spherical shape, a spheroidal shape, a torus shape (doughnut shape), or a hollow cylindrical shape. It may be in the shape of a body of revolution. In this embodiment, as shown in FIG. 1, the case where the container 11 has a cylindrical shape with an open top will be mainly described.

A disturbance imparting means 12 imparts disturbance to the sample 5 in the container 11 . This turbulence is applied to cause the sample 5 to have a predetermined flow velocity. As will be described later, this turbulence is applied to the sample 5, for example, to induce various modes that decay to a stationary state (a state in which the flow velocity is 0), which is a linearly stable steady state. The method by which the disturbance imparting means 12 causes the sample 5 to be disturbed does not matter. The disturbing means 12 may cause the disturbance by, for example, stirring the sample 5 and stopping the stirring. For example, the disturbance imparting means 12 may stir the sample 5 with a stirring blade, a stirring member, or the like. In this case, the disturbance imparting means 12 may have, for example, a stirring blade, a rotating shaft to which the stirring blade is fixed, and a driving means for rotating the rotating shaft. Then, the sample 5 may be stirred by inserting the stirring blade into the sample 5 and rotating it. Further, the disturbance imparting means 12 may be a magnetic stirrer. Further, the disturbance imparting means 12 may rotate the container 11 itself. This is because by rotating the container 11, the sample 5, which is the content of the container 11, can be rotated. Such a disturbing means 12 may be a turntable for rotating the container 11 containing the sample 5, as shown in FIG. When repeating the measurement of the attenuation rate (attenuation coefficient) of the sample 5, it is preferable to rotate the sample 5 in the same manner each time. From that point of view, it is preferable that the disturbance imparting means 12 rotates the container 11 itself. The container 11 itself is rotated at a constant number of rotations by the disturbance imparting means 12, and by stopping the rotation, the sample 5, which is the contents of the container 11, rotates with respect to the container 11. , can be made the same each time. In addition, when the container 11 is sealed, it is difficult to insert a stirring blade or the like into the container 11, so it is preferable to perform stirring using a rotating table. In this embodiment, a case where the disturbance imparting means 12 imparts disturbance to the sample 5 by stirring will be mainly described.

The turbulence imparted by the turbulence imparting means 12 is preferably carried out so as to generate a target flow velocity in the sample 5 in the container 11 . For example, the stirring may be performed by the disturbance imparting means 12 so that the axis of rotational symmetry of the container 11, which is in the shape of a body of revolution, coincides with the stirring axis. For example, when the disturbance imparting means 12 has a rotation axis, the stirring may be performed so that the rotation axis coincides with the rotationally symmetrical axis of the container 11 . Further, for example, when the disturbance imparting means 12 is a turntable, stirring may be performed so that the rotation axis of the turntable and the axis of rotational symmetry of the container 11 coincide. Moreover, the flow velocity generated in the sample 5 by stirring may satisfy a predetermined condition. For example, when the container 11 has a cylindrical shape, the sample 5 in the container 11 may be stirred so that the flow velocity is axially symmetrical with respect to the central axis of the container 11, as will be described later. That is, the sample 5 in the container 11 may be stirred axially symmetrically so that the velocity is mainly in the circumferential direction. In this case, the sample 5 preferably has no velocity in the radial direction of the container 11, and even if it does have a velocity in the radial direction, it is preferably sufficiently small compared to the velocity in the circumferential direction. is. The turbulence imparting means 12 may stand still after imparting a predetermined turbulence. A blade, a rotating shaft, or the like may be removed from the sample 5 .

Further, the turbulence imparted by the turbulence imparting means 12 may be performed, for example, by blowing a predetermined gas onto the sample 5 so as to generate a target flow velocity in the sample 5, which is liquid in the container 11. For example, in a cylindrical container 11 whose top is open, in order to generate a flow velocity in the circumferential direction, the turbulence imparting means 12 is arranged in the circumferential direction with respect to the liquid surface of the sample 5, which is the liquid in the container 11. Gas may be blown.

Moreover, in the sample 5 in the container 11, as long as the flow velocity corresponding to the target mode is generated, the flow velocity may be generated as a superimposition of various modes. Therefore, as long as the flow velocity corresponding to the desired mode is sufficiently large, the sample 5 in the container 11 may be stirred randomly to some extent to give the disturbance.

Even if the sample 5, which is a fluid, flows, it is usually difficult to observe the flow from the outside. Thus, for example, a tracer may be introduced into the sample 5 in order to be able to observe the flow situation of the sample 5 . For example, a tracer that floats on the sample 5 may be put into the container 11 whose top is open. Further, for example, a tracer having a specific gravity similar to that of the sample 5 may be put into the sealed container 11 . The tracer may be, for example, a small piece, particle, or the like that is visually distinguishable from the sample 5 . Also, the number of tracers may be, for example, one or plural. In the latter case the tracer may be, for example, tracer particles dispersed in the sample 5 . In order not to affect the measurement of the kinematic viscosity coefficient, the tracer is preferably of such a size that it can be ignored with respect to the amount of the sample 5 put in the container 11 .

