Yelisieiev V., Lutsenko V., Ruzova T., Harasek M. Oscillatory motion of liquid in composite capillaries

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Parent Category: Geo-Technical Mechanics, 2025

Category: Geo-Technical Mechanics, 2025, Issue 173

Geotech. meh. 2025, 173, 50-61

 

OSCILLATORY MOTION OF LIQUID IN COMPOSITE CAPILLARIES

¹Yelisieiev V.

¹Lutsenko V.

²Ruzova T.

²Harasek M.

¹M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine

²Technische Universität Wien, Institute of Chemical, Environmental and Bioscience Engineering

UDC 532.7:534.1

Language: English

Abstract. The paper presents an analysis of the dynamic behavior of oscillatory flows in elements of capillary systems based on previously conducted studies. Considered configurations include two capillaries of different diameters connected in series, as well as a pipe with two branching capillaries (a branching system element). Such elements are typical for hydraulic and capillary structures found in both technical and biological systems. The purpose of this research was to extend the previously obtained results to more complex cases involving sharp changes in the cross-section of capillaries and their branching. In this case, composite capillaries were understood as systems of connected capillary pipes with different lengths and diameters.

The study begins by applying the theory of laminar flow and established approaches from the literature to determine flow rates through a capillary of constant diameter under oscillatory inlet conditions. Next, the phase shift between the oscillations of flow rate and pressure within the capillary is calculated as a function of the capillary radius. It was found that the phase shift decreases with decreasing capillary radius, but increases with increasing oscillation frequency. Using mass conservation laws, the phase shifts of flow and pressure oscillations in different sections of a composite linear capillary are then derived. It is shown that the phase shift of flow rate relative to pressure oscillation depends on the diameters of the two sections. The phase shift of pressure also varies relative to the first capillary, but the sum of the phase shifts of pressure and flow rate in each section remains constant. Further analysis of a branching system element leads to a general and simple rule: the sum of phase shifts in each branch of a capillary junction remains constant.

Thus, the previously established patterns for capillaries with weakly varying diameters are also valid for more complex composite capillary systems — those with sharp changes in diameter and branching geometries. This result may be useful for evaluating the distribution of total flow within complex branching capillary networks.

Keywords: capillary, liquid, flow rate, mass transfer, oscillations/

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yelisieiev volodymyr, Candidate of Physics and Mathematics Sciences, Ph.D.(Phys.-Mat.),Senior Researcher in Department of Mine Energy Complexes, M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine (IGTM of the NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. .

Lutsenko Vasyl, Candidate of Technical Sciences Ph.D.(Tech.), Senior Researcher in Department of Mine Energy Complexes, M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine (IGTM of the NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. (Corresponding author).

Ruzova Tetiana, Candidate of Technical Sciences Ph.D.(Tech.), Project Assistant, Technische Universität Wien, Institute of Chemical, Environmental & Bioscience Engineering, Computational Fluid Dynamics, This email address is being protected from spambots. You need JavaScript enabled to view it. .

Harasek Michael, Univ.Prof. DI Dr., Technische Universität Wien, Institute of Chemical, Environmental & Bioscience Engineering, Research Unit Separations Engineering and Simulation, This email address is being protected from spambots. You need JavaScript enabled to view it. .

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