Experimental setup for investigating the dynamics of the ascent of a cluster of bubbles in a liquid

There is a scheme of experimental setup providing preparation of the compact cluster of monodispersed bubbles of the given diameter presented in the work. Further, in this research we have calculated setup parameters that are necessary for preparation of the compact air bubble cluster in glycerin at room temperature.


Introduction
The behavior of fluid containing bubbles is distinctly different from behavior of homogeneous fluids under different physical and physical-chemical influence.These differences are abundantly used in industry -boiling, heat transfer in the two-phase mediums, cavitation, foaming, flotation.There is a question of the bubble cluster of given size generation in a number of problems, in particular, while researching an ignition of fluid electric discharge in fluids by way of specially created cavitational bubbles [1], while researching surfactants and acoustic waves on dynamics of bubble clusters [2][3].
In practice of the experimental studies there are setup relating to aeration devices, aim to gas introduction to the liquid fluid.The carried out analysis devices work [4][5] showed that setups are intended for creation of the continuous flow of bubbles in fluid.The [6] disadvantage is impossibility of cluster generation from monodispersed bubbles of millimetric sizes and also complexity of the setups realizing these methods.The method [7] does not allow to generate a bubble cluster of controlled form.
In this paper, the experimental scheme of setup allowing to provide a compact cluster of monodispersed bubbles of the given diameter was described.

The scheme of the experimental setup
The experimental setup for generation of a compact cluster of monodispersed bubbles [8] is presented in Fig. 1.The setup includes collector 3 that placed in a lower part of receiver 1 with fluid 2 with gas-permeable upper cover 4, connected by branch pipe 5 with a source of compressed gas.Receiver 1 is executed in the form of a cuvette with plane-parallel walls https://doi.org/10.1051/matecconf/201819401005HMTTSC-2018 Matec Web of Conferences from optical glass of 0.3 0.30.6 m in size for visualization possibility of upfloat process of bubbles cluster.
In upper cover 4 of collector 3 are executed in its center and for equidistant concentric circles of perforation in which central 6 and peripheral tubes 7 of identical diameter are established which height that is identical to the tubes located on each circle and linearly decreases with increase of circle radius.Injection medical needles are used as tubes.
Cylinder 8 with the compressed gas, connected through low pressure reducer 9 and also through high pressure reducer 11 and electropneumatic valve 13 with branch pipe 5 of collector 3 is used as a source of gas.Work of the setup is carried out as follows.The constant pressure pmin controlled by a pressure gage 10 is settled by means of the reducer 9, it hinders fluid 2 flowing through tubes 6, 7 into the collector 3.By means of high pressure reducer 11 and the electropneumatic valve 13 the compressed gas is pulsewise supplied under the pressure pmax through the branch pipe 5 into the collector 3. Gas from the collector 3 through tubes 6, 7 in the form of bubbles comes to ambient liquid 2. After bubbles departure from tubes 6, 7 in liquid 2 the compact cluster of spherical shape bubbles floating up is formed.

Results of the experimental study
Let`s consider the results of the compact cluster preparation of air monodispersed bubbles in glycerin at room temperature.Parameters of the device, necessary for calculations, are specified in Now we are calculating parameters of the setup.For determination of the tubes height hi located on circle radius ri, we consider similar triangles of ABC and AB1C1 (Fig. 2).

Fig. 2. Similar triangles of ABC and AB1C1.
From the similarity condition follows: From Fig. 1 follows: where hi, tube height of located on radius ri (i = 1, 2,...,к).Substituting (2) in (1), we are getting: h0/R = hi/(Rri), from here follows the ratio: The ratio (3) provides linear reduction of tubes height from h0 to hk with increase in radius of circle ri.The results of calculations of tubes height located on a circle with radius ri are provided in table 3. The smallest hydrostatic pressure is implemented for the central tube with height h0 for which h = H -h0. From (4) follows:

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During the development of the setup we experimentally get more specific condition (5): While performing ratio (6) gas doesn't come into liquid through the central tube and also through the tubes located on concentric circles, because hydrostatic pressure is higher for them, than for the central tube.
Under a pressure in the collector equal to the maximum pressure quantity of gas pmax, gas should come through the tubes into liquid.It is provided under the following condition: The largest hydrostatic pressure is implemented for peripheral tubes with height hk for which h = Hhk.From (7) follows: During the development of the setup we experimentally get more specific condition (8): While performing ratio (9) gas bubbles come into liquid through the tubes located on peripheral circle radius rk and also through other tubes, because hydrostatic pressure is less for them, than for peripheral tubes.
For determination of impulse duration  of the electropneumatic valve openning we will consider the formula of gas consumption through the tube [10]: where Q, volume consumption of gas; consumption coefficient; Heat and mass transfer in the thermal control system of technical and technological energy equipment The input of gas portion with volume Vg forms a bubble which volume is equal to the volume of the entered gas: From ( 11), ( 12) the ratio for definition follows  : When calculating  the value of the consumption coefficient  = 0.5 is defined according to [10,11].

Conclusion
 The modified scheme of experimental setup providing the compact cluster preparation of monodispersed bubbles of the given diameter is presented in the work.
 An increase in the ascent rate of a cluster of bubbles was found, compared to the velocity of a single bubble in a pure liquid.
 Performing perforations in the top cover of the collector at its center and along equidistant concentric circles makes it possible to obtain an axisymmetric bubble cluster.
 The use of microtubules of the same diameter, installed in perforations, provides the formation of monodisperse bubbles.
 The use of microtubules of equal height located along each of the concentric circles ensures the simultaneous formation of a "ring" of bubbles for each of the circles.

Fig. 1 .
Fig. 1.The scheme of the experimental setup for creation of a compact cluster of monodispersed bubbles.

Fig. 3 .
Fig. 3.The video frames of upfloating of the monodispersed bubbles compact cluster.

table 1
Heat and mass transfer in the thermal control system of technical and technological energy equipment diameter of a tube; h0height of the central tube; Rradius of the upper cover of a collector; Hheight of fluid column in the receiver over the collector upper cover.
, where Dthe required diameter of the formed bubble; dinside

Table 1 .
[9]ameters of a setup.Physical characteristics of air and glycerol[9]at a temperature of 20°C, are shown in table2, where ρdensity; patmatmospheric pressure; σcoefficient of superficial liquid tension.

Table 2 .
Physical characteristics of air and glycerin.

Table 3 .
Height of the tubes located on a circle radius ri.