Viscoelastic planar elongational flow past an infinitely long cylinder

Abstract

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.