A general formula for the drag on a solid of revolution body at low Reynolds numbers in a microstretch fluid

摘要

This paper presents an analytical formula for the calculation of drag on an axially symmetric body moving steadily with a uniform speed in a microstretch fluid. The body is assumed to move axially in such a way that an axisymmetric flow around it is produced. The formula is constructed under the assumptions of steady creeping flow regardless of boundary conditions satisfied at the boundaries. The obtained formula is an extension of a corresponding one obtained by Happel and Brenner (Low Reynolds number hydrodynamics, Noordhoff, Leiden, 1973) for viscous fluids and it is also an extension of the formula obtained by Ramkissoon and Majumdar (Phys Fluids 19:16-21, 1976) for micropolar fluids. It is quite interesting to note that the derived formula has no contribution to the scalar microstretch function and therefore, it applies as well to micropolar fluids. As an application of the obtained formula, the motion of a spherical particle at the instant it passes the center of a spherical cavity filled with micorstretch fluid is considered. The slip boundary conditions for both the velocity and microrotion are used at the surface of the spherical particle. It is found that, the wall correction factor increases with the slip parameters, the micropolarity parameter and the radius ratio.