Steady sphere translation in a viscoelastic fluid with slip on the surface of the sphere

Abstract We study analytically the effect of Navier type slip on the surface of a spherical particle which translates with constant velocity U in a viscoelastic ambient fluid. We assume steady state, isothermal and creeping flow conditions. The fluid is modelled with the Upper Convected Maxwell (UCM), Oldroyd-B, exponential Phan-Thien and Tanner (ePTT), and Giesekus constitutive equations. The solution for all the dependent flow variables is expanded as asymptotic power series with the small parameter being the Weissenberg number, Wi=λU/R, where λ is the single relaxation time of the fluid and R the radius of the particle. The resulting sequence of equations is solved analytically up to fourth order in Wi. Techniques that accelerate the convergence of series solutions are also applied in order to derive more accurate expressions for the drag force on the particle applicable to an extended range up to order unity Weissenberg number. The effects of viscoelasticity, the rheological parameters, and the slip coefficient are presented and discussed. For fixed Weissenberg number, the relative drag with respect to the Newtonian value increases with increasing slip.