Sessile drop coalescence with surfactants

Coalescing drops form finite‑time singularities when a liquid bridge emerges from zero radius. Surfactants — ubiquitous in applications such as inkjet printing, emulsions and oil recovery — couple interfacial chemistry and hydrodynamics and thus change this universal behavior. High‑fidelity lubrication simulations and asymptotic analysis are used to study how an insoluble monolayer on one drop dictates how it coalesces with a clean one. The problem is governed by three dimensionless parameters: surfactant strength number β (relative surface tension reduction), a Peclet number Pe comparing advection with surface diffusion, and the initial contact angle θ. When diffusion dominates (Pe << 1), the neck height grows linearly in time as h₀ ~ (1-Γ₀/2)θ⁴t, preserving self-similarity but with a reduced capillary driving. Moreover, Marangoni stresses break the left-right symmetry and drive horizontal motion x₀ ~ t^3/2. When advection dominates (Pe >> 1), surfactants fundamentally change the singularity: above a critical strength, Marangoni stresses arrest coalescence, while below this threshold the singularity escapes via vorticity generation. In the purely advective limit, new singularities appear: kinematic shocks with discontinuous velocity and pressure fields described by Burgers‑like equations. These findings show how surfactants modify and even create singular behaviors, offering new strategies for controlling drop coalescence and self‑similar flows in industrial and natural settings.