THE NORMAL FORCE EXERTED BY A SECOND ORDER FLUID ON A SMALL SPHERE TOUCHING A PLANE

Abstract

The hydrodynamic force experienced by a small solid sphere of radius a _p resting on a solid plane wall in an axisymmetric stagnation creeping flow of a viscoelastic fluid is computed at order one in Weissenberg number. The solution utilises the method of the reciprocal theorem of Lorentz and the corresponding solution of the Newtonian problem to get the normal force without the need of solving for the velocity field. The resulting expression is a volume integral which has to be solved numerically. The result obtained shows that elastic effect of the constant viscosity second order fluid causes a reduction in the normal force beyond that of a Newtonian fluid of the same viscosity.

KEYWORDS:

• Second order fluid
• Creeping flow
• Contacting particles