The measuring means 13 measures the attenuation rate of a predetermined mode with respect to the flow velocity of the sample 5 after being disturbed by the disturbance applying means 12, and includes an imaging means 13a and a calculating means 13b. For example, when the turbulence is applied by stirring, the measuring means 13 measures the attenuation rate of the predetermined mode with respect to the flow velocity of the sample 5 after stopping the stirring. The measurement of the damping factor of the predetermined mode is usually performed by measuring the flow velocity of the predetermined mode and calculating the damping factor using the measured flow velocity. As described above, the flow velocity attenuates with the lapse of time after the turbulence is applied to the stationary state. There are various modes of attenuation (eigenfunctions), and the attenuation rate of a specific mode related to the flow velocity is measured by the measuring means 13 . The specific mode may be, for example, the mode with the slowest attenuation, or may be any other mode. In the former case, the damping rate should be measured after the damping of the other modes is sufficiently completed (that is, after the effects of the other modes are sufficiently negligible). That is, the attenuation rate measured after a sufficient time has elapsed after the disturbance is applied is the attenuation rate of the slowest mode. Therefore, from the viewpoint that the attenuation rate can be easily measured, it is preferable that the predetermined mode is the slowest attenuation mode.

When measuring the attenuation rate of a mode other than the slowest attenuation mode, it is necessary to measure so as not to be affected by the mode whose attenuation rate is slower than the mode of the attenuation rate to be measured. Therefore, for example, a position that is not affected by a mode with a slower attenuation than the mode of the attenuation rate to be measured, that is, a mode with a slower attenuation than the mode of the attenuation rate to be measured, the flow velocity of the mode with the slower attenuation is 0 The attenuation factor of the mode to be measured may be measured at the position where .

In the present embodiment, as will be described later, the case where the tracer of the sample 5 is photographed, the flow velocity is calculated by tracking the tracer, and the attenuation factor related to the flow velocity is obtained using the calculated flow velocity will be mainly described. Needless to say, the flow velocity may be obtained by other methods. For example, the tracer particles in the sample 5 may be irradiated with a laser beam, and the flow velocity may be obtained using the Doppler effect in which the frequency of the scattered light from the tracer particles changes slightly according to the velocity of the tracer particles (laser Doppler current meter). Also, as described above, it may be necessary to measure the flow velocity at a specific position when measuring the damping rate of modes other than the slowest damping mode. In such a case, for example, the flow velocity at the location where the flow velocity is desired may be measured by irradiating the location where the flow velocity is desired with a laser beam and photographing the reflected light from the tracer particles. Alternatively, a laser Doppler anemometer may be used to measure the flow velocity at a location where the flow velocity is desired.

Moreover, when measuring the flow velocity, it is preferable to keep the temperature and pressure of the sample 5 constant throughout the sample 5 . By doing so, it is possible to clarify to which temperature and pressure the kinematic viscosity coefficient calculated based on the damping factor measured using the flow velocity corresponds.

The imaging means 13a performs imaging for acquiring the flow velocity of the sample 5 after the disturbance is imparted by the disturbance imparting means 12 . A moving image of the tracer of the sample 5 may be obtained by this photographing. The photographing means 13a may acquire moving images of the tracer at a predetermined frame rate, for example, using an imaging device such as CMOS or CCD.

The calculation means 13b acquires the flow velocity of the sample 5 by tracking the position of the tracer using the moving image photographed by the photographing means 13a. Further, the computing means 13b computes the attenuation factor of the predetermined mode regarding the flow velocity of the sample 5 using the flow velocity thus acquired. Details of the calculation of the attenuation factor will be described later.

The storage means 14 stores information necessary for calculating the dynamic viscosity coefficient of the sample 5 using the measured damping factor. The storage means 14 may store, for example, a theoretically calculated damping factor for a predetermined mode relating to the flow velocity of the sample 5 in the container 11, and a formula for calculating the kinematic viscosity coefficient (for example, Equation (10), Equation (15), etc.) may be stored. Details of the calculation of the attenuation rate will be described later. The theoretically calculated attenuation rate is the theoretically calculated attenuation rate based on the shape of the sample 5, etc., and the measured attenuation rate is measured based on the actual flow velocity in the sample 5. is the attenuation rate.

Also, the process by which the information is stored in the storage means 14 is irrelevant. For example, information may be stored in the storage means 14 via a recording medium, information transmitted via a communication line or the like may be stored in the storage means 14, or Information input via an input device may be stored in the storage means 14 . The storage means 14 is preferably implemented by a non-volatile recording medium, but may be implemented by a volatile recording medium. The recording medium may be, for example, a semiconductor memory, a magnetic disk, an optical disk, or the like.

In the present embodiment, the storage means 14 stores the equation for calculating the damping factor of the predetermined mode or the kinematic viscosity coefficient, which is calculated for the sample 5 having a predetermined shape in the container 11. However, in the kinematic viscosity measuring device 1, when the container 11 of an arbitrary shape is used, or when the amount of the sample 5 put in the container 11 is arbitrary, the measurement The damping factor of the predetermined mode with respect to the flow velocity of the sample 5 may be calculated for each time. In that case, the kinematic viscosity coefficient measuring device 1 may be provided with damping rate calculation means for calculating the damping rate of a predetermined mode based on, for example, an aspect ratio or the like, which will be described later. The attenuation rate calculation means may receive, for example, an aspect ratio or the like, which will be described later, from an operator or the like, and use them to calculate the attenuation rate of a predetermined mode.

