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We analyze the migration characteristics of a droplet in an oscillatory flowfield in a parallel plate micro-confinement. Using phase filed formalism, wecapture the dynamical evolution of the droplet over a wide range of thefrequency of the imposed oscillation in the flow field, drop size relative tothe channel gap, and the capillary number. The latter two factors imply thecontribution of droplet deformability, commonly considered in the study ofdroplet migration under steady shear flow conditions. We show that the imposedoscillation brings in additional time complexity in the droplet movement,realized through temporally varying drop-shape, flow direction and the inertialresponse of the droplet. As a consequence, we observe a spatially complicatedpathway of the droplet along the transverse direction, in sharp contrast to thesmooth migration under a similar yet steady shear flow condition. Intuitively,the longitudinal component of the droplet movement is in tandem with the flowcontinuity and evolves with time at the same frequency as that of the imposedoscillation, although, with an amplitude decreasing with the frequency. Thetime complexity of the transverse component of the movement pattern, however,cannot by rationalized through such intuitive arguments. Towards bringing outthe underlying physics, we further endeavor in a reciprocal identity basedanalysis. Following this approach, we unveil the time complexities of thedroplet movement, which appear to be sufficient to rationalize the complexmovement patterns observed through the comprehensive simulation studies. Theseresults can be of profound importance in designing droplet based microfluidicsystems in an oscillatory flow environment.

Droplet migration characteristics in confined oscillatory microflows