This study presents an exact solution for the flow of two immiscible fluids under a general oscillatory time-dependent pressure gradient in a channel with one porous floor. The oscillatory behavior of the time-dependent pressure gradient is expressed in terms of Fourier series. At the interface, continuity of velocities and shear stresses is assumed. Equations governing the flow are solved using the slip condition at the permeable interface whereas the generalized Darcy`s law in the porous region. The unsteady flow depends upon the Reynolds numbers of the fluids, slip parameter and porous parameter. Analytical expressions are provided for the mass flow rate and wall shearing stresses. Numerical results are presented considering water and mercury as the two immiscible fluids for the uniform pressure gradient as well as for the sinusoidal time-dependent pressure gradient. Since the formulation of the problem is general, it is possible to examine the unsteady flow of any two immiscible fluids under any specified oscillatory time-dependent pressure gradient. This study will be useful in learning how the pressure and viscous forces exert their influence to produce different flow patterns.
Sai K.S., , N.S. Swamy , H.R. Nataraja , S.B. Tiwari and B. Nageswara Rao , 2006. Unsteady Flow of Two Immiscible Fluids under an Oscillatory Time-dependent Pressure Gradient in a Channel with One Porous Floor. Trends in Applied Sciences Research, 1: 194-203.