Timescale and spatial distribution of local plastic events in a two-dimensional microfluidic crystal

When a microfluidic crystal consisting of a concentrated emulsion flows in a convergent channel, the boundary conditions enforce a sequence of droplet rearrangements, also known as T1 events. At low flow rates, these T1 events are shown to be periodic both in space and in time, giving rise to a surprisingly ordered flow pattern. At high flow rates, however, the order is lost. To understand the transition from order to disorder, this paper examines the timescale and the spatial distribution of T1 events during the flow of a monolayer of monodisperse droplets within a concentrated emulsion confined in a convergent tapered microchannel. We show that the duration of a single T1 event consists of three distinct regimes with two transitions upon an increase in the applied flow rate. The first transition can be understood as a change in the forces that dominate during the T1 event, and the second transition can be associated with the emulsion transitioning from a solidlike state to a liquidlike state. Our results suggest that the loss of order in the flow of the concentrated emulsion, or the microfluidic crystal, is directly associated with the solidlike to liquidlike transition of the emulsion. Practically, our results are significant in understanding the relationship between the macroscopic property and the microscopic flow structures of the emulsion, as well as in guiding the design of flow control elements in microfluidic devices.