Crossover from Shear-Driven to Thermally Activated Drainage of Liquid-Infused Microscale Capillaries

The shear-driven drainage of capillary grooves filled with viscous liquid is a dynamic wetting phenomenon relevant to numerous industrial processes and novel lubricant-infused surfaces. Prior work has reported that a finite length $L_\infty$ of the capillary groove can remain indefinitely filled with liquid even when large shear stresses are applied. The mechanism preventing full drainage is attributed to a balance between the shear-driven flow and a counterflow driven by capillary pressures caused by deformation of the free surface. The final equilibrium length $L_\infty$ is uniquely determined by physical properties of the filling liquid as well as the geometry and wettability of the capillary. In this work, we examine closely the approach to the final equilibrium length $L_\infty$ and report a crossover to a slow drainage regime that cannot be described by conventional dynamic models considering solely hydrodynamic and capillary forces. The slow drainage regime observed in experiments can be instead modeled by a kinetic equation describing a sequence of random thermally activated transitions between multiple metastable states caused by surface defects with nanoscale dimensions. Our findings provide new insights on the critical role that natural or engineered surface roughness with nanoscale dimensions can play in the imbibition and drainage of capillaries and other dynamic wetting processes in microscale systems.