Scaling laws in steady-state aqueous foams including Ostwald ripening

This paper presents scaling laws governing the steady-state behavior of pneumatic foams produced by injecting gas in aqueous surfactant solutions under isothermal conditions. Dimensional analysis of the governing equation for the time rate of change of bubble radius in foams due to Ostwald ripening yielded a dimensionless similarity parameter representing the ratio of the average contact time between bubbles to the characteristic time for gas permeation. This dimensionless number was combined with two other dimensionless numbers previously derived for high viscosity fluids and ignoring foam coarsening. Semi-empirical parameters of a power-law relation between these three dimensionless numbers were determined from experimental data collected in the present study as well as from the literature for various gases and aqueous surfactant solutions. They cover a wide range of physical parameters including foam thickness, superficial gas velocity, solubility, surface tension, and average bubble radius.