SU1716388A1 - Method of measuring viscosity of non-newton liquids - Google Patents

Abstract

The invention relates to a measurement technique, in particular to methods for measuring viscosity. The aim of the invention is to expand the functional capabilities of the method while at the same time increasing labor productivity by determining the dependence of viscosity on shear rate. The goal is achieved by the fact that the method, which involves pumping fluid through the capillary and determining the stress and shear rate on the capillary wall, additionally determines the velocity profile in the capillary, the stress and shear rate over the entire flow section, and and shear rates are determined from the expression g Testify (x), where the viscosity of the fluid is Pas-s. -Ey) is the shear stress, Pa; y (x) is the shear rate at x, respectively.

Description

The invention relates to a measurement technique, in particular to methods for measuring viscosity.

A known method for measuring the viscosity of a fluid, including determining the expiration of a fixed volume of fluid through a capillary of a known cross section ..., :: The disadvantage of this method is the inability to measure the viscosity of a fluid exhibiting non-Newtonian properties.

Closest to the invention is a method comprising pumping a fluid through a channel of a known size, determining the voltage and shear rate on the channel wall.

The disadvantage of this method is the impossibility of determining for a given

flow rates depending on viscosity on shear rate. To obtain such a functional relationship, a series of measurements is necessary, which requires a lot of testing time, especially when working in the field of low shear rates.

In addition, working in a wide range of shear rates requires the use of a set of instruments, since it is not possible to create a capillary viscometer with appropriate functionality. ; The purpose of the invention is to expand the functionality of the method by determining the dependence of viscosity on the shear rate at a given flow rate.

The goal is achieved by the fact that in the method involving pumping a fluid

ABOUT

s

Through a capillary tube of known size and determination of the stress and shear rate on the channel wall, the velocity profile in the channel is additionally determined, and the dependence of viscosity on the shear rate is determined from the expression

 M-Nim, (1)

where ij is the viscosity of the fluid. Pass; r (x) is the shear stress, Pa;

y (x) is the shear rate, (c 1) at x, respectively.

The essence of the invention is as follows.

Consider the flow of a fluid in a circular channel (Fig. 1). The pressure drop over a section of length L is an AP. Then for a steady-state simple shear flow, the force acting on a cylinder of a fluid of radius r will be

Fi-Drlg2. (2)

C. On the other hand, the expression for the friction force acting on this cylinder is

R2 2yyyy tL, (3)

where t is the tangential stress. .

For a simple shear flow in the steady state, the equality

FI F2, i.e. D P g2 2zg rtL. (four)

From equation (4) it follows

, A p g, w

t. . ™

The velocity distribution over the cross section for laminar movement in a pipe is described by the expression

V VMaKc 1r () (b)

Then the velocity gradient is

dV ,, 2 g.: -J7. “.- -R-; (7)

Taking into account that in a simple shear flow the maximum velocity is equal to twice the average velocity, the velocity gradient on the wall is equal.

 .4 (3 37 # #

where Q is the fluid flow.

From Newton's law for a fluid, the relationship between shear rate and stress is known.

d. (9)

From equations (9) and (5) we obtain the expression

for viscosity

„T DRg, 1P d V / d r dV / dr2L uu

where DR is the pressure drop in the capillary

plot length L;

(eight)

dV / dr is the velocity gradient at the measurement point;

g - the current coordinate along the channel radius.

Using expression (10) and experimentally measured values, g; DR; L; dV / dr, you can determine the viscosity of the fluid. In addition, for Newtonian liquids, to determine the viscosity r, it is sufficient to measure the velocity gradient dV / dr at one point in the stream.

For non-Newtonian liquids this is not enough, since the viscosity of such liquids depends on shear rates (gradient

speed).

In a simple, shear flow, knowing the velocity profile, it is possible to determine the velocity gradient at each point of the flow cross section, and hence the dependence of viscosity, determined by expressions (1) and (10), on the shear rate in a wide range of variation of this parameter. . To do this, you need the exact value of the speed profile. The use of the method of laser Doppler anemometry, which has a high accuracy and rapid determination, makes it possible to solve this problem.

The considered method, like all known ones, allows determining the viscosity of liquids only with a simple shear flow. With more complex flow, i.e. when the viscosity depends on the components of the stress tensor, known methods cannot be applied. The proposed method allows to measure all components of the velocity vector and determine the viscosity from the following more general dependence pVrVj

avr

b | , and Jx + axi

(eleven)

where / density of the liquid;

Vi, Vj - components of the velocity vector, m / s;

avi avi

ltg d x | the corresponding components of the shear rate

FIG. Figure 1 shows a round section channel used to remove the ratio (10); in fig. 2 - installation for

carrying out the method; in fig. 3- velocity profile for a solution of a biopolymer; in fig. 4 shows the dependence of viscosity on shear rate for this polymer.

