Does liquid slippage within a rough channel always increase the flow rate?

Slippage of liquid over rough superhydrophobic surfaces that induce the Cassie-Baxter state decreases frictional force on the flow. This may easily lead to a hasty conclusion that liquid slip enhances the flow rate in rough channels. Here, we show that flow rates can be rather reduced by roughening and hydrophobizing microchannel walls to support liquid slippage, depending on the topography of the roughness. We consider theoretical models that predict liquid flow rates in channels of different roughness and wetting conditions, to construct criteria for the surface structure that determine whether slip or no-slip would be advantageous in enhancing flow rates. It is shown that liquid slips are advantageous only in channels with highly hydrophobic, short, sparsely distributed protrusions. We corroborate our theoretical predictions with microchannels decorated with micropillars of varying we…