A model of bubble coalescence in the presence of a nonionic surfactant with a low bubble approach velocity

A bubble coalescence model for a solution with a nonionic surfactant and with a small bubble approach velocity was developed, in which the mechanism of how coalescence is hindered by Marangoni stress was quantitatively analyzed. The bubble coalescence time calculated for ethanol-water and MIBC-water systems were in good agreement with experimental data. At low surfactant concentrations, the Marangoni stress and bubble coalescence time increased with bulk concentration increase. Conversely, in the high concentration range, the Marangoni stress and coalescence time decreased with bulk concentration. Numerical results showed that the nonlinear relationship between coalescence time and surfactant concentration is determined by the mass transport flux between the film and its interface, which tends to diminish the spatial concentration variation of the interface, i.e., it acts as a “damper”. This damping effect increases with increased surfactant concentration, therefore decreasing the coalescence time at high concentrations.

Marangoni stress induced by rotation frustration in a liquid foam

Bubble rotation during foam deformation is deduced from the Marangoni stress consistency.

Sedimentation of a surfactant-laden drop under the influence of an electric field

The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the combined effect of electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric drop is sedimenting in another leaky dielectric fluid, the Marangoni stress can oppose the electrohydrodynamic motion severely, thereby causing corresponding changes in the internal flow pattern. Such effects further result in retardation of the drop settling velocity, which would have otherwise increased due to the influence of charge convection. For non-spherical drop shapes, the effect of Marangoni stress is overcome by the ‘tip-stretching’ effect on the flow field. As a result, the drop deformation gets intensified with an increase in sensitivity of the surface tension to the local surfactant concentration. Consequently, for an oblate type of deformation the elevated drag force causes a further reduction in velocity. For similar reasons, prolate drops experience less drag and settle faster than the surfactant-free case. In addition to this, with increased sensitivity of the interfacial tension to the surfactant concentration, the asymmetric deformation about the equator gets suppressed. These findings may turn out to be of fundamental significance towards designing electrohydrodynamically actuated droplet-based microfluidic systems that are intrinsically tunable by varying the surfactant concentration.