Simulation of liquid mixing inside micro-droplets by a lattice Boltzmann method

We investigated the fundamental aspects of liquid mixing process inside micro-droplets using a recently developed numerical model (Riaud et al., 2014. Phys. Rev. E 89, 053308). Specifically, a two-phase color-gradient model was applied to simulate the generation of droplets in microchannels, while passive tracers only soluble in the dispersed phase were added into the model to characterize the mixing of the solutes without influence on the macroscopic flow field. After introducing the dilute species redistribution scheme and its implementation, the model was validated extensively. We used this numerical method to study the internal mixing of droplets and slugs moving in microchannels. Some of the major influencing factors such as the moving velocity, shape and dimensions of the micro-droplets were tuned to get a comprehensive characterization of the mixing behavior. Depending on flowing time, two successive mixing mechanisms in plugs/droplets moving in a straight channel were disclosed. Firstly there is a fast unsteady convection-dominated stage, at which the mass transfer in the slugs/droplets is controlled by the recirculation motion. However, it turns out to have some stagnant points where convection is inefficient in moving slugs and droplets. The second mixing mechanism is a slower molecular diffusion. At this stage, the solute gradually escapes from the stagnant regions of the droplet and improves the mixing. We further demonstrated that the slow liquid mixing in the latter stage could be spared by adding baffles in the channel to arbitrarily manipulate the two independent circulation zones so as to avoid the existence of the stagnation points in droplets/slugs.