Yelisieiev V.I., Lutsenko V.I., Berkout V.D. Oscillatory liquid motion in capillaries, the geometry of which changes weakly

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Parent Category: Geo-Technical Mechanics, 2022

Category: Geo-Technical Mechanics, 2022, Issue 163

Geoteh. meh. 2022, 163, 174-182

https://doi.org/10.15407/geotm2022.163.174

 

OSCILLATORY LIQUID MOTION IN CAPILLARIES, THE GEOMETRY OF WHICH CHANGES WEAKLY

¹Yelisieievv.I., ¹Lutsenkov.I., ²Berkout V.D.

¹Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine; ²MassTech Inc.

UDC 532.7:534.1                                       

Language: English

Abstract. In this paper, on the basis of previously performed studies, the oscillatory motions of a liquid in a narrow channel, the width of which varies slightly, are considered. The solution of the problem was carried out on the basis of the boundary layer model for the case of a flat arrangement, which to some extent simplified the analytical description compared to the axisymmetric problem and at the same time did not qualitatively change the physical features of the investigated process. Asymptotic methods with a small parameter were used to obtain solutions. Three different variants of the task are considered, which differ from each other in the patterns of changes in the width of the channel along the longitudinal axis. As a result of the solution, it is shown that when the width of the channel changes monotonically, the ratio of pressure gradients also changes monotonically. When the width of the channel is the same at the ends of the analyzed section, the ratio of pressure gradients at the ends of the channel is also equal. With a sinusoidal change in the channel width, changes in pressure gradients also have a sinusoidal character. The main result of the work is the conclusion that when the width of the flat capillary changes, the phase shift of the pressure fluctuation relative to itself changes, at the same time the flow rate fluctuation relative to the pressure also changes, but the sum of these shifts remains a constant value. In known solutions for a constant channel diameter, the harmonic oscillations of flow and pressure also have a phase shift relative to each other that depends on the channel diameter but does not vary along the channel. It is also shown that with further approximations, components containing harmonics with a doubled frequency and a component that does not depend on time appear in the solution, i.e. with an oscillating flow in a capillary of non-constant width, a time-independent flow is formed in certain zones. The structure of such an internal flow, as follows from the solution, depends on the change in the diameter of the capillary and on the specified oscillation.
Keywords: capillary, liquid, diffusion, mass exchange, oscillations.

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About authors:

Yelisieiev Volodymyr Ivanovych, Candidate of Physics and Mathematics Sciences (Ph.D), Senior Researcher, Senior Researcher in Department of Mine Energy Complexes, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, (IGTM NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Lutsenko Vasyl Ivanovych, Candidate of Technical Sciences (Ph.D), Senior Researcher, Senior Researcher in Department of Mine Energy Complexes, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, (IGTM NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Berkout Vadym Dmytrovych, Candidate of Physics and Mathematics Sciences (Ph.D), Senior Researcher, Senior Researcher, MassTech Inc. (MTI), Columbia, Maryland USA, This email address is being protected from spambots. You need JavaScript enabled to view it.

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