Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid

Azza M. Algatheem, Hala H. Taha and Shreen El-Sapa ()
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Azza M. Algatheem: Department of Mathematics, Faculty of Science, University of Bisha, Bisha 61922, Saudi Arabia
Hala H. Taha: Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Shreen El-Sapa: Department of Mathematics and Computer Science, Faculty of Science, Damanhour University, Damanhour 22511, Egypt

Mathematics, 2025, vol. 13, issue 2, 1-22

Abstract: This study investigates the dynamics of two oscillating rigid spheres moving through an infinite porous medium saturated with Stokes fluid flow, addressing the problem of how fluid properties, permeability, frequency, and slip length influence the system. The objective is to model the interactions between the spheres, which differ in size and velocity as they move along the axis connecting their centers while applying slip boundary conditions to their surfaces. We derive the governing field equations using a semi-analytical method and solve the resulting system of equations numerically through a collocation technique. Our novel quantitative results include insights into the drag force coefficients for both in-phase and out-of-phase oscillations of each hydrophobic sphere, considering parameters such as diameter ratio, permeability, frequency, velocity ratios, slip lengths, and the distances between the spheres. Notably, when the spheres are sufficiently far apart, the normalized drag force coefficients behave as if each sphere is moving independently. Additionally, we present streamlines that illustrate the interactions between the spheres across a range of parameters, highlighting the novelty of our findings. A purely viscous medium and no-slip conditions are used to validate the numerical approach and results.

Keywords: interaction; fluctuations; drag force; hydrophobic; collocation method; permeability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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