The calculation means 15 calculates the dynamic viscosity coefficient of the sample 5 based on the damping factor measured by the measurement means 13 . Although the details of this calculation will be described later, the calculation means 15 calculates the kinematic viscosity coefficient by assuming that the measured attenuation factor is equal to the previously calculated attenuation factor stored in the storage means 14. Alternatively, the kinematic viscosity coefficient may be calculated by substituting the measured damping rate into the equation for calculating the kinematic viscosity coefficient stored in the storage means 14 . The dynamic viscosity coefficient calculated in this way is the dynamic viscosity coefficient of the sample 5 in the container 11 .

Note that the measurement of the attenuation rate by the measuring means 13 may be repeated. When the damping rate measurement is repeated in such a manner, for example, a representative value of the plurality of damping rate measurements may be used to calculate the kinematic viscosity coefficient. The kinematic viscosity coefficient may be calculated for each measurement, and a representative value of the calculated plurality of kinematic viscosity coefficients may be the final measured kinematic viscosity coefficient. The representative value may be, for example, an average value, a median value, or the like.

The output means 16 outputs the dynamic viscosity coefficient calculated by the calculation means 15 . Here, this output may be, for example, a display on a display device (for example, a liquid crystal display or an organic EL display), may be transmitted to a predetermined device via a communication line, may be printed by a printer, or may be a recording medium. It may be stored in or passed on to another component. Note that the output means 16 may or may not include a device for outputting (for example, a display device, a communication device, etc.). Also, the output means 16 may be realized by hardware, or may be realized by software such as a driver for driving those devices.

The control means 17 may control the disturbance imparting means 12 , the calculation means 13 b and the calculation means 15 . For example, upon receiving an instruction to measure the dynamic viscosity coefficient of the sample 5, the control means 17 causes the disturbance imparting means 12 to stir the sample in the container 11, and after the predetermined stirring is achieved, the stirring is performed. Disturbance may be caused by stopping Further, the control means 17 may output to the calculation means 13b that the stirring has been stopped. After a predetermined period of time has passed after receiving the fact that the stirring has been stopped, the calculating means 13b may acquire the flow velocity of the sample 5 and the attenuation factor related to the flow velocity. After that, the control means 17 may cause the calculation means 15 to calculate the dynamic viscosity coefficient of the sample 5 using the attenuation factor acquired by the calculation means 13b and the attenuation factor stored in the storage means 14. .

Next, the operation of the kinematic viscosity measuring device 1, that is, the method of measuring the kinematic viscosity will be described with reference to the flow chart of FIG. In this flowchart, it is assumed that the formula for calculating the coefficient of dynamic viscosity is stored in the storage means 14 in advance. Also, it is assumed that a predetermined amount of the sample 5 whose kinematic viscosity coefficient is to be measured is put into the container 11 . It is also assumed that agitation is applied by stirring.

(Step S<b>101 ) The control means 17 stirs the sample 5 in the container 11 by controlling the disturbing means 12 . This stirring is performed, for example, by rotating the container 11 .

(Step S<b>102 ) The control means 17 stops the stirring of the sample 5 by stopping the rotation of the container 11 by the disturbing means 12 . By stopping the rotation of the container 11 , the sample 5 in the container 11 rotates with respect to the container 11 . In this manner, the sample 5 is disturbed. The control means 17 may output to the computing means 13b that the stirring of the sample 5 has been stopped. In addition, when the stirring is stopped, the photographing means 13a acquires a moving image of the tracer of the sample 5 after the stirring is stopped.

(Step S103) The computing means 13b determines whether to start measuring the attenuation factor related to the flow velocity of the sample 5 or not. If the measurement is to be started, the process proceeds to step S104. If not, the process of step S103 is repeated until it is determined to start the measurement. The computing means 13b may determine, for example, to start measuring the attenuation rate after a predetermined period of time has elapsed since the stirring was stopped.

(Step S104) The computing means 13b acquires the flow velocity of the sample 5 using the moving image of the tracer of the sample 5 acquired by the photographing means 13a, and measures the attenuation rate, which is the time change of the acquired flow velocity.

(Step S105) The calculation means 15 calculates the dynamic viscosity coefficient of the sample 5 based on the damping factor measured by the calculation means 13b. The calculation means 15 may calculate the kinematic viscosity coefficient by substituting the measured damping rate into the formula stored in the storage means 14, for example.

(Step S<b>106 ) The output means 16 outputs the dynamic viscosity coefficient calculated by the calculation means 15 . Thus, a series of processes for measuring the coefficient of dynamic viscosity is completed.

In addition, although each process in the case of measuring the dynamic viscosity coefficient of the sample 5 using the dynamic viscosity measuring device 1 has been described in the flow chart of FIG. 2, this need not be the case. Instead of using such a device, the measurer may manually stir the sample 5 in the container 11 and photograph the tracer of the sample 5 in a laboratory or the like. In that case, for example, a series of processes for measuring the dynamic viscosity, i.e., a process for theoretically calculating the damping factor of a predetermined mode related to the flow velocity of the sample 5, and a process for measuring the dynamic viscosity It may include a process of obtaining an expression for calculation. Its mode is the same as the mode of the attenuation factor to be measured.

