SLOW MOTION OF AN ARBITRARY AXISYMMETRICAL BODY ALONG ITS AXIS OF REVOLUTION AND NORMAL TO A PLANE SURFACE

This paper presents a combined analytical-numerical study for the Stok es flow caused by an arbitrary body of revolution translating axisymme trically in viscous fluid toward an infinite plane, which can be eithe r a solid wall or a free surface. A singularity method based on the pr inciple of distribution of a set of Sampson spherical singularities al ong the axis of revolution within a prolate body or on the fundamental plane within an oblate body is used to find the general solution for the fluid velocity field which satisfies the boundary condition at the infinite plane. The no-slip condition on the surface of the translati ng body is then satisfied by applying a boundary collocation technique to this general solution to determine the unknown coefficients. The h ydrodynamic drag exerted on the body is evaluated with good convergenc e behavior for various cases of the body shape and the separation betw een the plane and the body. For the motion of a sphere normal to a sol id plane or a planar free surface, our drag results agree very well wi th the exact solutions obtained by utilizing spherical bipolar coordin ates. For the translation of a spheroid, prolate or oblate, along its axis of symmetry and perpendicular to a plane wall, the agreement betw een our results and the numerical solutions obtained using the boundar y integral method is also quite good. In addition to the solutions for a spheroidal body, the drag results for the axially symmetric motions of a Cassini oval towards a solid plane and a planar free surface are also presented.