Abstract
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
Highlights
Superhydrophobic surfaces are commonly used to optimize transport in microfluidic and nanofluidic systems [1,2,3]
The same figure shows the corresponding total dissipation A by the flow, which is related to the effective slip length according to Eq (13)
This is similar to the optimum angle found by Davis and Lauga [11], their expression is derived for shear flow over a HAASE, WOOD, LAMMERTINK, AND SNOEIJER (a) bubble mattress in the dilute limit (ε 1)
Summary
Superhydrophobic surfaces are commonly used to optimize transport in microfluidic and nanofluidic systems [1,2,3]. The gas present in the microstructures of the slippery and water-repellent surfaces reduces the overall friction between a flowing liquid and the wall, compared to flat nonslippery surfaces. The menisci of the gas bubbles are often assumed to be shear-free. This leads to small but finite effective slip velocities at the interface, which can enhance interfacial transport. The amount of wall slip is commonly expressed by the slip length b, as expressed by Navier’s law [4]. When considering slip over superhydrophobic surfaces, b denotes the effective slip length experienced by the flow on scales larger than the bubbles
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