Next, the calculation of the attenuation factor related to the flow velocity of the sample, which is a fluid, will be described. Motion of a fluid considering viscosity is expressed by the following equations (1) and (2). Note that the summation convention is used for the subscript j.

Here, equation (1) is the Navier-Stokes equation, and equation (2) is a continuity equation indicating that the fluid is incompressible. It should be noted that equation (2) is naturally satisfied if the fluid is a liquid, and even if the fluid is a gas, if the steady state is a stationary state with a constant temperature, the density can be regarded as constant. can be fulfilled. In the above equations, v _i is the i component of the velocity of the fluid, k _i is the volumetric force per unit mass, p is the pressure of the fluid, ρ is the density of the fluid, and ν is the fluid is the dynamic viscosity coefficient of Also, t is time and x is a coordinate. The subscripts i and j are integers from 1 to 3, and the subscripts i and j from 1 to 3 are the x component and the y component in the three-dimensional orthogonal coordinate system (x, y, z), respectively. , corresponding to the z component.

The Navier-Stokes equation cannot be solved analytically because it is a nonlinear equation, but it can be linearized around the steady state. For example, considering a situation in which a fluid is in a stationary state where the velocity is 0 and a disturbance (perturbation) is added, if the disturbance is small, the second term on the left side of equation (1) is small enough to be ignored. As a result, equation (1) can be converted into a linear equation, and by setting the time dependence of the linear equation to exp(-λt), the eigenvalue λ and the eigenequation for the eigenfunction (mode) v are derived. be able to. By linearizing the above equation (1) and making it dimensionless, the following equation (3) is obtained. That is, the formulas (1) and (2) become the following formulas (3) and (4). When the modes are defined by linear equations, if the real parts of all eigenvalues are positive, the disturbance applied to the above steady state is attenuated, which is called linear stability. Equation (3) below is obtained by linearizing the Navier-Stokes equation around the static state, which is a linearly stable steady state.

Here, the volumetric force k _i per unit mass is included in the pressure P newly defined assuming a potential field in which the fluid is in a stationary state. This eigenequation is the so-called Stokes eigenmode. Although it is usually difficult to solve this eigenequation numerically, it can be solved analytically by setting predetermined constraints and boundary conditions. Specifically, it is assumed that the sample 5 is placed in a cylindrical container 11 as shown in FIG. Here, let R be the radius of the inner bottom surface of the cylindrical container 11 and let H be the height of the sample 5 . Also, let the aspect ratio of the radius and the height be α=H/R. Also, since the sample 5 is in contact with the container on the bottom and side surfaces, it is assumed that there is no slippage (that is, the speed is 0), and that the upper surface is open to the atmosphere, so that there is slippage (that is, the slope is 0). These are the boundary conditions. In addition, when the velocity of the sample 5 is axially symmetrical with respect to the cylinder axis and a constraint condition is set that it does not have a velocity component in the radial direction about the cylinder axis, the velocity in the circumferential direction and the eigenvalue (velocity can be analytically solved as follows:

where u _θ(n,m) (r,z) is the dimensionless circumferential velocity component (eigenfunction) in the (n,m) mode at the position r,z, and λ _{( n,m)} is the dimensionless damping rate (eigenvalue) in the (n,m) mode. Also, J ₁ (x) is a Bessel function of the first kind with an order of 1, and x _n is the nth non-zero zero of the Bessel function of the first kind J ₁ (x), which is known. However, n is an integer of 1 or more, and m is an integer of 0 or more. For example, _x1 is "3.8317...". Also, r is the distance from the center of the cylindrical shape of the container 11, and is set to be 0 at the center and 1 at the position of the side wall (the position of the radius R). Also, z is the height from the bottom surface of the container 11, and is set so that the bottom surface is 0 and the upper end of the sample 5 (the position of the height H) is α. This is because they are made dimensionless by R, respectively. The state in which the sample 5 placed in the container 11 is not disturbed is the stationary state, which is the above-mentioned linearly stable steady state, and the above-mentioned disturbance is the flow of the sample 5 caused by the disturbance applying means 12. is.

It should be noted that the following is an expression showing the time change U _θ (r, z, t) of the velocity distribution in the circumferential direction inside the container 11 using the expressions (5) and (6). where A _(n,m) is a predetermined coefficient for each mode. As can be seen from the following equation, after enough time, only velocities with small decay rates λ _(n,m) will remain.

Equations (5) and (6) show the dimensionless velocity component and damping factor in the circumferential direction. Note that L is the representative length used for non-dimensionalization, where L=R.

In the above formulas (6) and (8), the mode with the slowest attenuation is the (n, m)=(1, 0) mode. The dimensional attenuation rate λ ^(d) _(1,0) of the (1,0) mode is given by the following equation.

