Effects of Hall current and permeability on the stability of peristaltic flow

Abstract

Pumping molecules and atoms near or along surfaces under the perturbing influence of surface acoustic wave is important in micro-flow systems. These micro-flow systems can circulate heat-transfer fluids over silicon chips, reconstitute dried drugs and possibly synthesize chemicals from liquid to solid constituents. The stability of acoustic streaming flow induced by a small-amplitude surface acoustic wave propagating along the walls of a confined parallel-plane channel with a magneto incompressible fluid through a porous medium is considered. The stability related to the flow initiated by the peristaltic waves propagating along the deformable walls is explored numerically. The neutral stability boundary is gotten by understanding the significant Orr–Sommerfeld condition. The Chebyshev collocation method is employed to solve the resulting generalized eigenvalue problem. The critical Reynolds number and the corresponding wave number are obtained for different values of $$K_{0}=c/u_{\max }$$ (ratio of the wave speed to the maximum speed of the basic flow), magnetic field M, Hall current $$\beta _{1}$$ and permeability parameter k. Different values of the critical Reynolds number are obtained when $$K_{0}=c/u_{\max }$$ =1 (rigid wall) and $$\ne 1$$ for deformable walls. It is found that the critical Reynolds number (when the wall is deformable; $$K_{0}=10$$ ) becomes 577.22 which is much less than conventional rigid-wall case [5772, obtained by Orszag using the spectral method (Orszag in J Fluid Mech 50:689–703. https://doi.org/10.1017/S0022112071002842 , 1971)]. The effect of incrementing of $$K_{0}$$ and k shows destabilizing effect on the fluid flow while increasing in the values of M and $$\beta _{1}$$ exhibits a stabilizing influence on the fluid flow. So, various kinds of noises like Hall current, permeability and peristaltic waves propagating along the walls will premature any instability mechanism considering the temporal growth of the disturbances. Also, the range of wave numbers relevant to the peristaltic wave or the Reynolds number of this basic flow must be carefully selected for the optimal flow control usage in bio-MEMS.