Simulation of interfacial mass transfer by droplet dynamics using the level set method

A unique approach to simulate mass transfer across the moving droplet where mass transport equations and governing equations of the levels set method are solved separately is proposed in this work. Mass transfer coefficients of the chemical species can be computed by equating the diffusive flux and the mass transfer flux at the interface, which are found to be of the same order of magnitude as of those obtained using an empirical correlation. Simulations underestimate mass transfer coefficients by roughly 25% across the range of low Reynolds number studied systematically. The level set method is used to track the motion of the interface to study droplet dynamics and mass transfer across a moving droplet because of the ease in defining the local curvature of the interface and in capturing any topological changes. We perform various numerical simulations by varying the physical properties of the system, in order to analyze the influence of dimensionless numbers such as the Reynolds number (Re), the Eotvos number (Eo) and the Morton number (M  ) on the shape of a buoyancy-driven droplet and compare them with the various shape regimes of drops and bubbles reported by Clift et al. [1978. Bubbles, Drops and Particles. Academic Press, New York]. It is shown that larger deformation occurs for buoyancy-driven droplets when interfacial forces are considerably greater than viscous forces (M⩽1M⩽1 and Eo>10Eo>10) and the droplets are almost undeformed when viscous forces dominate interfacial forces (M>103M>103 and Eo>10Eo>10).