RU2795373C1 - Method for obtaining a compact cluster of monodispere drops of a given size - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: development of methods and devices for laboratory studies of physical processes and properties of a liquid, in particular, for studying the patterns of motion of a compact cluster of drops. The method includes a pulsed supply of liquid from a supply vessel through a set of capillaries of the same diameter, evenly spaced on the lower lid of the vessel. A solution of a surface-active substance (surfactant) is preliminarily prepared in a liquid with a given concentration. The supply vessel, made in the form of a closed container, is filled through a branch pipe located on the bottom cover of the vessel with a prepared solution with the possibility of expelling air from the vessel through capillaries and a branch pipe located on the top cover of the vessel. Form steadily hanging at the ends of the capillaries drops by slowly increasing the pressure of the solution in the vessel to the value of p ₁. Provide simultaneous detachment of drops from the capillaries with the formation of a compact cluster by creating a pressure pulse in the solution with amplitude p ₂. The concentration of surfactants in the liquid solution, the diameter of the droplets formed, the diameter of the capillaries, the distance between them and the pressure value p ₁, p ₂ are determined from mathematical formulas.

EFFECT: obtaining a stable and reproducible compact cluster of monodisperse droplets with the ability to control the droplet size.

1 cl, 4 dwg

Description

The invention relates to the development of methods and devices for laboratory studies of physical processes and properties of liquids, in particular, for studying the patterns of motion of a compact cluster of drops. The invention can be used for metered supply of specified volumes of liquid when conducting scientific research in the field of hydrodynamics and heat and mass transfer of liquid-drop aerosol systems in various fields of chemistry, biology, medical technology, etc.

The bulk of information on methods and devices for obtaining drops refers to single drops. Known medical dropper [1], containing a reservoir with a needle for injection into a vessel with a medicinal product, connected to an elastic tube having an injection needle at the end, and also containing a roller regulator for the flow rate of the medicinal product. The reservoir of the medical dropper is made integral with the side chamber, hermetically separated from it by an elastic elastic membrane with a rocker arm built into it. At the end of the rocker, a bowl with a drainage hole is fixed, designed to control the completion of the process of instillation of the medical preparation.

A known method of obtaining small single drops of liquid, based on the physical phenomenon, which consists in the formation of a single drop when the liquid breaks. The device for implementing this method [2] is made in the form of a horizontal tube and a rod moving reciprocating along its axis. Fluid is continuously fed into the tube. When the rod periodically comes into contact with the meniscus of the liquid and when it is separated from the meniscus, the rod throws out a drop of liquid. The fluid supply is controlled by a needle located in the tube and movable in the axial direction.

A known method of obtaining a flow of drops with a controlled dispersed composition [3], including spraying liquid in a gaseous medium with a centrifugal nozzle containing a swirling chamber, inlet tangential channels and an outlet nozzle. In the process of liquid spraying, the total areas of the inlet tangential channels are changed by discrete overlapping of a part of the channels. This method does not make it possible to obtain monodisperse droplets, since a polydisperse droplet system is formed in the nozzle spray jet.

A known method of generating sequentially moving monodisperse liquid drops using devices [4, 5] The principle of operation of the devices is to form several identical drops at the ends of capillaries located horizontally at different heights. The liquid is fed into the capillaries through tubes from a vessel under pressure created by the compressor. Separation of drops from the capillaries is carried out by means of a sharp movement of the box with needles when the electromagnet is turned on. Drops of liquid, breaking away from the needles, remain in place, after which they continue their movement under the action of gravitational forces in a strictly vertical direction from top to bottom, at a fixed distance from each other.

This method makes it possible to obtain several sequentially falling drops and does not provide a compact cluster of drops.

The closest in technical essence of the present invention is a method for obtaining a cluster of drops proposed in [6]. In this method, a group of monodisperse drops is obtained by repeated pulsed supply of liquid from a measuring container through a set of evenly spaced capillaries of the same diameter. The formation of a group of drops is carried out by applying voltage pulses from the generator to the electropneumatic valve into the cavity of the measuring tank, at which pressure pulses occur.

