RU2703935C1 - Method of investigating deposition of a spherical cloud of polydisperse solid particles in a viscous liquid - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention relates to the field of development of methods and devices for laboratory research of physical processes, in particular for investigation of laws of motion of a cloud of solid particles in a viscous liquid. Method for investigating deposition of a spherical cloud of polydispersed solid particles in a viscous liquid involves mixing particles by exposing ultrasonic vibrations to a spherical container immersed into a liquid, made in the form of two hemispherical shells embedded into each other with the possibility of opening it during rotation of one of the shells around the axis of symmetry, introduction of particles into a cell with a viscous liquid, made from a transparent material, and visualization of the process of settling particles, is characterized by the fact that a spherical container made of solid shells is pre-filled with water, polydispersed particles are mixed with water, wherein during mixing gradually displacing water from container with viscous liquid with coefficient of dynamic viscosity corresponding to viscosity of liquid in cuvette, wherein time of water displacement by viscous liquid and time of container opening is selected in accordance with relations τ₁≥(3÷5) minutes,

and initial concentration of particles in cloud is determined by formula

where τ₁ – time of water displacement from container with viscous liquid, c; τ₂ is container opening time, s; D_k is diameter of container, m; μ_l is coefficient of dynamic viscosity of liquid, Pa⋅c; ρ_p is density of particles material, kg/m³.

EFFECT: high accuracy of determining main characteristics and dynamics of deposition of a plurality of polydisperse particles.

1 cl, 3 dwg, 1 tbl

Description

The invention relates to the field of development of methods and devices for laboratory studies of physical and chemical processes, in particular for studying the patterns of motion of a cloud of solid particles in a viscous medium during deposition of gravity in a field.

The processes of gravitational deposition of a cloud of particles are of practical importance in environmental problems (cleaning water bodies from impurities), in the coal industry (hydropress suppression of dust in coal mines), in the power system (burning atomized fuels), in chemical technology (precipitation columns) and in a number of other branches of technology and technology [1].

The nature of the motion of the aggregate of solid particles during their deposition in a liquid or gaseous medium substantially depends on the shape of the cloud of particles and their initial concentration [2]. A theoretical analysis of the problem does not allow us to unambiguously determine the dynamics of the change in shape, drag coefficient, and, consequently, the deposition rate of a particle population [3]. To obtain reliable dependencies, as a rule, the results of experimental studies are used.

Known methods for studying the laws of gravitational deposition of a set of solid particles in a liquid, based on the introduction of particles into a liquid and their visualization during movement [4-6]. These methods differ in the mechanism of introducing into the liquid a set of particles.

A known mechanical method of introducing a set of particles based on the use of cassettes and two plates in which the same number of holes is drilled at equal distances [4]. The plates are attached to the cartridge in such a way that when one of the plates moves with the help of solenoids and the holes of both plates are aligned, the particles are ejected with an adjustable vertical distance between the particles.

Known methods for creating a spherical cloud of monodisperse particles based on preliminary wetting of the particles with a working fluid, placing them on the surface of a flat disk in the form of a spherical segment or in hemispherical cells made on the surface of the disk [7, 8]. When a disk is immersed in a liquid, a cloud of particles is formed in a shape close to spherical.

(глицерин).The closest in technical essence to the claimed invention is the method [9], according to which the particles are pre-introduced into a spherical container made in the form of two embedded hemispherical shells with perforated walls and particles are mixed with liquid in the container by exposure to ultrasonic vibrations. Then, by turning one of the shells, a container is opened for introducing a cloud of particles into the working fluid. This method provides the creation of a spherical cloud of monodisperse particles in a liquid with a dynamic viscosity coefficient of not more than

(glycerol).

(например, силиконовое масло), обеспечивающего равномерное распределение частиц в облаке, нулевую начальную скорость осаждения и заданную начальную концентрацию частиц в облаке.The technical result of the present invention is to develop a method for studying the process of gravitational deposition of a spherical cloud of polydisperse solid particles in a liquid with a dynamic viscosity coefficient

(for example, silicone oil), providing a uniform distribution of particles in the cloud, zero initial deposition rate and a given initial concentration of particles in the cloud.

The technical result of the invention is achieved by the fact that a method for studying the deposition of a spherical cloud of polydisperse solid particles in a viscous liquid is developed, which includes mixing the particles by ultrasonic vibrations in a spherical container immersed in liquid, made in the form of two hemispherical shells inserted into each other with the possibility of opening it during rotation one of the shells around the axis of symmetry, the introduction of particles into a cell with a viscous liquid made of a transparent material, and visualization tion particle deposition process. A spherical container made of continuous shells is pre-filled with water, polydisperse particles are mixed with water, and during mixing, water is gradually displaced from the container with a viscous liquid with a dynamic viscosity coefficient corresponding to the viscosity of the liquid in the cuvette. The time of water displacement by a viscous liquid and the opening time of the container are chosen in accordance with the ratios

τ ₁ ≥ (3 ÷ 5) minutes,

and the initial concentration of particles in the cloud is determined by the formula

where τ ₁ is the time of displacement of water from the container by a viscous liquid, s;

τ ₂ - container opening time, s;

D _k is the diameter of the container, m;

- коэффициент динамической вязкости жидкости, Па⋅с;

- dynamic fluid viscosity coefficient, Pa⋅s;

ρ _p is the density of the particle material, kg / m ³ ;

- плотность жидкости, кг/м³;

- fluid density, kg / m ³ ;

D _max - the diameter of the largest particles, m;

g is the acceleration of gravity, m / s ² ;

With _o - the initial volumetric concentration of particles;

N _i is the number of particles of the i-th fraction;

D _i is the particle diameter of the i-th fraction;

n is the number of particle fractions.

