A simple and fast microfluidic control of two Hele-Shaw droplets towards coalescence

We present a simple and fast strategy to steer two channel-spanning (Hele-Shaw) soft particles along independent and arbitrary paths by utilizing the hydrodynamic force in a six-port, two stagnation point microfluidic device. Using the conformal mapping technique, the analytical solution of the flow field that accounts for the perturbation of the flow due to the hydrodynamic interactions between the particles was developed and implemented in the control loop to calculate the flow rates. In this method, the particles move along the straight line connecting their instantaneous position to the final position, at the velocity prescribed by the user through a single control parameter. The control parameter that is the ratio of the time required for fluid motion to the time scale of the control can also adjust the number and location of the stagnation points. These features were exploited to design and perform controlled head-on and glancing collisions for ~100 μm radius Hele-Shaw perfluorodecalin drops moving at O(100 μm/s) in silicone oil. The coalescence time between two Hele-Shaw drops undergoing a head-on collision in a dimpled mode was found to be independent of the strain rate of the hydrodynamic flow. For Hele-Shaw drops undergoing glancing collision on the other hand, the dimensionless coalescence time increases with the capillary number (ratio of the viscous to interfacial force) and reduces with the initial offset.