Role of natural convection in the dissolution of sessile droplets
Abstract
The dissolution process of small (initial (equivalent) radius $R_0 < 1$ mm) longchain alcohol (of various types) sessile droplets in water is studied, disentangling diffusive and convective contributions. The latter can arise for high solubilities of the alcohol, as the density of the alcoholwater mixture is then considerably less as that of pure water, giving rise to buoyancy driven convection. The convective flow around the droplets is measured, using microparticle image velocimetry ($\mu$PIV) and the schlieren technique. When nondimensionalizing the system, we find a universal $Sh\sim Ra^{1/4}$ scaling relation for all alcohols (of different solubilities) and all droplets in the convective regime. Here Sh is the Sherwood number (dimensionless mass flux) and Ra the Rayleigh number (dimensionless density difference between clean and alcoholsaturated water). This scaling implies the scaling relation $\tau_c \sim R^{5/4}$ of the convective dissolution time $\tau_c$, which is found to agree with experimental data. We show that in the convective regime the plume Reynolds number (the dimensionless velocity) of the detaching alcoholsaturated plume follows $Re_p \sim Sc^{1} Ra^{5/8}$, which is confirmed by the $\mu$PIV data. Here, Sc is the Schmidt number. The convective regime exists when $Ra > Ra_t$, where $Ra_t = 12$ is the transition Ranumber as extracted from the data. For $Ra < Ra_t$ and smaller, convective transport is progressively overtaken by diffusion and the above scaling relations break down.
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 May 2016
 DOI:
 10.1017/jfm.2016.158
 arXiv:
 arXiv:1601.05226
 Bibcode:
 2016JFM...794...45D
 Keywords:

 Physics  Fluid Dynamics