Modeling capillary droplet breakup when flowing through microfluidic obstacle arrays

The dynamics of the breakup of capillary droplets flowing through microfluidic obstacle arrays is governed by surface tension, viscous forces, and spatially non-uniform flow fields. We present a phenomenological deformable particle (DP) model for droplet breakup in quasi-two-dimensional systems. We carry out simulations of the DP model for a single droplet interacting with a single obstacle as a function of the droplet-obstacle impact parameter, capillary number Ca, and ratio r of the sizes of the droplet and obstacle. We find that the boundary in parameter space separating droplet break-up from no break-up scales as (Ca*r)^λ, where λ≈ -0.74, which is consistent with experiments on quasi-2D oil droplets in water flowing past a single obstacle. Using the DP model, we then carry out simulations of multiple droplets flowing through arrays of randomly distributed obstacles. The droplets undergo repeated breakups, reaching a steady-state average size distribution after the droplets travel a distance d through the array. We show that the average size of the daughter droplets depends on the minimum spacing between obstacles and the obstacle size.