The method is carried out as follows:

at once.

Through a cylindrical channel of known cross-section, a fluid is flowing. In this case, the conditions for the implementation of a simple shear flow must be met.

In the area between points 1 and 2, with a distance between them L, the pressure drop of the differential pressure gauge is measured.

Using a laser Doppler anemometer (LDA), the velocity profile is measured. Thereafter, the derivative of the velocity over the radius (velocity gradient) is found at each point of the cross section.

If we know the shear rate (velocity gradient) at each point of the cross section g and the pressure drop DS, we determine the viscosity from the expression

,, f (y (r),

those. We determine the dependence of viscosity on the shear rate.

For the implementation of the method, an installation was created consisting of a hydrodynamic part in which a simple shear flow is implemented with the possibility of measuring the pressure drop over a certain part of the measuring part intended for determining the velocity profile (Fig. 2).

For contactless measurement of the velocity profile, a laser Doppler anemometer (LDA) was created with

inverse differential circuit (Fig. 2). A laser with a wavelength of 0.63 µm and a power of 15 mW (type LG-52/1) was used as a source of coherent radiation.

The laser beam 1 passes through the lens 2 and is focused in the examined stream 3. Then it passes through the lens 4, the front focus of which coincides with the back focus of the lens 2. After passing the lens A, the laser beam falls on an angular reflector 5 by a parallel beam. the beam goes in the opposite direction. Thus, an additional resonator is formed, consisting of an output mirror and an angle reflector 5. The use of an angle reflector significantly reduces the sensitivity of the LDA to vibrations.

The light scattered from the measurement area passes through the lens 2, the spatial frequency filter 6, mirror 7, 8, hits the photodetector 9 (PMT-79). The spatial frequency filter 6 is a screen with three holes mi (for measuring one component of the velocity vector). One hole is located on the optical axis and a probe laser beam passes through it. The other two holes are at the same distance from the center of the first hole, mirrors 7 and 8 serve for the spatial alignment of parallel beams of scattered light.

On the path of one of the scattered light beams is a frequency shift device.

- frequency modulator 10, which serves for the initial frequency shift, which eliminates uncertainty in the direction of the measured speed.

Simultaneously initial frequency

The 0 shift allows the processed signal to be led away from the low-frequency noise region, which makes it possible to measure small velocities of the stream under study. For the selection of the Doppler signal, a spectrum analyzer (type SK-4-58) was used.

A glass capillary p 11 with an internal diameter of 7 mm and a length of L 450 mm was used as the hydrodynamic channel. The channel was placed on a special

0 table with the required number of degrees of freedom. Nozzles 13,14 were made in the capillary 11 to measure the pressure drop. The rate of fluid flow and the size of the initial portion was chosen with

5 creating a simple shear flow (laminar flow). The flow rate of the fluid was kept constant by means of a vessel from which the fluid flowed into the capillary. Moving the capillary along the beam determines the velocity value at each point of the capillary section, and thereby determines the velocity profile. These data for water and solution, of Acinotobacter exopolysaccharide with a concentration of 0.05% before 5, are shown in FIG. 3. For each point of the channel cross section, dV / dr and are determined. substituting this value into expression (10), we find the dependence of viscosity on the shear rate, which coincides quite well with the known data (Fig. 4).

The polysaccharide solution exhibits non-Newtonian properties in a wide range of shear rates. Above, a method has been described for measuring the dependence of the viscosity of a non-Nuto’s liquid on shear rate in a simple shear flow at a constant (same) flow rate.

In a number of cases, in order to increase the accuracy of measurements, it is advisable to carry out measurements at one point of the cross section of the flow, but the flow rate of the liquid (maximum speed) and thus the speed gradient change. In this case, it is necessary to constantly monitor the preservation of a simple 5th shear flow.

Thus, the proposed method makes it possible to expand the possibility of a known method for measuring the viscosity of a liquid and to accelerate research by measuring in one mode the entire dependence of viscosity on the shear rate of more than one point. In addition, L YES conducts velocity measurements with a sufficiently high accuracy with high spatial resolution. This makes it possible to create simple and highly accurate viscometers based on the proposed method.

Claims (1)

The invention The method of measuring the viscosity of non-neonotonic liquids, including pumping a liquid through a capillary, determining the shear stress and shear rate at the wall 0 Channel, characterized in that, in order to expand its functionality by determining the dependence of viscosity on shear rate, the velocity profile in the channel is additionally determined, and the dependence of viscosity on shear rate is determined from the expression H () where g) is the viscosity of the fluid, g (x) is the shear stress. Pa; (x) - shear rate, s 1; x is the current coordinate. / 3 FIG. 2 : fa iO 50