Lattice–Boltzmann simulations of dynamic interfacial tension due to soluble amphiphilic surfactant

An amphiphilic Lattice–Boltzmann approach is adopted to model dynamic interfacial tension due to non-ionic surfactant. In the current system, the surfactant adsorption kinetics is diffusion dominated and the interface separates two immiscible fluids. A rotational relaxation time and a diffusive/viscous relaxation time are associated with the surfactant. The model results are compared with experimental data for the dynamic interfacial tension of a pendant oil droplet in water, with oil soluble surfactant. We demonstrate how to adapt and calibrate the model to capture the adsorption timescale of the surfactant and the magnitude of interfacial tension reduction due to surfactant. A scheme to overcome numerical instabilities due to the relatively low surfactant concentration, is devised. We are able to qualitatively match the Frumkin equation of state for the interfacial tension.