Singularities with surfactants

Drop coalescence originates from a finite-time hydrodynamic singularity--the moment when two interfaces merge and a liquid bridge forms from zero radius. This topological transition exemplifies how singular events in fluid mechanics exhibit self-similar dynamics and universal scaling laws, providing fundamental insights into nonlinear phenomena. While these singularities have been extensively studied in pure fluids, most practical liquids, such as those used in inkjet printing, pharmaceutical emulsions, food products, and oil recovery, contain surfactants that fundamentally alter the singular behavior by coupling surface chemistry to flow. Here we investigate how insoluble surfactants modify coalescence singularities through high-fidelity numerical simulations and theoretical modeling, considering a surfactant-laden drop merging with a clean drop.