Transient Movement of a Hydrophobic Particle in a Cavity Containing a Brinkmann Medium

Faltas, Mokhtar; Saad, Elsayed; Sherief, Hany; Aamer, Ahmed Saeed

doi:10.21608/ejmaa.2025.379897.1340

Transient Movement of a Hydrophobic Particle in a Cavity Containing a Brinkmann Medium

Document Type : Regular research papers

Authors

¹ Department of Mathematics and Computer Science, Faculty of Science, Alexandria,University, Alexandria, Egypt

² Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt

³ Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt

⁴ Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt.

10.21608/ejmaa.2025.379897.1340

Abstract

This study investigates the transient motion of a hydrophobic colloidal spherical particle within a concentric cavity filled with a polymer gel operating under conditions of low Reynolds number. The polymer gel is modeled as a porous medium with a specified permeability, determined through experimental measurements. Fluid flow movement within the porous matrix is induced by a sudden application of a steady body force along the line connecting the particle and cavity centers. The transient Brinkman equation governs the fluid dynamics within the cavity and is analytically solved using the Laplace transform method. The study highlights the long-range hydrodynamic interactions
between the colloidal particle and the surrounding polymer gel medium, leading to an analytical
expression for the transient velocity of the particle as a function of key system parameters. This
work provides insight into particle mobility in polymer gels, with implications for applications
in controlled drug delivery and biocompatible material design.

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