RU2080584C1 - Method of liquid viscosity measurement - Google Patents

Abstract

FIELD: liquid viscosity measurement. SUBSTANCE: the method consists in acceleration of a ball probe in liquid under test to the predetermined speed, its free emersion in liquid under its own momentum, measurement at definite time moments of the value of coordinate, or speed, or acceleration, calculation of decelerated motion exponent time constant T and determination of viscosity by calculation. EFFECT: facilitated procedure. 1 dwg

Description

 The invention relates to methods for measuring the physicochemical characteristics of liquid media, in particular their viscosity.

и определяют вязкость η по соотношению

Однако недостатком известного способа является снижение точности измерения при больших скоростях движения зонда, при которых закон Стокса перестает выполняться.Closest to the proposed is a method for measuring the viscosity of a liquid, including immersing a ball probe of radius R and density ρ in a liquid with an initial speed V ₀ , measuring the speed of uniform movement of the probe V _p and determining the viscosity. The coordinate L, or velocity V, or acceleration dv / dt is measured in the area of accelerated probe motion at time t, the accelerated motion time constant T is determined as a solution to the corresponding equation from the following three:
LV _p • t T • (V _p V ₀ ) • (1 - e ^{-t / T} );
VV _p (V _p V ₀ ) • e ^{-t / T} ;

and determine the viscosity η by the ratio

However, the disadvantage of this method is the decrease in measurement accuracy at high probe speeds, at which the Stokes law ceases to be satisfied.

 EFFECT: increased accuracy of measurement.

 The essence of the method is illustrated in the drawing, which shows a structural diagram of a device that implements it.

 The device comprises a ball probe 1, an accelerator 2, a motion parameter meter 3, and a computing unit 4. The test fluid is indicated by index 5 in the drawing.

 The proposed method can be implemented as follows.

Example 1. At the beginning of the measurement, the computing unit 2, supplying voltage to its own outputs, turns on the accelerator 2 and the meter 3. When the accelerator 2 is activated, the ball probe 1 accelerates to a vertical speed not exceeding a certain maximum permissible value. Since the probe 1 moves in the liquid under investigation and vertically upward, its speed continuously decreases until it stops at some point in time t _m (subsequent immersion of the probe 1 in the liquid is not used for measurement). The meter 3, which produces an analog voltage proportional to the height of the probe 1, transmits this voltage to the input of the computing unit 4. At the instants of time t _i caused by the program, an analog-to-digital conversion of the voltage applied to the input of the computing unit 4 is performed, during which a discrete code is formed that determines the value of the height of the probe 1 when measuring. The next pair of values of t _i and h _{i is} recorded in the memory of computing unit 4. After the experiment, i.e. after the probe 1 reaches the upper point of the trajectory, the computing unit 4 turns off the accelerator 2 and the meter 3. Then it performs processing of the collected information, i.e. calculation of the time constant of the exponent T by solving a system of equations obtained by substituting the next pairs of values in a ratio that determines the dependence of the ascent height of the probe 1h on time t and other motion parameters. The resulting system of equations is solved, in particular, by one of the methods for solving systems of nonlinear equations. After calculating the exponential time constant T, the computing unit 4 calculates the measured viscosity value and prints the result.

Example 2. Basically, the experiment of the previous example is repeated, but in the process of moving the ball probe 1 in the liquid, meter 3 generates an analog voltage at its own output, proportional to the current value of the vertical component of the speed of movement. This voltage is transmitted to the information input of the computing unit 4. At the specified time t _i, this unit measures the current value of the speed V _i . The pairs of values of t _i and V _{i are} recorded in the memory of the computing unit 4. The calculation of the measured value of the time constant of the exponent T is performed by solving a system of nonlinear equations obtained by sequentially substituting the pairs of values into a relation connecting the current speed V with the immersion time t.

Example 3. The experiment of Example 1 is basically repeated. However, during the movement of the probe 1, the meter 3 generates an analog voltage proportional to the current value of the acceleration of the probe 1. This voltage is transmitted to the information input of the computing unit 4. At the specified time t _i , the current value of the acceleration is measured (dV / dt) _i . The pairs of values of t _i and (dV / dt) _{i are} recorded in the memory of computing unit 4. The system of nonlinear equations, the solution of which allows us to estimate the measured value of the time constant of the exponent T, is obtained by sequentially substituting the pairs of values of t _i and (dV / dt) _i in the relation linking the current acceleration (dV / dt) with the dive time t.

 The basis of the method is the following regularity.

As a result of acceleration of the probe 1, the vertical component of its velocity at t 0 has a value of V ₀ . By inertia, the probe 1 moves upward with a constantly decreasing speed until the time t _m , when its speed turns out to be zero: V _m 0.

In accordance with Newton’s second law, the acceleration of the probe 1 in the process of motion is determined by the equality
m • a F _B P _s F _s , (1)
where m is the mass of the probe 1;
a its acceleration;
F _In the buoyant force acting on the probe 1;
P _{s the} weight of the probe 1;
F _{with the} force of resistance to the movement of the probe 1 from the side of a viscous liquid.

