Effects of interfacial rheology on solutocapillary convection near the air–liquid interface

The roles of interfacial rheology in solutocapillary convection near the air–liquid interface driven by a point mass source are investigated. First, the assumption of the conically similar viscous flow is successfully extended to treat the effects of interfacial rheology on solutocapillary convection near the air–liquid interface. By taking the surface viscosity as a small parameter, the steady solutocapillary convection is analyzed by applying the matched asymptotic expansion method. For small Re numbers and small/large Sc numbers, the exact solutions of the solutocapillary convection are shown. It is found that, to generate the first-order surface tension, the interfacial rheology related to the leading order solution is more dominant than the first-order concentration gradient of surfactant. Moreover, for general physical parameters, the governing equations of the solutocapillary convection for the perturbation solutions are numerically solved by applying the shooting method. In comparison with basic solutions for the solutocapillary convection near the air–liquid interface without the interfacial rheology, the interfacial rheology enhances both the divergent flow near the interface and the convergent flow far from the interface. Its effects on the distribution of surfactant depend on Pe number. For small/large Pe numbers, the interfacial rheology slightly/greatly increases the distribution of the surfactant near the interface and slightly/greatly decreases the distribution of the surfactant near the symmetric axis.