STUDY OF INSTABILITY OF STREAMING RIVLIN-ERICKSEN FLUID IN POROUS MEDIUM

Abstract

There are many elastoviscous fluids that can be characterised neither by Maxwell’s constitutive relations nor by Oldroyd’s constitutive relations. One such class of viscoelastic fluids is the Rivlin– Ericksen’s fluid. RIVLIN and ERICKSEN] have proposed a theoretical model for such viscoelastic fluid. The behaviour of surface waves propagating between two Rivlin–Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients.