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We develop an agent-based computational simulation to investigate the complex behavior exhibited by an initially regularly spaced train of immiscible droplets passing through a simple two-branch microfluidic network wherein a channel splits into two asymmetric branches that reconnect downstream. As observed by Fuerstman et al. (M. J. Fuerstman, P. Garstecki and G. M. Whitesides, Science, 2007, 315, 828-832), variations in the flow rates within each segment induced by the droplets cause complex droplet spacing patterns to occur in the outlet, leading to periodic and aperiodic behavior. Our model utilizes a highly efficient agent-based modeling approach, where the flow-rates in each section of the network are determined using fundamental concepts of viscous and interfacial flows. Simulations spanned physical parameter space that includes variation in droplet spacing, surface tension, viscosity and geometry. These simulations demonstrate qualitative agreement with the findings of Fuerstman et al., including the prediction of interspersed periodic and aperiodic domains. We predict that decreasing droplet contribution to the overall pressure drop (reducing the tube radius or surface tension, increasing the viscosity) would result in increased complexity. The geometric configuration of the system is also critical to pattern formation; a greater disparity in branch length generally results in higher-order periodicities in the outflow channel. The aperiodic results indicate the likelihood of chaotic behavior arising from this purely deterministic system. The consideration of fundamental fluid mechanical principles coupled to the agent-based simulation technique may provide a highly efficient means for the design and analysis of more complex systems.

Agent-based simulations of complex droplet pattern formation in a two-branch microfluidic network