Also, when the sample 5 in the container 11 is disturbed and the decay rate for the flow velocity is measured after a sufficient period of time has passed, it is equal to λ ^(d) _(1,0) . Therefore, if the damping rate thus measured is λ ^(m) , the kinematic viscosity coefficient ν can be calculated as follows. In the right side of equation (10), the attenuation factor λ ^(m) is a measured value, and L and α are values determined according to the shape of the container 11 and the height of the sample 5 . Since the others are constants, the right side of Equation (10) can be calculated. Thus, the kinematic viscosity coefficient ν of the sample 5 can be measured.

If the imaginary part of the eigenvalue is 0, it will be overdamped and will decay exponentially. In this case, if the attenuation is expressed as A×exp(−λt), λ (real number) becomes the attenuation rate λ ^(m) . On the other hand, when the imaginary part of the eigenvalue is not 0, damped oscillation occurs and damps while vibrating. In this case, the attenuation rate λ ^(m) can be obtained from the time variation of the maximum or minimum value.

In measuring the attenuation rate, when measuring the attenuation rate of the mode with the slowest attenuation, as described above, the attenuation rate of the mode with the slowest attenuation (in the above example, the attenuation rate of the (1, 0) mode) Only has to be calculated in advance. On the other hand, when it is not determined which mode's attenuation rate is to be measured, the eigenfunction and A combination for each mode with an eigenvalue may be calculated in advance. Then, by referring to the eigenfunction and eigenvalue for each mode, the mode for measuring the attenuation rate may be determined.

As described above, in the dimensional case, the theoretically calculated damping rate includes the kinematic viscosity coefficient ν ^. , the kinematic viscosity coefficient ν can be calculated as shown in Equation (10). The kinematic viscosity coefficient ν thus calculated is the kinematic viscosity coefficient ν measured by the kinematic viscosity measuring device 1 according to the present embodiment. In addition, in the kinematic viscosity measuring device 1 shown in FIG. 1, the aspect ratio α is determined by determining the height H of the sample 5 placed in the container 11 . Also, since the radius R (=L) of the container 11 and x ₁ are also known, the right side of Equation (10) can be C×λ ^(m) . Here, C is a real number corresponding to L ² /(x ₁ ² +(π/(2α)) ² ). Therefore, when ν=C×λ ^(m) is stored in the storage means 14, the calculation means 15 substitutes the measured damping rate λ ^(m) into the formula to obtain the kinematic viscosity coefficient ν can be calculated. In the formula corresponding to formula (10): ν = C × λ ^(m) , the part other than λ ^(m) , that is, the part of "ν/C" corresponds to the calculated attenuation rate, so the calculated When ^the means 15 calculates the dynamic viscosity coefficient ν using the formula, the dynamic viscosity coefficient ν is calculated.

The dimensionless attenuation rate depends only on the shape of the sample 5, the boundary conditions of the sample 5, and the stirring conditions of the sample 5, and does not depend on the type of the sample 5. Therefore, in the situation where the disturbance is imparted axisymmetrically within the cylindrical container 11 as described above, the dimensionless attenuation rate depends only on the aspect ratio, as shown in Equation (6), and the container 11 When the aspect ratio α of the sample 5 inside is constant, that is, when the shape of the sample 5 is similar, the values are the same. Therefore, by making the attenuation factor dimensionless, there is an advantage that it is not necessary to repeat the calculation of the attenuation factor when the aspect ratio of the sample 5 is constant.

The relationship between the dimensionless (1,0) mode attenuation rate and the measured attenuation rate λ ^(m) is given by the following equation. Therefore, the dynamic viscosity coefficient ν can also be calculated using the following equation. Note that if formula (11) is transformed, it becomes the same as formula (10) above.

As is clear from the above description, when dimensionless, the calculated attenuation rate λ _(1,0) is a numerical value, and the measured attenuation rate λ ^(m) and the calculated attenuation rate The kinematic viscosity coefficient ν will be included in equation (11) relating the rate λ _(1,0) . On the other hand, in the dimensional case, the calculated λ ^(d) _(1,0) includes the kinematic viscosity coefficient ν as shown in Equation (8).

Here, the case where the top of the container 11 is open has been described, but when the top of the container 11 is not open, that is, when the container 11 is a closed container, the kinematic viscosity coefficient can be similarly calculated. can be calculated. In this case, the dimensional decay rate of the slowest decaying (1,0) mode is given by the following equation.

Therefore, when the container 11 is a closed container, the kinematic viscosity coefficient ν can be calculated using the following equation. Note that λ' ^(m) is the damping rate of the (1, 0) mode measured for the sample 5 in the sealed container 11 having an aspect ratio of α and a radius of R (=L). .

In this case, since the container 11 is hermetically sealed, it is possible to measure the kinematic viscosity of a gas or a volatile liquid. In addition, the kinematic viscosity can be measured even if the container 11 is tilted in any direction. That is, the bottom surface of the container 11 does not have to be horizontal.

In the above description, the attenuation rate is measured and calculated for the slowest attenuation mode, but this need not be the case. By measuring and calculating the damping rate in the second slowest damping mode, etc., the kinematic viscosity coefficient can also be measured in the same manner as described above. However, in that case, it is preferable to measure the attenuation rate so as not to be affected by modes other than the intended mode. For example, if the flow velocity of the second slowest damping mode can be measured at a node location for the slowest damping mode, i.e., a location where there is no velocity component for the slowest damping mode, then so measure. The kinematic viscosity coefficient can also be calculated using the measurement result of the damping rate related to the flow velocity of the sample 5 in the second slowest damping mode and the theoretical calculation result of the damping rate.

