Steady Stokes flow of a non-Newtonian Reiner-Rivlin fluid streaming over an approximate liquid spheroid

Abstract

The investigation is carried out to study steady Stokes axisymmetrical Reiner-Rivlin streaming flow over a fixed viscous droplet, and this droplet to be deformed sphere in shape. As boundary conditions, vanishing of radial velocities, continuity of tangential velocities and shear stresses at the droplet surface are used. The very common configuration of approximate sphere governed by polar equation r ̃ = a[1 + αmθm (ζ)] has been considered for the study to O(αm) describing the distortion. Based on the Stokes approximation, an analytical investigation is achieved in the orthogonal curve linear framework in an unbounded region of a Reiner-Rivlin fluid. In constraining cases, some earlier noted outcomes are obtained. Also, the yielded outcomes for the drag have been compared with solution existing in the literature. Further, the change for both force and pressure are evaluated showing deflection w.r.t. the parameters of interest and shown through table and graphs.

Keywords

• stokes flow
• stream function
• drag
• reiner-rivlin fluid
• deformation parameter