Single bubble velocity profile: Experiments and numerical simulation

A new technique to study the dynamic adsorption of a surfactant on a rising bubble is established, which combines the single bubble velocity profile and numerical solution of the governing equations. Through investigation of the single bubble velocity profiles in water and surfactant solutions, a physical model describing the surface retardation of the bubble and surfactant mass transfer is proposed. A pseudo-steady state approach is employed to solve the mass transfer and fluid flow interactively. Various models are tested against the velocity profile of a 0.8 mm bubble in Triton X-100 solutions as a function of concentration and temperature. The combination of stagnant cap model and boundary layer mass transfer gave good agreement with experiment at 6°C and 25°C. Failure of the model to converge at 45°C is discussed. Terminal velocity in water and surfactant solutions was defined from the profiles and tested against the available models. A new empirical correlation is proposed to estimate terminal velocity in pure water. Surfactant concentration on the bubble surface was estimated from the numerical solution and showed a bubble size and temperature dependence. The application of single bubble velocity profiles to systems of practical interest is considered.