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1 Journal of Applied Mathematics and Computational Mechanics

1 2024

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Slow flow of micropolar fluid past an immiscible micropolar fluid sphere

Madasu Krishna Prasad, Goyal Nidhi

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 2

54--65

The Stokes axisymmetric flow of an incompressible micropolar fluid past an another immiscible micropolar fluid sphere is studied analytically under small Reynolds numbers. A spherical coordinate system is used to solve the Stokes equations for the fluid velocities, pressures and microrotation vectors inside and outside the micropolar fluid drop. The boundary conditions on the micropolar fluid drop surface are satisfied by vanishing of a normal component of velocity inside and outside the micropolar fluid sphere, tangential components of velocities are continuous, tangential components of stresses are continuous, and the microrotation vector inside and outside the micropolar fluid sphere vanishes. Numerical results for the drag force acting on the micropolar fluid drop are obtained for various values of the relative viscosity of the fluid drop, micropolar parameters (vortex viscosity parameters), and shear spin viscosity parameters. It is found that the drag force exerted on the viscous drop in a micropolar fluid and the micropolar fluid drop in a viscous fluid increase with an increase in the viscosity ratio. Additionally, the findings demonstrate that the drag force acting on the micropolar drop in a micropolar fluid increases as the viscosity ratio increases, and the drag force on the gaseous bubble is less than that of a solid sphere. Well-known results are reduced, and comparisons are made with a classical viscous-viscous droplet, a micropolar-viscous droplet and a viscous-micropolar droplet. The present study has significant applications in natural, biological, and industrial processes, such as sedimentation phenomena, liquid-liquid extraction, the study of blood flow, and the rheology of emulsions.