The engulfment of aqueous droplets on perfectly wetting oil layers

TL;DR

This study investigates the dynamics of aqueous droplets being engulfed by a layer of oil, revealing how droplet size, viscosity, and gravity influence the process, with implications for understanding oil spill behavior.

Contribution

It provides a detailed analysis of droplet engulfment dynamics across different sizes and viscosities, highlighting the roles of capillary and gravitational forces in the process.

Findings

Engulfment time depends on droplet size and oil viscosity.

Two distinct stages of engulfment: rapid capillary-driven and slow gravity-driven.

Power law relationship between viscosity and engulfment time.

Abstract

Place a droplet of mineral oil on water and the oil will spread to cover the water surface in a thin film -- a phenomenon familiar to many, owing to the rainbow-faced puddles left behind leaking buses on rainy days. In this paper we study the everted problem: an aqueous droplet deposited onto a deep layer of silicone oil. As it is energetically favourable for the oil phase to spread to cover the droplet surface completely, the droplet is ultimately engulfed in the oil layer. We present a detailed study of engulfment dynamics, from the instant the droplet first impacts the oil surface until it finally sediments into the less dense oil. We study a broad range of droplet sizes (micrometric to millimetric) and oil kinematic viscosities ($10^2$ to $10^5$ cSt), corresponding to a viscosity-dominated parameter regime with relevance to oil spills. Our investigation primarily examines droplet engulfment dynamics over two distinct stages: a rapid earlier stage in which the droplet is almost entirely submerged, driven by capillary forces in the oil surface, and cloaked by a thin layer of oil; and a much slower later stage in which gravity pulls on the drop adhered to the oil surface, thus driving a peeling flow. This means that gravitational effects are essential to complete the engulfmet of the droplet, even for micrometric droplets. We observe the longest engulfment times for droplets of intermediate size. Experiments at fixed droplet size reveal a power law dependence of engulfment time on oil kinematic viscosity.