Wetting dynamics of a collapsing fluid hole

TL;DR

This study models the collapse of a wetting fluid hole in a rotating bucket, revealing how gravity, surface tension, and centrifugal forces influence the dynamics and collapse time, with results aligning with experimental observations.

Contribution

It introduces a lubrication theory-based evolution equation capturing the effects of capillary, gravity, and centrifugal forces on fluid hole collapse, including volume dependence and complex dynamics.

Findings

Gravity accelerates collapse time.

Surface tension dominates for small holes, showing a universal power law.

Centrifugal forces slow collapse and cause stalled spreading.

Abstract

The collapse dynamics of an axisymmetric fluid cavity that wets the bottom of a rotating bucket bound by vertical sidewalls are studied. Lubrication theory is applied to the governing field equations for the thin film to yield an evolution equation that captures the effect of capillary, gravitational and centrifugal forces on this converging flow. The focus is on the quasi-static spreading regime, whereby contact-line motion is governed by a constitutive law relating the contact-angle to the contact-line speed. The collapse time, as it depends upon the initial hole size, is reported showing that gravity accelerates the collapse process. Surface tension forces dominate the collapse dynamics for small holes leading to a universal power law whose exponent compares favorably to experiments in the literature. Volume dependence is predicted and compared with experiment. Centrifugal forces slow the collapse process and lead to complex dynamics characterized by stalled spreading behavior that separates the large and small hole asymptotic regimes.