Role of natural convection in the dissolution of sessile droplets

The dissolution process of small (initial (equivalent) radius R-0 < 1 mm) long-chain 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 alcohol-water mixture is then considerably less than that of pure water, giving rise to buoyancy-driven convection. The convective flow around the droplets is measured, using micro-particle image velocimetry (mu PIV) and the schlieren technique. When non-dimensionalizing the system, we find a universal Sh similar to 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 is the Rayleigh number (dimensionless density difference between clean and alcohol-saturated water). This scaling implies the scaling relation tau(c) alpha R-0(5/4) 0 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 alcohol-saturated plume follows Re-p similar to 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 Ra number as extracted from the data. For Ra 6 Ra-t and smaller, convective transport is progressively overtaken by diffusion and the above scaling relations break down.