Modeling and simulation of droplet dynamics for microfluidic applications

Abstract

Design of microchannel geometry plays a key role for transport and manipulation of liquid droplets and contraction microchannel has been widely used for many applications in droplet-based microfluidic systems. This study first aims to investigate droplet dynamics in contraction microchannel for more details and then to propose a simplified model used for microfluidic systems to describe droplet dynamics. In particular, for contraction microchannel, three regimes of droplet dynamics, including trap, squeeze and breakup are characterized, which depends on capillary number (Ca) and contraction ratio (C). Theoretical models have been also proposed to describe transitions from one to another regime as a function of capillary number and contraction ratio. The critical capillary number of transition from trap to squeeze has been found as a function of contraction ratio expressed as CaIc=a(CM-1), whereas critical capillary number CaIIc = c1C-1 depicts the transition from squeeze to breakup. Additionally, the deformation, retraction and breakup along downstream of the contraction microchannel have been explored for more details. To describe dynamics of droplet in microfluidic system, one-dimensional model based a Taylor analogy has been proposed to predict droplet deformation at steady state and transient behavior accurately. The characteristic time for droplet reaching steady state is dependent on viscosity ratio and the droplet deformation at steady state is significantly influenced by viscosity ratio of which the order of magnitude ranges from -1 to 1. Finally, theoretical estimation of condition for droplet breakup was also proposed in the present study, which shows a good agreement with experimental result in the literature.