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Slip at the surface of a general axi-symmetric body rotating in a viscous fluid

Ashmawy E. A.

Archives of Mechanics

2011

Vol. 63, nr 4

341-361

The rotational motion of an arbitrary axi-symmetric body in a viscous fluid is discussed using a combined analytical-numerical technique. A singularity method based on a continuous distribution of a set of Sampson spherical singularities, namely Sampsonlets, along the axis of symmetry within the body, is applied to find the general solution for the fluid velocity that satisfies the general slip boundary condition. Employing a constant and linear approximation for the density functions and applying the collocation technique to satisfy the slip boundary condition on the surface of the body, a system of linear algebraic equations is obtained to be solved numerically. The couple exerted on a prolate and oblate spheroid and on a prolate and oblate Cassini ovals is evaluated for various values of the aspect ratio a/b and for different values of the slip parameter, where a and b are the major and minor semi-axes of the particle respectively. The CPU time elapsed during numerical calculations is measured and tabulated. Numerical work shows that convergence to at least six decimal places is achieved.