Stability of particle clusters bound by capillary bridges in extensional flow

Capillary suspensions are commonly encountered in a wide array of applications, but their stability in flow is not fully understood. Here, we investigate the stability of a two-particle capillary cluster in extensional flow using a combination of theory and experiments. A linear stability analysis reveals the existence of a critical capillary number Caj = (8/45) cos 0 that depends only on the contact angle 0. For Ca > Cac, clusters are unconditionally unstable, regardless of initial conditions. For Ca < Cac, a nonlinear analysis shows the existence of a Ca-dependent minimum interparticle separation beyond which breakup occurs. The analytical model further supports the experimentally observed slowdown in relaxation dynamics. Theoretical predictions are supported by precise flow experiments using a Stokes trap, where active flow modulation is used to stabilize an initially unstable cluster in extensional flow. Overall, these results provide a quantitative understanding of capillary suspension stability in flow.