|M.Sc Thesis||Department of Mechanical Engineering|
|Assoc. Prof. Gendelman Oleg|
|Full Thesis text|
The current study investigates the influence of the concentration dependent diffusion coefficient on the bubble growth process. Three different diffusivities, which are based on different physical models, are considered. Isothermal growth was assumed and it was shown that the concentration boundary layer remained thin for all the cases, thus validating the assumption. The problem is solved numerically for constant and variable pressure assumptions and also for the equilibrium Henry's law and kinetic boundary conditions.
All the numerical solutions were obtained with a finite difference method which was second order accurate in both time and coordinate. Crank-Nicolson scheme was used for all cases.
Similarity solution was obtained for the constant bubble pressure case and its validity was tested against the numerical solution. The similarity solution agreed with the numerical solution, except for the very early stages of the growth. It was also shown that the similarity solution provides a good approximation even when solving the problem with variable bubble pressure or the kinetic boundary condition.
It was shown that the solution with the kinetic boundary condition does not differ much from the solution with equilibrium Henry's law.
The study showed that higher values of diffusivity usually result in higher growth rates, but other physical parameters have to be considered in modeling the bubble growth. It was shown that high values of viscosity - the practical case in concentrated polymer solutions - can slow the growth considerably. Same happens with high values of the surface tension.
The main result of the study was the following - for sufficiently large times the bubble radius will grow as square root of time for all possible combinations of concentration dependent diffusivities and boundary conditions.