The resulting positive effect of the invention is due to the following factors.

1. Pre-filling a container made of waterproof (continuous) shells with water provides isolation of the container cavity from a viscous liquid in the cuvette and allows mixing of the polydisperse particles with water.

позволяет интенсифицировать процесс перемешивания под воздействием ультразвуковых колебаний.2. Mixing particles with water ensures uniform distribution of polydisperse particles in the cavity of a spherical container, since the low coefficient of dynamic viscosity of water

allows you to intensify the mixing process under the influence of ultrasonic vibrations.

3. The gradual displacement of water from the container by a viscous liquid ensures the uniform distribution of particles in the cavity of the container until the water is completely replaced by a liquid with a dynamic viscosity coefficient corresponding to the viscosity of the liquid in the cuvette. With increasing viscosity of the liquid in the container, the mobility of the particles decreases, which helps to maintain a uniform distribution of particles.

4. The time of displacement of water from a container by a viscous liquid t≥ (3 ÷ 5) minutes is determined experimentally from the condition that the pressure of the viscous liquid supplied to the container minimally affects the structure of the particle cloud in the container.

5. The opening time of the container is selected from the condition of minimum deformation of the cloud during the opening period. The distance traveled by the particle during deposition over time τ ₂ is

where u is the particle deposition rate.

The condition for minimum cloud deformation is formulated as the inequality

- смещение границы облака за счет осаждения частиц.Where

- displacement of the cloud boundary due to the deposition of particles.

не превышает 2.5% от его диаметра.Condition (4) means that the displacement of the cloud boundary

does not exceed 2.5% of its diameter.

The stationary deposition rate of a single particle in a viscous fluid is [10]

where D _max is the diameter of the largest particle in the cloud.

Substituting (5) in (3), (4), we obtain condition (1) for determining the opening time of the container:

6. The initial volumetric concentration of particles in the container is determined by the formula

where V _p is the total volume of particles;

V _to - the volume of the container.

The total volume of polydisperse particles is

The volume of the container is

Substituting (7), (8) in (6), we obtain the formula (2):

Implementation example

The essence of the invention is illustrated by the scheme (Fig. 1). A sample of solid polydisperse spherical particles 3 was introduced into a container consisting of a fixed 1 and a moving 2 hemispherical shells. A movable shell 2 is rigidly connected to the axis 4, which can rotate in bearings 5. By rotating the shell 2, the container was closed (Fig. 1a) and placed in a cuvette with a liquid. After mixing the particles with the liquid by rotating the movable shell 2 through 180 degrees, the container was opened (Fig. 1b). In this case, a spherical cloud of particles began to precipitate in a cell with a liquid.

A diagram of an apparatus for studying the process of particle cloud deposition is shown in FIG. 2. A container with particles was placed in a cuvette 6 with a viscous liquid 7. Through the pipe 8 with valve 9, water was introduced into the container from the tank 10. After the container was completely filled, excess water was displaced through the drain pipe 11.

The particles were mixed with water in the container by the action of ultrasonic vibrations from a generator 12 of type UZGM-10-22MS. In the process of mixing, water was gradually displaced by a viscous liquid supplied to the container from the tank 13 through the valve 14 and nozzle 15. Excess viscous liquid was displaced from the container through the drain pipe 11. After the water was completely replaced with viscous liquid, the container was opened by turning the movable shell 2.

The process of deposition of a cloud of particles was visualized using shooting through the transparent walls of the cell 6 with two high-speed digital cameras 16 of the Citius C 100 type in two angles with a shooting rate of (50 ÷ 100) frames per second. Video sequences were processed using a computer, which received information from video cameras. According to the results of processing, the regularity of the evolution of the cloud shape, the change in its volume, the concentration of particles in the cloud, the velocity of the center of mass of the cloud and the drag coefficient of the particle cloud were determined.

В экспериментах использовали стальные шарики (ρ_р=7748 кг/м³) в диапазоне размеров D_p=(1÷3) мм=(1÷3)⋅10^-3 м. (Диаметр наиболее крупного шарика D_max=3⋅10^-3 м).The effectiveness of the proposed method is confirmed by conducting experiments on the deposition of polydisperse solid spherical particles in a viscous liquid. As the liquid used silicone oil PMS-10000

In the experiments, steel balls were used (ρ _p = 7748 kg / m ³ ) in the size range D _p = (1 ÷ 3) mm = (1 ÷ 3) ⋅10 ^-3 m. (The diameter of the largest ball D _max = 3⋅10 ^-3 m).

