Retraction of levitating drops

TL;DR

This study investigates the physical mechanisms and regimes involved in the retraction of levitating drops under zero-gravity, using theoretical analysis and numerical simulations to identify key forces and scaling laws.

Contribution

It introduces a comprehensive analysis of retraction regimes and a new dimensionless parameter, the retraction number, linking retraction time with physical effects.

Findings

Identification of three retraction regimes: capillary-inertial, mixed, and viscous.

Development of a retraction number linking time and physical effects.

Numerical simulations elucidate flow patterns and energy transfer during retraction.

Abstract

This theoretical and numerical study focuses on the physical mechanisms driving the retraction of levitating Newtonian micrometric/millimetric/centimetric drops surrounded by air and under zero-gravity conditions. The drops present a pancake-like initial shape, gradually converging towards a spherical one under surface tension effects. Three drop retraction regimes are observed: capillary-inertial; mixed capillary-inertio-viscous; and capillary-viscous. In the first regime, the retraction is essentially driven by a competition between capillary pressure and inertial stresses, which induces a complex flow with equivalent shear, uniaxial and biaxial components. As the viscous stress becomes comparable to the capillary and the inertial stresses, the second regime emerges while shear-based deformations tend to vanish. Lastly, the third regime is dominated by a balance between capillary and viscous stresses, essentially exhibiting axial deformation. These physical features are underlined through multiphase three-dimensional numerical simulations and analysed in light of retraction dynamics, energy transfer and scaling laws. Our results are rationalised in a two-dimensional diagram linking the drop retraction time with the observed retraction regimes through a single dimensionless parameter combining capillary, inertial, viscous and geometrical effects, i.e., the retraction number.