  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.
