Darcy–Brinkman Flow Through a Corrugated Channel

Abstract

A perturbation analysis is carried out to the second order to give effective equations for Darcy-Brinkman flow through a porous channel with slightly corrugated walls. The flow is either parallel or normal to the corrugations, and the corrugations of the two walls are either in phase or half-period out of phase. The present study is based on the assumptions that the corrugations are periodic sinusoidal waves of small amplitude, and the channel is filled with a sparse porous medium so that the flow can be described by the Darcy-Brinkman model, which approaches the Darcian or Stokes flow limits for small or large permeability of the medium. The Reynolds number is also assumed to be so low that the nonlinear inertia can be ignored. The effects of the corrugations on the flow are examined, quantitatively and qualitatively, as functions of the flow direction, the phase difference, and the wavelength of the corrugations, as well as the permeability of the channel. It is found that the corrugations will have greater effects when it is nearer the Stokes' flow limit than the Darcian flow limit, and when the wavelength is shorter. For the same wavelength and phase difference, cross flow is more affected than longitudinal flow by the corrugations. Opposite effects can result from 180 • out-of-phase corrugations, depending on the flow direction, the wavelength, as well as the permeability.

Electro-osmotic flow through a thin channel with gradually varying wall potential and hydrodynamic slippage

“…The opposite is true forδ ⊥ eff . This finding concurs with that of Wang (1976Wang ( , 1979 and Ng and Wang (2010), who found that the resistance to flow between two corrugated plates depends on the flow direction as well as on the phase of the corrugations. Slip length is the distance by which the no-slip plane is shifted outward from the physical wall.…”

Electromagnetohydrodynamic (EMHD) flow between two transversely wavy microparallel plates

“…Chu [41] studied the slip flow in an annulus with corrugated walls. Ng and Wang [42] discussed the effects of both longitudinal and transverse wall corrugations on the [43] discussed the effects of near-wall slip induced by surface roughness on the pressure rise and flow rate of a single rotating-disk viscous micropump operating with Newtonian water. Wang [44] studied the low Reynolds number flow in a tube with helical corrugations.…”

Unsteady rotational motion of a composite sphere in a viscous fluid using stress jump condition

“…Many researchers are utilizing this model to discuss the behaviour of viscous fluid flows in porous regions e.g. [8][9][10][11]. Lately, the most important boundary condition that has widely used is the stress jump condition on a porous-fluid interface developed by OchoaTapia and Whitaker [12,13].…”