Shape and motion of drops in the inertial regime

TL;DR

This study experimentally investigates the shape and motion of mercury droplets in a rotating cylinder at high Reynolds numbers, revealing distinct regimes and refining existing models for contact angle transitions and dissipation.

Contribution

The paper introduces modified dissipation estimates near the solid surface and identifies three droplet regimes, providing experimental validation for extended de Gennes and Cox-Voinov models.

Findings

Identified three droplet regimes: oval, corner, cusping.

Transition at a finite receding contact angle of 950.

Close agreement between extended de Gennes model and experimental critical contact angle ratio.

Abstract

In this paper, we report experimental results on the shape and motion of a mercury droplet, placed in a horizontally rotating cylinder in the rpm range 8-93, so that the Reynolds number of the drop 2500<Re<26000 and its capillary number 0.0002<Ca<0.0023. When contact angle variations can be neglected at low speeds (Re<8150), the velocity of the drop is much lower than that predicted by the Ho. Young Kim's [6] relation. This observed discrepancy is overcome by modifying Kim's relation by substituting the dissipation estimated from a boundary layer near the solid surface instead of bulk dissipation. Based on the changes at the rear side of the mercury droplet, there are three distinct regimes identified with varying speeds of rotation (i) oval or rounded regime (ii) corner regime and (iii) cusping regime. The oval to corner transition happens at a finite receding contact angle of 950. The ratio of critical contact angle ({\theta}c) at which the transition occurs to the static receding contact angle ({\theta}s) was found to be 0.657. The de Gennes model [4], extended to high contact angle by substituting the dissipation for wedge flow, predicts a critical contact angle ratio ({\theta}c/{\theta}s) that is in close agreement with the experimental value. At higher Re, the dynamic contact angle variation with velocity was compared with Cox-Voinov model [3]. Though the trend of the variation of data is approximately represented by the model, the fit coefficient according to experimental data is very high when compared to theoretical value.