Passive mixing rate of trapped squeezed nanodroplets—A time scale analysis

The elegance of digital microfluidics is in incorporating high quantities of manipulated micro and nanodroplets on-chip, each of which can be considered a small-volume carrier of various chemical and biological reagents. Therefore, the analysis of on-demand manipulation of these micro and nanocarriers is extremely important in developing an optimized lab on a chip. In this work, passive coalescence and mixing between two trapped, squeezed nanodroplets inside a closed microfluidic device was investigated. The droplets are composed of glycerol dyed in blue and red, dispersed inside oleic acid as the carrier oil. A microwell with a circular cross section was fabricated on the top wall of the microchannels to trap the first droplet for increasing the mixing precision and minimizing the viscous shear stress imposed on the droplets from the channel walls. The energy minimization theory was used to develop a parametric study for this trapping technique and to choose the optimum design parameters for droplet trapping in terms of efficiency. Image processing was performed on the snapshots of the trapped glycerol nanodroplets during mixing. Growth in passive mixing percentage was demonstrated to be asymptotical and was formulated with an empirical equation of exponential form as a function of the passive mixing relaxation time. The required time for the passive mixing of a glycerol droplet pair was measured considering various thresholds for the final standard deviation of the gray intensity indices. This finding was of the order of magnitude of the diffusive mixing time scale and physically consistent with the Stokes flow regime.