The disadvantage of this method is the lack of stability and reproducibility of obtaining a cluster of drops (non-simultaneous detachment of drops from the capillary cut, the formation of an incomplete cluster of drops). These effects are apparently associated with the formation of air bubbles in the liquid and an air gap in the capillaries.

The technical result of the present invention is the development of a stable and reproducible method for obtaining a compact cluster of monodisperse droplets, as well as the ability to control the droplet size.

The technical result is achieved by the fact that a method has been developed for obtaining a compact cluster of monodisperse drops of a given size, including a pulsed supply of liquid from a supply vessel through a set of capillaries of the same diameter, evenly spaced on the bottom cover of the vessel. A solution of a surfactant in a liquid with a given concentration is preliminarily prepared, the supply vessel, made in the form of a closed container, is filled through a pipe located on the bottom cover of the vessel with the prepared solution with the possibility of completely displacing air from the vessel through the capillaries and the pipe located on the top cover vessel. Drops stably hanging at the ends of the capillaries are formed by slowly increasing the pressure of the solution in the vessel to the value p ₁ and simultaneous detachment of the drops from the capillaries with the formation of a compact cluster is ensured by creating a pressure pulse with the amplitude p ₂ in the solution.

The concentration of the surfactant in the solution, the diameter of the droplets formed, the maximum diameter of the capillaries, the distance between them and the pressure value p ₁ , p ₂ are determined from the ratios

where C is the concentration of the surfactant in the solution, mol/m ³ ;

C _cr - critical concentration of micellization, mol/m ³ ;

D is the diameter of the droplets formed, m;

d external (for wetting liquids) or internal (for non-wetting liquids) capillary diameter, m;

σ(C) - coefficient of surface tension of the solution for the value of the concentration of surfactant C, N/m;

ƒ=0.6 - empirical coefficient;

ρ is the density of the liquid solution, kg/m ³ ;

g - free fall acceleration, m/s ² ;

d _max - maximum capillary diameter, m;

σ _max - the maximum value of the coefficient of surface tension of the solution (at C=0), N/m;

- расстояние между осями капилляров, м;

- distance between the axes of the capillaries, m;

D _max - the maximum diameter of the droplets formed (in the absence of a surfactant in solution, C=0), m;

p ₁ - the pressure required for the formation of stable drops, Pa;

S is the cross-sectional area of the capillary channel, m ² ;

p ₂ - the pressure required to separate the drops, Pa.

The essence of the invention is illustrated by the following figures.

Fig. 1 - Graphs of the dependence of the surface tension coefficient of distilled water solutions on the concentration of the surfactant in the solution: a - sodium dodecyl sulfate CH3(CH2)11OSO3Na, b - ammonium perfluoroligoethermonocarboxylate CF3CF2CF2O[CF(CF3)CF2O]2CF(CF3)COONH4.

Fig. 2 - Diagram of a laboratory setup for implementing the proposed method.

Fig. 3 - Photograph of the original cluster of monodisperse drops formed at the ends of the capillaries.

Fig. 4 - Photograph of a cluster of monodisperse droplets in the process of settling in a gravity field.

The achievement of the positive effect of the invention is provided by the following factors.

1. It is known that the introduction of even a small amount of a surfactant into a liquid significantly reduces its surface tension coefficient [7]. Preliminary preparation of a surfactant solution in a liquid with a given concentration provides a change in the surface tension coefficient of a surfactant solution in a liquid and, consequently, a change in the size of monodisperse droplets formed at the ends of capillaries.

2. Filling the supply vessel, made in the form of a closed container through a pipe located on the bottom cover of the vessel, with a prepared solution with the possibility of completely displacing air from the vessel through the capillaries and the pipe located on the top cover of the vessel, ensures the absence of air bubbles in the capillaries. This allows the formation of stable drops in all capillaries, providing a compact cluster of monodisperse drops. Air bubbles can interfere with the process of drop formation and the formation of a stable cluster of monodisperse droplets.

3. A slow increase in the pressure of the solution in the vessel to a value of p ₁ ensures the formation of identical stably hanging drops at the ends of the capillaries. Preliminary experiments have shown that with a rapid or pulsed change in pressure, the detachment of drops from capillaries does not occur simultaneously.

