  A theoretical formulation is proposed for forced mass transport by pressure
gradients in a liquid binary mixture around a spherical bubble undergoing
volume oscillations in a sound field. Assuming the impermeability of the bubble
wall to both species, diffusion driven by pressure gradients and classical
Fick-diffusion must cancel at the bubble wall, so that an oscillatory
concentration gradient arises in the vicinity of the bubble. The Peclet number
Pe is generally high in typical situations and Fick diffusion cannot restore
equilibrium immediately, so that an asymptotic average concentration profile
may progressively build up in the liquid over large times. Such a behavior is
reminiscent of the so-called rectified diffusion problem, leading to slow
growth of gas bubble oscillating in a sound field. A rigorous method formerly
proposed by Fyrillas & Szeri (1994) to solve the latter problem is used in this
paper to solve the present one. It is based on splitting the problem into a
smooth part and an oscillatory part. [...] For driving pressures sufficiently
high to yield inertial oscillations of the bubble, the oscillatory problem
predicts a periodic peak excess concentration of the heaviest species at the
bubble wall at each collapse, lingering on several tens of time the
characteristic duration of the bubble rebound. The two effects may compete for
large molecules and practical implications of this segregation phenomenon are
proposed for various processes involving acoustic cavitation.