As an example, consider a container with a diameter of D _k = 30 mm = 30⋅10 ^-3 m. Let us calculate the opening time of the container according to formula (1):

To calculate the initial volume concentration of a cloud of particles, we consider a polydisperse system of 100 balls (table 1).

In accordance with formula (1), the initial volume concentration of particles in the cloud is

By varying the diameter of the container, the number of particle fractions n, the diameter D _i and the number N _{i of} particles of each of the fractions, one can vary the initial concentration of particles in a wide range. In particular, in FIG. Figure 3 shows the video frames of the deposition of a bidispersed system of particles (balls D ₁ = 1 mm; N ₁ = 35; D ₂ = 3 mm; N ₂ = 35) from a container with a diameter of D _k = 15 mm at an initial volume of particle concentration C ₀ = 0.28.

При этом обеспечиваются равномерное распределение частиц в облаке, нулевая начальная скорость осаждения и заданная начальная концентрация частиц в облаке.Thus, from the above example it follows that the proposed method ensures the achievement of the technical result of the invention — it allows to study the process of gravitational deposition of a spherical cloud of polydisperse solid particles in a liquid with a dynamic viscosity coefficient

This ensures a uniform distribution of particles in the cloud, zero initial deposition rate and a given initial concentration of particles in the cloud.

LITERATURE

1. Romankov P.G., Kurochkina M.I. Hydromechanical processes of chemical technology. - L .: Chemistry, 1982. - 288 p.

2. Sow S. Hydrodynamics of multiphase systems. - M .: Mir, 1971. - 536 p.

3. Brownstein B.I., Fishbein G.A. Hydrodynamics, mass and heat transfer in dispersed media. - L .: Chemistry, - 1977 .-- 279 p.

4. Horguani V.G. On the nature and rate of fall of a system of particles of the same size // Izvestiya AN SSSR. Physics of the atmosphere and the ocean. - 1966. - T. 2, No. 4. - S. 394-401.

5. Metzger B., Nicolas M., Guazzelli E. Falling clouds of particles in viscous fluids // Journal of Fluid Mechanics. - 2007. - Vol. 580. - P. 283-301.

6. Daniel W.B., Ecke R.E., Subramanian G., Koch D.L. Clusters of sedimenting high-Reynolds-number particles // Journal of Fluid Mechanics. - 2009. - Vol. 625. - P. 371-385.

7. RF patent No. 2610607, IPC G01N 15/04. A method for studying the process of gravitational deposition of a set of solid particles in a liquid / V.A. Arkhipov, A.S. Usanina, G.R. Schrager. - Publ. 02/14/2017, Bull. No. 5.

8. RF patent No. 2617167, IPC B01L 1/00. Installation for the study of the deposition of aggregate solid particles in a liquid / V.A. Arkhipov, A.S. Usanina, N.N. Zolotoryov. - Publ. 04/21/2017, bull. No. 12.

9. RF patent No. 2620761, IPC G01N 21/85 Method for studying the deposition of a spherical cloud of solid particles in a liquid / V.A. Arkhipov, A.S. Usanina, S.N. Polenchuk. - Publ. 05/29/2017, Bull. No. 16.

10. Arkhipov V.A., Usanina A.S. The motion of particles of a dispersed phase in a carrier medium. - Tomsk: Publishing House of Tomsk State University, 2014. - 252 p.

Claims (17)

A method for studying the deposition of a spherical cloud of polydisperse solid particles in a viscous liquid, including mixing particles by means of ultrasonic vibrations in a spherical container immersed in a liquid, made in the form of two hemispherical shells inserted into each other with the possibility of opening it when one of the shells rotates around the axis of symmetry, introduction particles in a cell with a viscous liquid made of a transparent material, and visualization of the process of deposition of particles, characterized in that the spherical to a continuous container made of continuous shells is pre-filled with water, polydisperse particles are mixed with water, and during mixing, water is gradually displaced from the container by a viscous liquid with a dynamic viscosity coefficient corresponding to the viscosity of the liquid in the cuvette, while the time of displacement of water by a viscous liquid and the opening time of the container selected in accordance with the ratios τ ₁ ≥ (3 ÷ 5) minutes,

and the initial concentration of particles in the cloud is determined by the formula

where τ ₁ - the time of displacement of water from a container with a viscous liquid, s; τ ₂ - container opening time, s; D _k is the diameter of the container, m; μ _l - dynamic fluid viscosity coefficient, Pa⋅s; ρ _p - the density of the material of the particles, kg / m ³ ; ρ _l is the density of the liquid, kg / m ³ ; D _max - the diameter of the largest particles, m; g is the acceleration of gravity, m / s ² ; With ₀ - the initial volumetric concentration of particles; N _i is the number of particles of the i-th fraction; D _i is the particle diameter of the i-th fraction; n is the number of particle fractions.

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