Effect of surfactant on bubble rising velocity in viscous liquid

This paper presents a study of the rising velocity of a single gas bubble in a viscous liquid with a dissolved surfactant and the characteristics of hydrodynamic and diffusion processes on the free surface under conditions of dominance of viscous friction forces over gravitational forces. The original computational method accounting for the surface tension forces and the Marangoni effect caused by the surfactant concentration gradient along the boundary is presented. The mathematical formulation of the problem includes the equations of motion, continuity, and convective diffusion. The boundary conditions on the free surface are written with account for the discontinuity of shear and normal stresses. The surfactant transport on the surface is described in accordance with the Langmuir model. The free surface motion is carried out in compliance with the kinematic condition. The approach is based on the simultaneous use of the finite volume method and the method of invariants, which allows one to explicitly identify a free surface with valid natural boundary conditions. The effect of concentration of surfactants on the characteristics of hydrodynamic and diffusion processes is demonstrated.