4. The creation of a pressure pulse with amplitude _p2 in the solution ensures the simultaneous detachment of preformed drops at the ends of the capillaries with the formation of a compact cluster of monodisperse drops.

5. In FIG. 1 shows graphs of the dependence of the surface tension coefficient of the solution on the mass concentration of some surfactants - sodium dodecyl sulfate (Fig. 1a ) and ammonium perfluoroligoethermonocarboxylate (Fig. 1b) - in distilled water σ(C) [8]. It follows from the given graphs that the value of σ decreases monotonically with an increase in the surfactant concentration up to a certain value of _Сcr (critical micelle concentration) [7, 8]. With a further increase in the concentration of surfactants (C>C _cr ) the surface tension coefficient of the solution does not change (σ(C)=const). Therefore, the surfactant concentration in the liquid solution must be chosen from condition (1):

6. To calculate the diameter of the formed monodisperse drops, we use the Tait law [9], according to which the critical condition for the detachment of a drop from a capillary is the equality of the forces of gravity and surface tension acting on the drop:

where: m is the mass of the drop, kg.

Substituting in (7) the mass of a spherical drop m=ρ(πD ³ /6), we obtain formula (2) for calculating the drop diameter:

6. To determine the capillary diameter, consider the condition of droplet deformation under the action of gravity. The criterion for the onset of deformation of an immobile drop due to the development of the Rayleigh-Taylor instability is the Bond number [10]:

The violation of the sphericity of a stationary drop occurs due to the Rayleigh-Taylor instability occurs under the condition [10]

Expressing from (8) the drop diameter, we obtain:

Taking into account (9), from (10) follows the formula for calculating the maximum possible diameter of a drop that retains a spherical shape:

Expressing from (1) the capillary diameter d, we obtain:

Let's calculate d _max for the maximum value of the surface tension coefficient σ _max (at С=0). Taking into account (11) and (12), we obtain formula (3) for calculating the maximum capillary diameter:

When calculating according to formula (3), the outer diameter of the capillary (for non-wetting liquids) or its inner diameter (for wetting liquids) is determined.

7. The minimum distance between the axes of the capillaries is determined from the relation (4):

where D _max is the maximum diameter of the droplets formed (in the absence of a surfactant in solution, C=0), m.

Выполнение соотношения (4) позволяет исключить слияние (коагуляцию) исходных капель, формируемых на концах капилляров.This ratio was obtained from the results of experiments with varying the distance between the capillaries

The fulfillment of relation (4) makes it possible to exclude the coalescence (coagulation) of the initial drops formed at the ends of the capillaries.

8. Pressure value ρ ι determined by formula (5)

obtained from the results of experiments with varying pressure p ₁ and corresponds to the condition that the pressure force F ₁ =p ₁ S acting on the drop does not exceed 10% of the drop weight

9. Pressure value p ₂ determined by formula (5)

obtained from the results of experiments with varying pressure amplitude р ₂ and corresponds to the condition of stable detachment of the entire cluster of drops from the capillaries.

Implementation example

The essence of the invention is illustrated by a diagram of a laboratory setup that implements a method for obtaining a compact cluster of monodisperse drops of a given size. The diagram of the laboratory setup is shown in Fig. 2. The installation consists of a supply vessel 1 fixed with the help of mounting brackets 11 on a rigidly fixed vertical support 10. The vessel 1 is filled with a solution of a surfactant in a liquid with a given concentration. On the bottom cover of the supply vessel there is a branch pipe 13 with a shut-off valve 14, on the upper cover of the vessel there is a branch pipe 8 with a shut-off valve 16.

