| Popis: |
The fundamental gas bubble expansion/contraction rate equation derived in Chapter 3, for a spherical gas bubble suspended in a simple liquid medium, i.e., dR/dt=3RTDR(∂c/∂r)R,t−R2dPh/dt3PhR+4γ is solved in this chapter for a range of different conditions and approximations. Its solution, i.e., its integrated form—which provides the bubble radius R vs. time t explicitly—requires an explicit expression for the dissolved solute concentration gradient in the medium at the bubble’s surface (∂c/∂r)R, t. However, the form obtained for this term depends on a variety of choices that can be made. It depends on whether one solves the full diffusion equation or the simpler Laplace equation (the steady-state approximation of the diffusion equation) and on the details of the gas bubble diffusion model that is chosen. Here we provide solutions for the radius vs. time of a dissolving gas bubble for both the full diffusion equation and the Laplace equation, for fixed and variable ambient pressures, for Dirichlet vs. Neumann boundary conditions applied at the gas bubble/medium interface, and for both two-region (infinite diffusion medium) and three-region (finite diffusion medium) gas bubble diffusion models. A comparison of the results obtained by applying Dirichlet, as opposed to Neumann, boundary conditions at the bubble/medium interface indicated that both methods provide essentially the same predictions for small gas bubbles ( |
