Axi-symmetric translational motion of an arbitrary solid prolate body in a micropolar fluid

Abstract

The translational motion of an arbitrary body of revolution in a micropolar fluid is investigated by a combined analytical–numerical method. The governing equations are obtained under the assumption of Stokesian flow. A singularity method based on a continuous distribution of a set of micropolar Sampsonlet singularities along the axis of symmetry within a prolate body is used to find the general solution for the fluid velocity and microrotation components. Employing a constant/linear approximation for the density function and applying the collocation technique to satisfy the boundary conditions on the surface of the body, a system of linear algebraic equations is obtained and solved numerically. The drag force exerted on a prolate spheroid is evaluated for various values of the aspect ratio and for different values of the micropolarity parameters. Numerical results show that convergence to at least four decimal places is achieved. It is found that the drag force on the prolate spheroid increases monotonically with an increase of the aspect ratio of the spheroid and also with an increase of the micropolarity parameters. In order to demonstrate the generality of the present method, the technique is also applied to the prolate Cassini ovals and shows good convergence.