В качестве капилляров использовались инъекционные иглы марки 30G фирмы Vogt Medical с внутренним диаметром d_вн=0.16 мм, наружным диаметром d_нр=0.31 мм и длиной

On the bottom cover of the supply vessel 1, 60 coaxial capillaries 2 are vertically placed, the axes of which are spaced from each other by a distance

As capillaries, injection needles of the 30G brand from Vogt Medical with an inner diameter d _int = 0.16 mm, an outer diameter d _nr = 0.31 mm and a length

A system for slowly increasing the pressure of the solution in the vessel to a value of p ₁ and to create a pressure pulse with an amplitude of p ₂ is fixed on a tripod 10 using brackets 11. The system for creating a given pressure includes a syringe 5, the piston of which is connected to a micrometer screw 6. The micrometer screw 6 is driven by a micromotor-reducer 7, the speed of which is controlled by the electric pulse duration generator 12. The internal cavity of the syringe 5 is connected through a flexible hose 3 and a shut-off valve 4 with supply vessel 1. The pressure in the supply vessel is controlled by a manometer 15.

The method for obtaining a compact cluster of monodisperse drops of a given size is implemented as follows. For the selected working fluid and surfactant composition, a solution with a given concentration is preliminarily prepared. Through the pipe 13 and the open shut-off valve 14, the supply vessel 1 is filled under pressure with the prepared solution. In the process of liquid supply, air is forced out through the pipe 8 and the open shut-off valve 16, as well as through the capillaries 2. After the supply vessel is completely filled, the liquid flows out through the pipe 8 and capillaries 2. By closing the shut-off valves 14, 16, the supply vessel 1 is sealed.

Slowly increase the pressure of the solution in the vessel to a value of p ₁ using a syringe 5 and a micrometer screw 6 with a motor-reducer 7 at a given (slow) mode of operation of the electric pulse duration generator. In this case, 2 drops 9 stably hanging at the ends of the capillaries are formed (Fig. 3).

Create a pressure pulse with amplitude p ₂ using a syringe 5 and a micrometer screw 6 with a motor-reducer 7 at a given (fast) mode of operation of the electric pulse duration generator. When this occurs, the simultaneous detachment of drops from the capillaries with the formation of a compact monodisperse cluster (Fig. 4).

The implementation of the method carried out on the example of a solution of surfactants in distilled water. Ammonium perfluoroligoether monocarboxylate was used as a surfactant. For this surfactant composition of FIG. 1b it follows that the value of the critical concentration of micelle formation C _cr =1.4 mol/m ³ . The surface tension coefficient of the solution varied from σ=72 mN/m at C=0 (distilled water) to σ=14 mN/m.

For this solution, calculations were carried out using formulas (1) - (7) for the following values of the initial parameters: ρ=10 ³ kg/m ³ ; g=9.81 m/s ² ; ƒ=0.6; C _cr =1.4 mol/m ³ ; σ(0)=72 mN/m; σ(C _cr )=14 mN/m; d=3.1⋅10 ^-3 m; S=2.0-10 ^-6 m ² .

1. Calculation of surfactant concentration according to formula (1).

С≤С _cr =1.4 mol/m ³ .

2. Calculation of the diameter of the droplets formed according to formula (2).

Since the solution is a wetting liquid (for the material of the capillary), the outer diameter of the capillary d=3.1 10 ^-3 m was used in the calculations.

For C=0:

For C=C _cr :

3. Calculation of the maximum capillary diameter using formula (3).

4. Calculation of the distance between the axes of the capillaries according to the formula (4).

5. Calculation of pressure p ₁ .

6. Calculation of pressure p ₂ .

p ₂ ≥5r ₁ = 5⋅20.8=104.0 Pa.

The photograph in Fig. 3 shows that the claimed method makes it possible to form an initial cluster of monodisperse droplets formed at the ends of capillaries. The photograph in Fig. 4 shows that the method ensures simultaneous detachment of all drops from the capillaries with the formation of a compact cluster of drops.

Comparison of the diameters of the droplets formed, measured from the video frames of the process, with the calculated values showed their close correspondence:

D _max =2.01 mm, D _min =1.16 mm - calculated values;

D _max =(2.2±0.2) mm, D _min =(1.2±0.2) mm - measured values.

Thus, the proposed method allows you to adjust the size of the droplets formed by 1.7 times (for a solution of the selected surfactant in distilled water).

The above example proves that when implementing the proposed method for obtaining a compact cluster of monodisperse drops of a given size, the positive effect of the invention is achieved, which consists in stable and reproducible obtaining of a compact cluster of monodisperse drops, as well as the ability to control the droplet size.

