Transient Movement of a Hydrophobic Particle in a Cavity Containing a Brinkmann Medium
Faltas, M., Saad, E., Sherief, H., Aamer, A. (2025). Transient Movement of a Hydrophobic Particle in a Cavity Containing a Brinkmann Medium. EKB Journal Management System, 13(2), 1-25. doi: 10.21608/ejmaa.2025.379897.1340
Mokhtar Faltas; Elsayed Saad; Hany Sherief; Ahmed Saeed Aamer. "Transient Movement of a Hydrophobic Particle in a Cavity Containing a Brinkmann Medium". EKB Journal Management System, 13, 2, 2025, 1-25. doi: 10.21608/ejmaa.2025.379897.1340
Faltas, M., Saad, E., Sherief, H., Aamer, A. (2025). 'Transient Movement of a Hydrophobic Particle in a Cavity Containing a Brinkmann Medium', EKB Journal Management System, 13(2), pp. 1-25. doi: 10.21608/ejmaa.2025.379897.1340
Faltas, M., Saad, E., Sherief, H., Aamer, A. Transient Movement of a Hydrophobic Particle in a Cavity Containing a Brinkmann Medium. EKB Journal Management System, 2025; 13(2): 1-25. doi: 10.21608/ejmaa.2025.379897.1340

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

Electronic Journal of Mathematical Analysis and Applications
Volume 13, Issue 2, 2025, Page 1-25  XML PDF (1.09 MB)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2025.379897.1340
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Authors
Mokhtar Faltas1; Elsayed Saad2; Hany Sherief3; Ahmed Saeed Aamer email orcid 4
1Department of Mathematics and Computer Science, Faculty of Science, Alexandria,University, Alexandria, Egypt
2Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt
3Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
4Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt.
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.
Keywords
Transient velocity; slow motion; polymer gel; concentric cavity
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