Mechanisms of mass transport during coalescence-induced microfluidic drop dilution

Confinement-guided coalescence of drops in microfluidic devices is an effective means to manipulate the composition of individual droplets. Recently, Sun et al. [Lab Chip 11, 3949 (2011)] have shown that coalescence between a long moving plug and an array of parked droplets in a microfluidic network can be used to flexibly manipulate the composition of the static droplet arrays. However, the transport mechanisms underlying this complex dilution process have not been elucidated. In this study, we develop phenomenological models and perform particle-based numerical simulations to identify the key mass transfer mechanisms influencing the concentration profiles of drops during coalescence-induced drop dilution. Motivated by experimental observations, in the simulations we consider (i) advection within the moving plug, (ii) diffusion in the moving plug and parked droplets, (iii) fluid advection due to initiation of coalescence, and (iv) advection in the coalesced plug due to the continuous phase flowing through the gutters in noncircular microchannels. We find that the dilution process is dominated by diffusion, recirculation in the moving plug, and gutter-flow-induced advection, but is only weakly affected by coalescence-induced advection. We show that the control parameters regulating dilution can be divided into those influencing the duration of mass transfer (e.g., plug length and velocity) and those affecting the rate of mass transfer (e.g., diffusion and gutter-flow-induced advection). Finally, we demonstrate that our simulations are able to predict droplet concentration profiles in experiments. The results from this study will allow better design of drop dilution microfluidic devices. Furthermore, the identification of gutter-flow-induced advection as an alternative mass transfer mechanism in two-phase flows could potentially lead to more efficient means of oil recovery from droplets trapped in porous media.