Scaling crossover in thin-film drag dynamics of fluid drops in the Hele-Shaw cell

TL;DR

This paper investigates the gravity-driven motion of fluid drops in a Hele-Shaw cell, revealing a new nonlinear drag regime governed by thin film dissipation and identifying a crossover to a different dissipation-dominated regime.

Contribution

It introduces a new scaling law for nonlinear drag in viscous liquids and demonstrates the crossover between different dissipation regimes in confined fluid drops.

Findings

Discovery of a new nonlinear drag scaling law.

Experimental data collapse using the new scaling law.

Identification of a crossover between thin film and internal dissipation regimes.

Abstract

We study both experimentally and theoretically the descending motion due to gravity of a fluid drop surrounded by another immiscible fluid in a confined space between two parallel plates, i.e., in the Hele-Shaw cell. As a result, we show a new scaling regime of a nonlinear drag friction in viscous liquid that replaces the well-known Stokes' drag friction through a clear collapse of experimental data thanks to the scaling law. In the novel regime, the dissipation in the liquid thin film formed between the drop and cell walls governs the dynamics. The crossover of this scaling regime to another scaling regime in which the dissipation inside the droplet is dominant is clearly demonstrated and a phase diagram separating these scaling regimes is presented.