Relaxation oscillations of solutal Marangoni convection at curved interfaces

Abstract

Relaxation oscillations in a two-phase system, consisting of paraffin oil and water, with 2-propanol initially dissolved in the oil phase, are observed as a periodic decay and re-amplification of interfacial convection. Due to the mass transfer of the weakly surface-active 2-propanol, concentration gradients and, by implication, density gradients exist. This leads to a periodic coupling of Marangoni instability, buoyant convection and the restoring effects of diffusion. The relaxation oscillations are facilitated by the presence of interfacial curvature, which imposes additional gradients of interfacial tension. This effect is particularly pronounced around drops or bubbles formed in the experiments. The markedly regular relaxation oscillations appearing in that case have been further studied by 2D Hele-Shaw simulations based on a diffuse-interface model. Interfacial tension is assumed to depend linearly on 2-propanol concentration without accumulation of matter at the interface. This simplified approach is capable of reproducing the relaxation oscillations observed experimentally.