On the Motion Past a Slip-Stick Sphere and a Shear Free Sphere in a Viscous Fluid

Abstract

The theoretical development of the complex fluid flows such as more than one obstacle with different shapes have great interest for scientists to understand flow phenomena and verify the model or approximate solution. The complex physical properties due to a uniform streaming motion past two fixed spheres is investigated having one with shear stress and another being shear stress-free. This study concerns analytical technique of a steady incompressible viscous fluid past to two fixed spheres. The Gegenbaur function and associated Legendre polynomials is used to derive the solution that simplify the process of the theoretical calculations. The mathematical expression for the flow fields are obtained in terms of stream functions by Gegenbaur function and associated Legendre polynomials. The physical properties of interest such as the Stokes stream function, the stress and its drag are calculated. It is understandable that for the uniform streaming motion around a sphere with the stress and its drag are affected owing to the presence of another stress-free are analyzed. The present result can be considered as a generalized by making other established results as a corollary of this solution. This theoretical study helps to the numerical or computational work for the verification of their approximated results of interest.