Next, examples relating to the method for measuring the kinematic viscosity coefficient and the measuring device 1 according to the present embodiment will be described. In this embodiment, a right cylindrical acrylic container 11 having an inner diameter of 29 cm, an outer diameter of 30 cm, and a height of 30 cm is placed on a horizontal table. Water, which is sample 5, was injected so as to be 8 cm. As a tracer, a polyethylene foam thin disk with a diameter of 2.7 cm with a black dot in the center was floated on the water. Then, the stirring member was put in from above so that the initial velocity distribution mainly had a flow that was axially symmetrical with respect to the central axis of the container 11, and the stirring member was lifted out of the water. For 20 minutes after the stirring operation was stopped, a photographing means 13a (Nikon D5100), which is a digital camera provided above the cylindrical container 11, was photographed. In addition, by analyzing the captured moving image with analysis software (kinovea 0.8.27), the flow velocity (pixels/second) at each time was measured by measuring the movement speed of the tracer after stirring was stopped. . Note that in this embodiment, one pixel (px) corresponds to 0.356 mm. An example of the measurement result is as shown in FIG. Moreover, in FIG. 3, the time change of the flow velocity is shown by the semi-logarithm. In addition, using flow velocities after 10 (pixels/second) shown in FIG. By approximation, the attenuation rate corresponding to the straight line 100 was obtained. 3 and 4, since the speed (vertical axis) is scaled logarithmically, the absolute value of the slope of the straight line 100 is the attenuation rate. The attenuation rate λ ^(m) was 0.00103 (1/sec). Before and after the start of the experiment, the average water temperature was 18.1°C measured in a state of almost static equilibrium. The pressure was 1 atm. In addition, in this example, since the attenuation rate is measured after a sufficient time has passed since the stirring was stopped, the attenuation rate in the above (1, 0) mode, which is the mode with the slowest attenuation, was measured. I did. Equation (10) for calculating the dynamic viscosity coefficient ν using the (1,0) mode damping rate λ ^(m) is as follows.

On the right side of the above equation (10), the measured attenuation rate λ ^(m) , the inner radius L=R=0.145 (meters) of the container 11, and the first kind Bessel function J ₁ (x) of order 1 Substituting the first non-zero zero point x ₁ =3.83 and the aspect ratio α=(H/R)=(0.08/0.145) of the container 11, the kinematic viscosity coefficient ν of water is 0.08/0.145. It was found to be 952×10 ⁻⁶ (square meters/second).

By interpolating the kinematic viscosity coefficient of water at 1 atm at 15 ° C. and 20 ° C. described in Rika Chronicle, the kinematic viscosity coefficient corresponding to a pressure of 1 atm and a water temperature of 18.1 ° C. is obtained. 0.055×10 ⁻⁶ (square meters/second). Therefore, in this example, the dynamic viscosity of water could be measured with a relative error of about 9.8%.

Normally, the kinematic viscosity coefficient is measured repeatedly at a constant temperature and pressure, and a representative value such as an average value is used as the final kinematic viscosity coefficient measurement value. Therefore, the accuracy when the kinematic viscosity coefficient is measured by averaging such a plurality of measurement results will be described. Here, the accuracy was examined using equation (11). In the same manner as in the above embodiment, the attenuation rate λ ^(m) obtained at a pressure of 1 atm and a water temperature in the range of 16 ° C. to 20 ° C., and the temperature of the water in the container 11 are interpolated in the same manner as above. The left-hand side of the equation (11) was calculated by substituting the calculated dynamic viscosity coefficient and the like into the left-hand side of the equation (11). By repeating such measurements and calculations 30 times, the average of the left side of Equation (11) was calculated. The average was 22.8. Calculating the right side of equation (11) using equation (6) gives 22.79. In addition, the standard deviation σ of the average value on the left side of Equation (11) was 0.984. Although details are omitted, the value obtained by dividing this standard deviation σ by the value on the right side of Equation (11) is the relative error of the dynamic viscosity coefficient, which is the average value, so 30 measurements are repeated and averaged. As a result, the kinematic viscosity coefficient was measured with a relative error of 4.3%. Therefore, by repeatedly measuring the kinematic viscosity using the kinematic viscosity measuring method and measuring device 1 according to the present embodiment and obtaining the average value, the kinematic viscosity can be determined with high accuracy even for fluids with low viscosity. It was confirmed that the measurement is possible.

As described above, according to the kinematic viscosity measuring method and the measuring device 1 according to the present embodiment, the kinematic viscosity can be measured by a totally new method different from the conventional one. For example, when the device is compact, L in equation (8) becomes small and the attenuation rate increases. Even a compact device can measure kinematic viscosity. The same is true when measuring the dynamic viscosity of a fluid with a large dynamic viscosity. On the other hand, when measuring the kinematic viscosity of a fluid with a small kinematic viscosity, the damping rate is small. can be done.

