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 ${\text{Ca}}_c=(8/45)cos\theta$ that depends only on the contact angle $\theta$. For $\text{Ca}>{\text{Ca}}_c$, clusters are unconditionally unstable, regardless of initial conditions. For $\text{Ca} < {\text{Ca}}_c$, a nonlinear analysis shows the existence of a $\text{Ca}$-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.

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• Capillary interactions
• Flow instability
• Colloids
• Suspensions
• Hydrodynamics