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