A tractable mathematical model for rectified diffusion

A core unresolved challenge in rectified diffusion is the lack of predictive models, which allow accurate modelling growth bubbles over millions cycles oscillation. The spherically symmetric problem involves two asymptotic regions space for convection and dissolved gas liquid, an inner region adjacent to bubble outer region. It also three time scales: shortest scale associated with oscillation, intermediate longest scales mass transport across interface region, respectively. analysed systematically using matched expansions multi-scales time, large parameter being Péclet number transfer. tractable mathematical model formulated diffusion. comprises Rayleigh–Plesset equation spherical oscillations on scale, ordinary differential a long length scale. Predictions this simplified have excellent agreement experimental results single bulk parametric study undertaken several new phenomena/features observed acoustic frequencies range 12 62 kHz, field $0.12$ $0.22$ bar initial concentration liquid $0.95$ $1.0$ saturation concentration.