Motion through a viscous liquid sphere enclosed by a solid core embedded into a Brinkman medium

Abstract

The flow around a solid spherical particle encased in a Newtonian liquid sphere and immersed in a couple stress fluid medium is studied. The problem is expressed by using the Brinkman and Stokes equations, which describe both the flow outside and inside the liquid sphere, respectively. The Gegenbauer polynomials and modified Bessel function are used to express the stream function solution for the internal and external regions. An analytical determination for the flow field in terms of stream function is examined by wielding the method of separation of variables. The drag force on a solid spherical particle placed in a permeable region is calculated. On the drag coefficient, the effects of the permeability 𝜅, the viscosity ratio 𝛾 2 , and the couple stress parameter 𝜆 are investigated.Corresponding dependencies (such as the permeability parameter, couple stress parameter, viscosity ratio, and separation parameter) are graphically represented and discussed. The findings shows when the separation parameter is increased the drag coefficient gradually increases, it refers to a sphere surface with a high level of flow resistance. Passages to the limits are used to describe known specific cases. The present study is essentially significant in the course through a layer developed by penetrable particles and has very important and persuasive applications both in nature and innovation, with various potential outcomes. Thus, the discoveries of this article are comprehensively pertinent to the investigation of the flow of permeable liquids past spherical permeable rocks, aloxite materials, sand beds, earthen soil, petrol supply rocks, and so forth. The present application will support in planning a productive bearing framework.