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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.

Following our previous work [K. D. Housiadas and R. I. Tanner, “Viscoelastic shear flow past an infinitely long and freely rotating cylinder,” Phys. Fluids 30, 073101 (2018)], we study analytically the effect of steady planar elongational flow past an infinitely long circular cylinder using asymptotic methods. The ambient fluid is assumed viscoelastic and modelled with the Upper Convected Maxwell, Oldroyd-B, exponential Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic model with the Peterlin approximation constitutive equations under isothermal and creeping flow conditions. The solution for all the dependent variables is expanded as an asymptotic power series with the small parameter being the Weissenberg number, Wi, which is defined as the product of the single relaxation time of the fluid times the constant rate of elongation. The resulting sequence of equations is solved analytically up to fourth order in the Weissenberg number. The solution derived here is the first analytical result in the literature for the planar elongational flow of viscoelastic fluids past a cylinder. It reveals the effect of viscoelasticity and all the relevant rheological parameters on the flow variables and the extensional viscosity of the fluid.Following our previous work [K. D. Housiadas and R. I. Tanner, “Viscoelastic shear flow past an infinitely long and freely rotating cylinder,” Phys. Fluids 30, 073101 (2018)], we study analytically the effect of steady planar elongational flow past an infinitely long circular cylinder using asymptotic methods. The ambient fluid is assumed viscoelastic and modelled with the Upper Convected Maxwell, Oldroyd-B, exponential Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic model with the Peterlin approximation constitutive equations under isothermal and creeping flow conditions. The solution for all the dependent variables is expanded as an asymptotic power series with the small parameter being the Weissenberg number, Wi, which is defined as the product of the single relaxation time of the fluid times the constant rate of elongation. The resulting sequence of equations is solved analytically up to fourth order in the Weissenberg number. The solution derived here is the first analytic...