Spreading or contraction of viscous drops between plates: single, multiple or annular drops

TL;DR

This paper combines theory and experiments to study the behavior of viscous drops between plates, revealing growth laws, stability conditions, and instabilities such as fingering and cavitation under different squeezing and pulling scenarios.

Contribution

It provides a comprehensive analysis of viscous drop evolution between plates, including effects of surface tension, stability, and instabilities like fingering and cavitation, supported by experimental validation.

Findings

Drop radius grows as t^{1/8} under constant force.

Circular drop boundary is stable to small perturbations.

Fingering instability occurs when plates are pulled apart or under certain conditions with trapped air.

Abstract

The behaviour of a viscous drop squeezed between two horizontal planes is treated by both theory and experiment. When the squeezing force F is constant and surface tension is neglected, the theory predicts ultimate growth of the radius a~ t^{1/8}, in excellent agreement with our experiment. Surface tension at the drop boundary is included in the analysis, although negligibly small in the squeezing experiments. The circular evolution is found to be stable under small perturbations. If the force is reversed (F < 0), so that the plates are pulled or levered apart, the boundary of the drop is subject to a fingering instability. The effect of a trapped air bubble at the centre of the drop is then considered. The annular evolution of the drop under constant squeezing is still found to follow a `one-eighth' power law, but this is unstable, the instability originating at the boundary of the air bubble. If the plates are drawn apart, the evolution is still subject to the fingering instability driven from the outer boundary of the annulus. This instability is realised experimentally by levering the plates apart at one corner: fingering develops at the outer boundary and spreads rapidly to the interior as the levering is slowly increased. At a later stage, small cavitation bubbles appear in the very low pressure region far from the point of leverage. This exotic behaviour is discussed in the light of the foregoing theoretical analysis.