Droplet dissolution driven by emerging thermal gradients and Marangoni flow

TL;DR

This study uncovers a new droplet dissolution regime driven by thermal gradients and Marangoni flow, where the lifetime scales as the fourth power of the initial radius, differing from classical diffusion and convection models.

Contribution

The paper introduces and explains a novel droplet dissolution behavior caused by thermal Marangoni flow induced by plasmonic heating, expanding understanding of dissolution dynamics.

Findings

Dissolution lifetime scales as R_0^4 under thermal Marangoni flow.

Thermal gradients modify solubility and induce flow, accelerating dissolution.

Droplet radius shrinks as (τ - t)^{1/4} during dissolution.

Abstract

The lifetime $\tau$ of an isothermal and purely diffusively dissolving droplet in a host liquid scales as $\tau \sim R_0^2$ with its initial radius $R_0$ [Langmuir, Phys. Rev. 12, 368 (1919)]. For a droplet dissolving due to natural convection driven by density differences, its lifetime scales as $\tau\sim R_0^{5/4}$ [Dietrich et al., J. Fluid Mech. 794, 45 (2016)]. In this paper we experimentally find and theoretically derive yet another droplet dissolution behavior, resulting in $\tau \sim R_0^4$. It occurs when the dissolution dynamics is controlled by local heating of the liquid, leading to a modified solubility and a thermal Marangoni flow around the droplet. The thermal gradient is achieved by plasmonic heating of a gold nanoparticle decorated sample surface, on which a sessile water droplet immersed in water-saturated 1-butanol solution is sitting. The resulting off-wall thermal Marangoni flow and the temperature dependence of the solubility determine the droplet dissolution rate, resulting in a shrinkage $R(t) \sim (\tau -t )^{1/4}$ of the droplet radius and thus in $\tau \sim R_0^{4}$.