LITERATURE

1. Patent of the Russian Federation No. 2504407 Medical dropper Paramoshko V.A. IPC A61M 5/168, Published on 01/20/2014, Bull. No. 2.

2. Patent of the USSR No. 84581 Device for obtaining small single drops of liquid Liventsov A.V. IPC G01N 11/04, Published 1950.10.10.

3. Patent of the Russian Federation No. 2690802 Method for obtaining a flow of drops with a controlled dispersed composition Arkhipov V.A., Konovalenko A.I., Maslov E.A., Perfilieva K.G. Zolotorev N.N. IPC B05B 1/34, Published on 06/05/2019, Bull. No. 16.

4. RF patent No. 2602996 Device for generating sequentially moving liquid drops Volkov R.S., Voitkov I.S., Zabelin M.V. IPC G01F 11/00, Published on 11/20/2016, Bull. No. 32.

5. RF patent No. 2606090 Device for generating sequentially moving liquid drops Volkov R.S., Piskunov M.V., Strizhak P.A. IPC G01F 11/00, Published on 01/10/2017, Bull. No. 1.

6. RF patent No. 2724140 Method for determining the evaporation rate of a group of drops Arkhipov V.A., Konovalenko A.I., Basalaev S.A., Zolotorev N.N., Perfilieva K.G., Usanina A.S. IPC G01N 25/12, Published on 06/22/2020, Bull. No. 18.

7. Abramzon A.A., Bocharov V.V., Gaevoy G.M. Surfactants: A Handbook. L.: Chemistry, 1979. 376 p.

8. Zhang J., Meng Y. Stick-slip friction of stainless steel in sodium dodecyl sulfate aqueous solution in the boundary lubrication regime. Tribol Lett. 2014. Vol. 56, no. 3. P. 543-552.

9. Adamson A. Physical chemistry of surfaces. M.: Mir, 1979. 570 p.

10. Nigmatulin R.I. Dynamics of multiphase media. M: Nauka, 1987. Part 1. 464 p.

Claims (22)

A method for obtaining a compact cluster of monodisperse drops of a given size, which includes pulsed supply of liquid from a supply vessel through a set of capillaries of the same diameter, evenly spaced on the bottom cover of the vessel, characterized in that a solution of a surfactant in a liquid with a given concentration is preliminarily prepared, a supply vessel made in the form of a closed container, it is filled through the branch pipe located on the bottom cover of the vessel with the prepared solution with the possibility of completely displacing air from the vessel through the capillaries and the branch pipe located on the top cover of the vessel, droplets hanging steadily at the ends of the capillaries are formed by slowly increasing the pressure of the solution in the vessel to values of p ₁ and provide simultaneous detachment of drops from capillaries with the formation of a compact cluster by creating a pressure pulse with amplitude p ₂ in the solution, while the concentration of the surfactant in the solution, the diameter of the droplets formed, the maximum diameter of the capillaries, the distance between them and the pressure value p ₁ , p ₂ are determined from the relations С ≤ С _cr ,

,

,

,

,

, where C is the concentration of the surfactant in the solution, mol/ ^m3 ; _Сcr is the critical concentration of micellization, mol/m ³ ; D is the diameter of the droplets formed, m; d is the outer diameter for wetting liquids or the inner diameter for non-wetting liquids, m; σ(С) is the surface tension coefficient of the solution for the concentration value of the surfactant С, N/m; f = 0.6 - empirical coefficient; ρ is the density of the liquid solution, kg/ ^m3 ; g - free fall acceleration, m/s ² ; d _max is the maximum capillary diameter, m; σ _max is the maximum value of the surface tension coefficient of the solution at С = 0, N/m; l is the distance between the axes of the capillaries, m; D _max is the maximum diameter of droplets formed (in the absence of a surfactant in solution, C = 0), m; p ₁ is the pressure required for the formation of stable drops, Pa; S is the cross-sectional area of the capillary channel, ^m2 ; p ₂ is the pressure required to separate drops, Pa.

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