Moreover, even in cases where the viscosity depends on the shear rate, such as in non-Newtonian fluids, the velocity on which the kinematic viscosity depends and the spatial gradient of the velocity are uniform in the linearly stable steady state. By adding a disturbance to a certain state (eg, a state where the total flow velocity of the sample is zero), the kinematic viscosity can be measured. In addition, the temperature and pressure of the sample become uniform, and spatial distribution can be prevented. Therefore, in the sense that it is possible to measure the kinematic viscosity at the limit where the predetermined temperature, the predetermined pressure, and the speed are 0, highly accurate measurement of the kinematic viscosity can be realized. Such measurements for non-Newtonian fluids are simply not possible with conventional methods, which cannot measure kinematic viscosity under near-zero shear rates. Moreover, unlike the conventional method, there is also the advantage that there is no need to correct the measured values.

For example, the kinematic viscosity coefficient of a low-viscosity fluid can also be measured by the conventional method. However, for example, in the case of the falling body type, it is necessary to make the diameter of the tracer sphere extremely small and lengthen the tube length, and to measure the motion of the sphere falling at a relatively high speed with high accuracy. Further, for example, in the case of a rotary type, it is necessary to make the inter-disc distance extremely small. Therefore, the rotation of the discs must be kept parallel to each other with high accuracy, and the small torques to be measured must be measured with high accuracy. As described above, in order to measure the kinematic viscosity coefficient of a low-viscosity fluid by the conventional method, a problem arises in measurement accuracy. The same applies to the vibration type and the like. On the other hand, in the method and apparatus 1 for measuring the kinematic viscosity coefficient according to the present embodiment, as can be seen from the above experimental examples, the merit is that sufficiently high-precision measurement can be realized by measurement using a commercially available digital camera. There is In addition, even when measuring a large kinematic viscosity coefficient or when measuring a kinematic viscosity coefficient with a compact device, the accuracy can be improved by increasing the time resolution using a digital camera capable of high-speed photography. Measurement of high kinematic viscosity can be achieved.

In this embodiment, the attenuation rate related to the flow velocity of the sample is measured or calculated, but the relaxation time related to the flow velocity of the sample may be measured or calculated. Also, the relaxation time is the reciprocal of the decay rate. That is, relaxation time=1/decay rate. Therefore, even when the relaxation time is measured or calculated, it can be considered that the damping rate is actually measured or calculated. Coefficient measurement can also be considered to be included in the measurement by the kinematic viscosity coefficient measurement method and measurement device 1 according to the present embodiment.

Further, in the present embodiment, the case where the container 11 is cylindrical has been mainly described, but as described above, it may not be cylindrical. Even when a container 11 having a shape other than a cylindrical shape is used, the damping factor of a predetermined mode can be measured in the same manner as described above by setting boundary conditions and constraint conditions that enable determination of eigenfunctions and eigenvalues. or theoretically calculate the damping factor of the predetermined mode, and measure the kinematic viscosity coefficient.

Further, in the present embodiment, the case where the coefficient related to viscosity is the coefficient of kinematic viscosity has been mainly described, but the coefficient related to viscosity may be a viscosity coefficient (absolute viscosity). The dynamic viscosity coefficient ν and the viscosity coefficient μ have the following relationship.
ν=μ/ρ

where ρ is the density of the fluid. The above relationship holds regardless of whether the fluid is Newtonian or non-Newtonian. Therefore, the above description of the kinematic viscosity coefficient is also applicable to the viscosity coefficient. It will be possible. Specifically, the calculating means 15 can calculate the viscosity coefficient μ by using the following equation (14) instead of the equation (10).

In this case, the output means 16 may output the viscosity coefficient μ calculated by the calculation means 15 . In this way, the viscosity-related coefficient measurement method and measurement device can also measure the viscosity coefficient of the sample 5, which is a fluid.

Also, in the present embodiment, the case where the linearly stable steady state is the stationary state has been mainly described, but this need not be the case. For example, a laminar Couette flow is a flow field with a constant velocity gradient and a linearly stable steady state. Therefore, by adding a disturbance to the laminar Couette flow and observing the change in flow velocity as it returns to the original laminar Couette flow, we can also measure the viscosity coefficient of a non-Newtonian fluid corresponding to a constant shear rate. . Note that in this case, the eigenequation system is different from that represented by the equations (3) and (4). In this way, it is also possible to accurately measure the viscosity coefficients corresponding to non-zero shear rates. The disturbance may be added by stirring the sample.

Also, in the present embodiment, the case of performing eigenvalue analysis has been mainly described, but this need not be the case. For example, as shown in the example of equation (11), if the container shapes are similar and the boundary conditions are the same, the nondimensionalized attenuation factor of a given mode does not depend on the type of sample. Therefore, the damping factor λ ₁ ^(m) of a predetermined mode is measured for the first sample whose viscosity-related coefficient is known in advance, and for the second sample whose viscosity-related coefficient is to be obtained, By measuring the damping rate λ ₂ ^(m) of the given mode using the same experimental set-up, the coefficient related to viscosity can also be calculated using the following equation (15). Here, it is assumed that the coefficient related to viscosity is the kinematic viscosity coefficient, and the kinematic viscosity coefficients of the first and second samples are ν ₁ and ν ₂ , respectively.

