Why bumpy is better: The role of the dissipation distribution in slip flow over a bubble mattress

It has been observed that the amount of effective slip for transverse flow over a bubble mattress is maximum for bubbles that protrude somewhat in the channel flow. In this paper we provide an explanation for this characteristic feature by analyzing the spatial distribution of viscous dissipation for bubbles of varying protrusion angles. Bubbles protruding in the channel act as obstacles and reduce the effective channel height, thereby increasing the viscous dissipation in the bulk flow. At small scales, however, our numerical analysis reveals that increasing the bubble protrusion angle reduces the dissipation near the contact points of the no-slip channel wall and the no-shear bubble surface. We obtain an analytical expression to quantify this effect based on classical corner flow solutions. The two antagonistic effects, decreased dissipation near the bubble corners and increased dissipation on larger scale, explain why the effective slip length is maximum for a bubble mattress that is slightly bumpy.