Convection-dominated dissolution for single and multiple immersed sessile droplets

Abstract

We numerically investigate both single and multiple droplet dissolution with droplets consisting of lighter liquid dissolving in a denser host liquid. The significance of buoyancy is quantified by the Rayleigh number Ra which is the buoyancy force over the viscous damping force. In this study, Ra spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number Sh, and the flow morphologies depend on Ra. For single droplet dissolution, we first show the transition of the Sh(Ra) scaling from a constant value to $Sh\sim R{a}^{1/4}$, which confirms the experimental results by Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45--67). The two distinct regimes, namely the diffusively- and the convectively-dominated regime, exhibit different flow morphologies: when Ra>=10, a buoyant plume is clearly visible which contrasts sharply to the pure diffusion case at low Ra. For multiple droplet dissolution, the well-known shielding effect comes into play at low Ra so that the dissolution rate is slower as compared to the single droplet case. However, at high Ra, convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. This has also been found in the experiments by Laghezza et al. (Soft Matter, vol. 12, 2016, pp. 5787--5796). We explain this enhancement by the formation of a single, larger plume rather than several individual plumes. Moreover, there is an optimal Ra at which the enhancement is maximized, because the single plume is narrower at larger Ra, which thus hinders the enhancement. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, that leads to non-trivial phenomena, contrasting the shielding effect.

18 pages, 11 figures, submitted to JFM

References in corpus (14)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Evaporation-triggered microdroplet nucleation and the four life phases of an evaporating Ouzo drop
• Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking
• Gravitational effect in evaporating binary microdroplets
• A multiple--resolution strategy for Direct Numerical Simulation of scalar turbulence
• Evaporation-triggered segregation of sessile binary droplets
• Diffusive interaction of multiple surface nanobubbles and nanodroplets: shrinkage, growth, and coarsening
• A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes
• Stick-jump mode in surface droplet dissolution
• Role of natural convection in the dissolution of sessile droplets
• Microdroplets nucleation by dissolution of a multicomponent drop in a host liquid
• Entrapment and Dissolution of Microbubbles Inside Microwells
• Generalizing Co-operative Evaporation in Two-Dimensional Droplet Arrays
• The effect of the liquid layer thickness on the dissolution of immersed surface droplets

Cited by in corpus (10)

• The effect of buoyancy driven convection on the growth and dissolution of bubbles on electrodes
• Sessile drop evaporation in a gap -- crossover between diffusion-limited and phase transition-limited regime
• Rayleigh-Taylor instability by segregation in an evaporating multi-component microdroplet
• Physiochemical hydrodynamics of the phase segregation in an evaporating binary microdroplet
• Interplay of transport mechanisms during the evaporation of a pinned sessile water droplet
• Universal dissolution dynamics of a confined sessile droplet
• Oscillatory droplet dissolution from competing Marangoni and gravitational flows
• Slug bubble growth and dissolution by solute exchange
• Collective effects of neighbouring melting ice objects
• Internal flow and concentration in neighbouring evaporating binary droplets and rivulets