Rough or patterned surfaces infused with a lubricating liquid display many of the same useful properties as conventional gas-cushioned superhydrophobic surfaces. However, liquid-infused surfaces exhibit a new failure mode: the infused liquid film may drain due to an external shear flow, causing the surface to lose its advantageous properties. We examine shear-driven drainage of liquid-infused surfaces with the goal of understanding and thereby mitigating this failure mode. On patterned surfaces exposed to a known shear stress, we find that a finite length of the surface remains wetted indefinitely, despite the fact that no physical barriers prevent drainage. We develop an analytical model to explain our experimental results, and find that the steady-state retention results from the ability of patterned surfaces to wick wetting liquids, and is thus analogous to capillary rise. We establish the geometric surface parameters governing fluid retention and show how these parameters can describe even random substrate patterns.

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We present a mathematical model and corresponding series of microfluidic experiments examining the flow of a viscous fluid past an elastic fibre in a three-dimensional channel. The fibre’s axis lies perpendicular to the direction of flow and its base is clamped to one wall of the channel; the sidewalls of the channel are close to the fibre, confining the flow. Experiments show that there is a linear relationship between deflection and flow rate for highly confined fibres at low flow rates, which inspires an asymptotic treatment of the problem in this regime. The three-dimensional problem is reduced to a two-dimensional model, consisting of Hele-Shaw flow past a barrier, with boundary conditions at the barrier that allow for the effects of flexibility and three-dimensional leakage. The analysis yields insight into the competing effects of flexion and leakage, and an analytical solution is derived for the leading-order pressure field corresponding to a slit that partially blocks a two-dimensional channel. The predictions of our model show favourable agreement with experimental results, allowing measurement of the fibre’s elasticity and the flow rate in the channel.