Creeping Flow of Couple Stress Fluid Over a Spherical Field on a Saturated Biporous Medium

Abstract

This problem emphasizes the dynamic interaction between a biporous medium and a couple stress fluid of laminar flow. The flow around a permeable field engulfed in a couple stress fluid is examined. When examining the motion of an oil droplet in a porous collector that is surrounded by an aqueous medium (oil-in-water emulsion) and is subject to an external pressure drop, this formulation of the problem is typical. A similar issue arises when lymph enters the tissues of humans or animals: the inside permeable spherical field saturated with viscous fluid and outside region saturated with couple stress fluid. The Brinkman equations are utilized to characterize the couple stress fluid flow in a saturated biporous medium. The couple stress tensor and velocity fields are expressed using Gegenbauer polynomials and Macdonald functions. For the axially symmetric motion, both pressure distribution and the stream function solution are explicitly solved. The method of variable separation is used to investigate an analytical resoluteness for the flow field. The drag force on a saturated biporous medium and the drag coefficient <i>D<sub>N</sub></i> are calculated, and the impacts of the permeability κ, the ratio of viscosity (γ<sup>2</sup> = μ<sub>1</sub> /μ<sub>2</sub>), the couple stress viscosity ratio (τ = η'/η), and the parameter of couple stress (λ = √μ/η). The appropriate dependencies are graphically delineated and reviewed, including the permeability κ, couple stress parameter λ, viscosity ratio γ<sup>2</sup>, and couple stress viscosities (η, η'). According to the findings, increasing permeability gradually raises the drag coefficient, which is used to describe a spherical field’s surface with a high level resistance of flow. Limits statements are used to illustrate specific cases that are well-known. The current study is significant primarily in the course through a layer formed by penetrable particles and has very important and compelling applications in both nature and innovation, with a variety of potential outcomes.