Therefore, the calculating means 15 calculates the coefficient (for example, kinematic viscosity coefficient ν ₂ ) related to the viscosity of the sample (second sample) to be measured by using the equation (15) to calculate the measured damping rate (λ ₂ ^(m) ).

Also, in the present embodiment, the case where the container 11 has a shape of a body of revolution has been mainly described, but this need not be the case. The container 11 may have a shape other than the shape of a body of revolution, such as a rectangular parallelepiped shape. The viscosity coefficient can be measured even for the container 11 having a shape other than the rotating body shape. Specifically, a magnetic fluid sample to be measured for the viscosity coefficient is placed in a closed rectangular parallelepiped container 11, and an initial disturbance is applied to the sample by applying a time-varying magnetic field from the outside of the container 11, A change in the flow velocity at each point after the initial disturbance by the magnetic field is measured, and the decay rate of the flow velocity may be obtained from the measurement result. Then, in Equation (15), the cuboid container 11 is used for the attenuation factor λ ₂ ^(m) measured for the sample to be measured and for the sample (for example, water) whose viscosity coefficient is known in advance. By substituting the damping rate λ ₁ ^(m) and the viscosity coefficient (for example, the kinematic viscosity coefficient ν ₁ ) measured by , the viscosity coefficient of the sample to be measured may be calculated.

Further, in the above embodiments, each process or function may be implemented by centralized processing by a single device or single system, or may be implemented by distributed processing by multiple devices or multiple systems. It may be realized by

Further, in the above-described embodiment, when the information is passed between the components, for example, when the two components that exchange the information are physically different, one of the components output of information and reception of information by the other component, or one component if the two components that pass the information are physically the same from the phase of processing corresponding to the other component to the phase of processing corresponding to the other component.

Further, in the above embodiments, information related to processing executed by each component, for example, information received, acquired, selected, or generated by each component, and information that each component can process. Information such as thresholds and formulas to be used may be stored temporarily or for a long period of time in a recording medium (not shown) even if they are not specified in the above description. Further, each component or an accumulation section (not shown) may accumulate information in the recording medium (not shown). Further, each component or a reading unit (not shown) may read information from the recording medium (not shown).

Further, in the above embodiment, if the information used in each component etc., for example, information such as threshold values and various setting values used in processing by each component may be changed by the user, the above description may be used. Even if not explicitly stated, the user may or may not be able to change such information as appropriate. If the information can be changed by the user, the change is realized by, for example, a reception unit (not shown) that receives a change instruction from the user and a change unit (not shown) that changes the information according to the change instruction. may The reception of the change instruction by the reception unit (not shown) may be, for example, reception from an input device, reception of information transmitted via a communication line, or reception of information read from a predetermined recording medium. .

Further, in the above embodiments, each component may be configured by dedicated hardware, or components that can be realized by software may be realized by executing a program. For example, each component can be realized by reading and executing a software program recorded in a recording medium such as a hard disk or a semiconductor memory by a program execution unit such as a CPU. During the execution, the program execution unit may execute the program while accessing the storage unit or recording medium.

Moreover, it goes without saying that the present invention is not limited to the above-described embodiments, and that various modifications are possible and are also included within the scope of the present invention.

As described above, according to the method and apparatus for measuring the coefficient related to viscosity according to the present invention, the effect that the coefficient related to viscosity can be measured by a method completely different from the conventional method is obtained, and it is useful as a method and device for measuring the coefficient related to viscosity. be.

REFERENCE SIGNS LIST 1 kinematic viscosity coefficient measuring device 5 sample 11 container 12 disturbance imparting means 13 measuring means 13a imaging means 13b computing means 14 storage means 15 calculating means 16 output means 17 control means

Claims (7)

A method for measuring a coefficient of viscosity of a fluid sample, comprising:
applying a disturbance to the sample in a container;
measuring the decay rate of a given mode with respect to the flow velocity of the sample after applying the disturbance;
and calculating a viscosity coefficient of the sample based on the measured attenuation factor. 2. The method of measuring a coefficient relating to viscosity according to claim 1, wherein said predetermined mode is a mode with the slowest attenuation. The container has a cylindrical shape,
3. The method of measuring a coefficient relating to viscosity according to claim 1, wherein in the step of imparting turbulence to said sample, said sample is stirred so as to have an axisymmetric flow velocity. 4. The method of measuring a coefficient relating to viscosity according to claim 3, wherein the container is open at the top. 4. The method of measuring a coefficient relating to viscosity according to claim 3, wherein said container is a closed container filled with said sample. 6. The method of measuring a coefficient related to viscosity according to claim 1, wherein the coefficient related to viscosity is a coefficient of dynamic viscosity or a coefficient of viscosity. A device for measuring the coefficient of viscosity of a fluid sample,
a container in which the sample is placed;
a disturbance imparting means for imparting disturbance to the sample in the container;
measuring means for measuring an attenuation rate of a predetermined mode with respect to the flow velocity of the sample after being disturbed by the disturbance applying means;
calculation means for calculating a coefficient related to the viscosity of the sample based on the measured attenuation factor;
and an output means for outputting the coefficient related to viscosity calculated by the calculating means.

Images