Thermocapillary and solutocapillary flows near the air–liquid interface with the interfacial rheology

Under the assumption of the extended conically similar viscous flow, the roles of interfacial rheology in thermocapillary and solutocapillary flows near the air–liquid interface driven by a point heat source and a point mass source are shown. By taking the surface viscosity as a small parameter and applying the second-order perturbation expansion method, the steady thermocapillary and solutocapillary flows at several system parameters are investigated. In the first-order solution, the velocity field displays the radial divergent motion near the interface and the radial convergent motion far from the interface. The heat and the soluble surfactant are transferred from the zone near the symmetric axis toward the interface. In the second-order solution, the velocity field shows the radial motion divergent or convergent at the interface. A single or double clockwise/counterclockwise rotating flow is formed beneath the interface. The heat and the soluble surfactant are basically transferred from the interface toward the zone near the symmetric axis and in reverse, respectively. In comparison with basic solutions for the thermocapillary and solutocapillary flows near the air–liquid interface without the interfacial rheology, the interfacial rheology still maintains the original distributions of the velocity, the temperature, and the concentration fields, but changes their amplitudes depending on the values of system parameters and the surface viscosity. The appropriate values of the surface viscosity are suggested in the comparison to the experimental results. Finally, the influence of surface tensions caused by the temperature and the concentration gradients on the steady thermocapillary and solutocapillary flows is explored.