An augmented lubrication theory for Moffatt eddies induced by contact line motion

For the contact line motion of a thin film liquid droplet or meniscus, the Stokes equations are known to allow for vortex flow solutions (a.k.a. Moffatt eddies) in the presence of a Navier slip condition with a spatially dependent slip coefficient that eliminates a divergent flow speed or shear stress towards the contact line. This emergent flow pattern inside the liquid wedge near the moving contact line, however, must be governed by the global fluid motion away from it, for which a unifying numerical approach is altogether missing. To this end, I will present a lubrication theory that (i) is not limited to high-aspect-ratio liquid films in contrast with conventional lubrication theories, (ii) can accommodate Moffatt vortex solutions near the contact line, (iii) yet simultaneously resolve the laminar far-field flows as with conventional lubrication theories. The numerical simulations of this augmented theory demonstrate the vortex creation, motion, and annihilation dynamics during contact line motion in conjunction with the transient self-consistent solutions of the liquid film height profiles.