The Plane Parallel Flow of a Binary Mixture of Fluids

Abstract

The flow of a binary mixture of chemically inert incompressible, Newtonian fluids over an infinite plate, set into motion in its plane by impulse and by oscillation, is studied. The binary mixture consists of (i) two different viscous density nonstratified fluids, and (ii) two different viscous density stratified fluids. The exact solutions are obtained using two methods, (i) Laplace transform and (ii) Hankel transform. To further study the velocities and the wall shear stress, asymptotic expansion are found for small and large times. Some other results of physical importance such as results for noninteracting fluids, strongly interacting fluids, and extremely different fluids are also derived and compared analytically with other results. Finally, to gain an insight into the patterns of the flow, numerical study of the results has been made in detail using digital computer. A strong motivation of the present analysis has been the hope that such a theory of fluids is useful in providing some insight in rheological properties of complex fluids as polymers, liquid crystals and, in particular, blood in the vessels of small diameter. Also the theory of fluids might provide an improved understanding of such diverse subjects as diffusion of proteins, swimming of micro-organism and particle deposition in respiratory tract.