Universal dissolution dynamics of a confined sessile droplet

Abstract

We experimentally investigate the dissolution of microscale sessile alcohol droplets in water under the influence of impermeable vertical confinement. The introduction of confinement suppresses the mass transport from the droplet to bulk medium in comparison with the non-confined counterpart. Along with a buoyant plume, flow visualization reveals that the dissolution of a confined droplet is hindered by a newly identified mechanism - levitated toroidal vortex. The morphological changes in the flow due to the vortex-induced impediment alters the dissolution rate, resulting in enhancement of droplet lifetime. Further, we have proposed a modification in the key non-dimensional parameters (Rayleigh number $Ra^{'}$ (signifying buoyancy) and Sherwood number $Sh^{'}$ (signifying mass flux)) and droplet lifetime $\tau_{c}^{'}$, based on the hypothesis of linearly stratified droplet surroundings (with revised concentration difference $\Delta C^{'}$), taking into account the geometry of the confinements. We show that experimental results on droplet dissolution under vertical confinement corroborate universal scaling relations $Sh^{'} \sim Ra^{' 1/4}$ and $\tau_{c}^{'} \sim \Delta C^{'-5/4}$. We also draw attention to the fact that the revised scaling law incorporating the geometry of confinements proposed in the present work can be extended to other known configurations such as droplet dissolution inside a range of channel dimensions, as encountered in a gamut of applications such as micro-fluidic technology and biomedical engineering.