Pressure loss in channel flow resulting from a sudden change in boundary condition from no-slip to partial-slip

Abstract

A semi-analytical model is presented for pressure-driven flow through a channel, where local pressure loss is incurred at a sudden change in the boundary condition: from no-slip to partial-slip. Assuming low-Reynolds-number incompressible flow and periodic stick–slip wall patterning, the problems for parallel-plate and circular channels are solved using the methods of eigenfunction expansion and point match. The present study aims to examine in detail how the flow will evolve, on passing through the cross section at which the change in the slip condition occurs, from a no-slip parabolic profile to a less sheared profile with a boundary slip. The present problem is germane to, among other applications, flow through a channel bounded by superhydrophobic surfaces, which intrinsically comprise an array of no-slip and partial-slip segments. Results are presented to show that the sudden change in the boundary condition will result in additional resistance to the flow. Near the point on the wall where a slip change occurs is a region of steep pressure gradient and intensive vorticity. The acceleration of near-wall fluid particles in combination with the no-slip boundary condition leads to a very steep velocity gradient at the wall, thereby a sharp increase in the wall shear stress, shortly before the fluid enters the channel with a slippery wall. Results are also presented to show the development of flow in the entrance region in the slippery channel. The additional pressure loss can be represented by a dimensionless loss parameter, which is a pure function of the slip length for channels much longer than the entrance length.