Slip at the surface of an oscillating spheroidal particle in a micropolar fluid

H. H. Sherief, M. S. Faltas, Elsayed I Saad


The axisymmetric rectilinear and rotary oscillations of a spheroidal particle in an incompressible micropolar fluid are considered. Basset type linear slip boundary conditions on the surface of the solid spheroidal particle are used for velocity and microrotation. Under the assumption of small amplitude oscillations, analytical expressions for the fluid velocity field and microrotation components are obtained in terms of a first order small parameter characterizing the deformation. For the rectilinear oscillations, the drag acting on the particle is evaluated and expressed in terms of two real parameters for the prolate and oblate spheroids. Also, the couple exerted on the spheroid is evaluated for the prolate and oblate spheroids for the rotary oscillations. Their variations with respect to the frequency, deformity, micropolarity and slip parameters are tabulated and displayed graphically. Well-known results are deduced and comparisons are made between the classical viscous fluids and micropolar fluids. The results of this study serve to improve the accuracy of viscosity measurements for micropolar fluids.

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rectilinear and rotary oscillations, prolate and oblate spheroids, micropolar fluid, slip condition

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