Satellite-droplet formation regimes in the natural breakup of clean and surfactant-laden liquid threads

We report a numerical study of the natural breakup of Newtonian liquid threads whose cylindrical interface is coated with insoluble surfactants. A parametric study is performed to quantify the influence of the Laplace number, La, and the elasticity parameter, β, on the volume of the satellite droplet formed just prior to pinch-off, V_sat, on the mass of surfactant trapped at its surface, Σ_sat, on the break-up time, and on its shape. For a clean interface, we provide a new scaling law for the satellite volume normalized with the total volume, namely V_sat = 0.00421 La^1.64, valid for 0.05<La<1. When La<0.05, V_sat becomes negligible, and for La>10 it reaches a plateau of about 3%. In the surfactant-laden case, for La>7.5, V_sat displays a local minimum in β, but has small relative variations around the 3%, while the mass of surfactant increases monotonously. For 1.69<La<7.5, there is a discontinuous transition at β = β_c(La), in V_sat and Σ_sat.