где R радиус шарового зонда 1;
ρ плотность его материала;
V скорость зонда 1;
dv/dt его ускорение;
g ускорение свободного падения;
r_ж плотность исследуемой жидкости;
η вязкость исследуемой жидкости.Taking into account the parameters of the probe and the properties of the investigated fluid, relation (1) can be converted to

where R is the radius of the ball probe 1;
ρ is the density of its material;
V probe speed 1;
dv / dt its acceleration;
g acceleration of gravity;
r _{W the} density of the test fluid;
η viscosity of the test fluid.

где V_р равномерная скорость погружения зонда 1 в жидкость под действием собственного веса.In accordance with Stokes law, the following relation

where V _{p the} uniform rate of immersion of the probe 1 in a liquid under the action of its own weight.

Разделяя переменные дифференциального уравнения (4) и вводя постоянную для конкретной жидкости величину V_р под знак дифференциала (что допустимо), получим следующее дифференциальное уравнение

Оно имеет аналитическое решение следующего вида

где

постоянная времени экспоненты.Expression (2) taking into account expression (3) can be converted to the form

Separating the variables of differential equation (4) and introducing a constant V _p for a specific fluid under the differential sign (which is permissible), we obtain the following differential equation

It has an analytical solution of the following form

Where

exponent time constant.

Из соотношений (8) и (9) можно получить следующее выражение для расчета постоянной интегрирования C

Подстановкой соотношения (10) в соотношение (9) получаем выражение для расчета V_p

Подстановкой соотношений (10) и (11) в соотношение (7) получаем следующую зависимость скорости всплытия зонда 1 от определяющих ее параметров:

Именно уравнение (12) используется в примере 2 для формирования системы из трех уравнений с тремя неизвестными, решение которой позволяет оценить значение постоянной времени экспоненты T.The potentiation of the right and left sides of relation (6) leads to the following equality
V + V _p C • e ^{-t / T.} (7)
The value of the integration constant C is determined from the boundary conditions that must be satisfied by the solution of differential equation (7). Substitution of the values of t 0 and VV ₀ into this equation allows us to obtain the equation:
V ₀ + V _p C. (8)
Substitution in equation (7) the values of tt _m and V 0 leads to the relation

From relations (8) and (9), we can obtain the following expression for calculating the integration constant C

Substituting relation (10) into relation (9), we obtain the expression for calculating V _p

Substituting relations (10) and (11) into relation (7), we obtain the following dependence of the ascent rate of probe 1 on the parameters determining it:

It is equation (12) that is used in Example 2 to form a system of three equations with three unknowns, the solution of which allows us to estimate the value of the time constant of exponent T.

В примере 3 уравнение (13) используется для формирования системы из трех нелинейных уравнений с тремя неизвестными.Differentiation in time of the left and right parts of equation (12) we obtain the equation characterizing the change in time of the acceleration of the probe 1 during ascent:

In example 3, equation (13) is used to form a system of three nonlinear equations with three unknowns.

в котором значение постоянной интегрирования C находят на основании условия, что при t t_м имеем h h_м:

Из этого соотношения находим:

Следовательно, соотношение, на основе которого в примере 1 формируется система из четырех нелинейных уравнений с четырьмя неизвестными, имеет вид:

Из соотношения (6), которым определяется взаимосвязь постоянной времени T и измеряемой вязкости η, получаем формулу для расчета вязкости после того, как постоянная времени экспоненты T определена:

Поскольку наибольшая скорость движения зонда 1 в жидкости определяется значением начальной скорости V₀, величину этой скорости всегда можно задать такой, чтобы условия закона Стокса были удовлетворены.And finally, the integration of equation (12) allows us to obtain a formula for calculating the ascent height of probe 1:

in which the value of the integration constant C is found on the basis of the condition that at tt _m we have hh _m :

From this relation we find:

Therefore, the ratio, on the basis of which in example 1 a system of four nonlinear equations with four unknowns is formed, has the form:

From relation (6), which determines the relationship between the time constant T and the measured viscosity η, we obtain the formula for calculating the viscosity after the time constant of the exponent T is determined:

Since the highest velocity of the probe 1 in the liquid is determined by the value of the initial velocity V ₀ , the magnitude of this velocity can always be set so that the conditions of the Stokes law are satisfied.

Claims (1)

A method for measuring the viscosity of a liquid, including the movement of a ball probe with a radius R and density of its material ρ, measurement at the time t of the coordinate h, or velocity v, or acceleration dv / dt, calculation of the time constant T of the slow motion exponent and determination of viscosity by the ratio η = (R ² • ρ) / (4,5 • T), characterized in that the probe is accelerated to a predetermined speed of movement, provide its free ascent in liquid by inertia, measurement at time t of the coordinate h, or speed v, or accelerations dv / dt carry out at the ascent of the probe and determine the time constant T of the slow motion exponent as a solution to the corresponding equation of the following three:

where v _{0 the} value of the ascent rate of the probe at time t ₀ 0;
h _{m is the} highest ascent of the probe;
t _{m is the} time the probe reaches the ascent trajectory with a height of h _m