# The effect of the liquid layer thickness on the dissolution of immersed surface droplets

## TL;DR

This study investigates how the thickness of the surrounding liquid layer influences the dissolution lifetime of surface droplets, combining numerical simulations and theoretical modeling to provide new insights for device design.

## Contribution

It introduces a theoretical model and numerical analysis showing that droplet lifetime scales with liquid layer thickness, which was previously neglected in models.

## Key findings

- Droplet lifetime is proportional to liquid layer thickness.
- Numerical simulations confirm the theoretical model.
- Provides guidelines for device design involving dissolving droplets.

## Abstract

Droplets on a liquid-immersed solid surface are key elements in many applications, such as high-throughput chemical analysis and droplet-templated porous materials. Such surface droplets dissolve when the surrounding liquid is undersaturated and the dissolution process is usually treated analogous to a sessile droplet evaporating in air. Typically, theoretical models predict the mass loss rate of dissolving droplets as a function of droplet geometrical factors (radius, constant angle), and droplet material properties (diffusion constant and densities), where the thickness of the surrounding liquid layer is neglected. Here, we investigate, both numerically and theoretically, the effect of the thickness of the surrounding liquid layer on the lifetime of dissolving surface droplets. We perform $3D$ lattice Boltzmann simulations and find that the lifetime is proportional to the thickness of the liquid layer. We propose a theoretical model based on a quasistatic diffusion equation which confirms the numerical results. Our results offer insight to the fundamental understanding of dissolving surface droplets and can provide valuable guidelines for the design of devices where the droplet lifetime is of importance.