Determining applicability limits for the analytical calculation of the effective radius in a two-capillary channel

About the authors:

Oleg A. Simonov, Cand. Sci. (Phys.-Math.), Deputy Director, Tyumen Scientific Center of the Siberian Branch of the Russian Academy of Sciences; s_o_a@rambler.ru, https://orcid.org/0000-0003-2362-3588

Lyudmila N. Filimonova,

Cand. Sci. (Phys.-Math.), Junior Researcher, Tyumen Branch of the Institute of Theoretic and Applied Mechanics named after S. A. Khristianovich of the Siberian Branch of the Academy of Sciences; Senior Lecturer, University of Tyumen, Tyumen, Russia; filimonovaln@mail.ru, https://orcid.org/0000-0001-6761-8292

Yuliya Yu. Erina,

Postgraduate Student, Department of Fundamental Mathematics and Mechanics, University of Tyumen; Research Engineer, Tyumen Scientific Centre of the Siberian Branch of the Russian Academy of Sciences, Tyumen, Russia; erina.yulya@inbox.ru, https://orcid.org/0000-0002-8577-1044

Abstract:

This paper analyzes an approach for calculating the effective radius of a channel consisting of two segments of cylindrical capillaries, through which the flow is hydrodynamically identical to the flow through a capillary with a constant effective radius. The article presents an analytical method for calculating the effective radius, based on the Poiseuille flow equation, which makes this approach a simple and convenient tool for constructing complex capillary models. A limiting factor of this method is its accuracy, requiring the assessment of the problem parameters within which the analytical approach is applicable. To address this, the paper compares the effective radius calculated using the analytical method with the results obtained from numerical experiments in the COMSOL environment. The study describes and analyzes the flow characteristics within such a channel, justifies possible reasons for discrepancies between the analytical approach and the numerical results, and defines the conditions under which the analytical method is applicable. It is shown that, within the framework of the Poiseuille equation, the applicability of the analytical approach is constrained by the geometric characteristics of the channel, such as the radius ratio and the relative channel length. A method for calculating the boundaries of allowable values for the geometric characteristics is proposed, and a graph of isolines for the relative error in the analytical calculation of the effective radius is presented.

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