Abstract
Interfacial convection due to the Rayleigh effect and the Marangoni effect can enhance mass transfer rates between fluids and is of importance to industrial engineering applications such as gas-liquid absorption and desorption.
Many linear analyses of the Rayleigh effect and the Marangoni effect can be found in scientific literature. However, most linear analyses have been based on the assumption that the liquid phase is stagnant. In the present thesis, the effect of Rayleigh and Marangoni instabilities on solute transfer between a gas phase and a liquid phase which are in parallel, cocurrent, laminar, stratified flow between two rigid horizontal plates has been investigated theoretically and experimentally. Model equations that describe the critical parameters for the onset of cellular convection have been derived, which take into account the effect of surface convection, surface diffusion and surface viscosity in the Gibbs adsorption layer. A piece-wise linear approximation to the penetration theory concentration profile and the non-linear velocity profile of Byers and King (1967) have been used in the model. The classical assumption of a frozen concentration profile has not been made. However, the simplifying assumption of a non-deformable interface has been made. An eigenvalue problem has been formulated for the linearised system. The critical parameters (the eigenvalues) have been numerically computed using a variational principle and the Rayleigh-Ritz method, for a variety of operating conditions.
The critical Rayleigh, Marangoni and wave numbers are found to be functions of the ratio of gas velocity to liquid velocity; the ratio of gas diffusivity to liquid diffusivity; the ratio of gas layer thickness to liquid layer thickness; the ratio of liquid viscosity to gas viscosity; the ratio of mean gas velocity to mean liquid velocity; the gas-liquid equilibrium Henry constant and the dimensionless downstream location. The effects of these ratios on the critical parameters have been investigated numerically for the Bénard-Marangoni problem and Rayleigh-Bénard-Marangoni problem, and compared to the linear analysis of Sun and Fahmy (2006) which used the more general nonlinear penetration theory concentration profile. It was found that the piece-wise linear approximation was a useful approximation, predicting the same trends for critical parameters as predicted by the non-linear concentration profile. In particular the linear analysis predicts that the system stability can be either enhanced or suppressed by increasing the surface convection number and the surface viscosity number, depending on where the operation line is on the Ra-Nia plane. The linear stability analysis also showed that the system would first become unstable at the exit end of the gas-liquid contactor.
An experimental setup, which makes some improvements on the system used by Sun et al. (2002), was used to validate some of the predictions of the theoretical analysis. The experimental setup and methods are described in detail. Experimental results for four sets of experiments involving CO₂ absorption into or desorption out of methanol or toluene films, including schlieren images and video are presented. These results confirm the theoretical prediction that instability would start at the exit end of the gas-liquid contactor and travel upstream as the driving concentration difference is increased. Furthermore, the theoretical prediction that an increase in the ratio of the gas velocity to the liquid velocity would increase the stability of the system, has been confirmed experimentally.
By fitting mass transfer enhancement factor versus driving concentration difference data to a correlation of the form proposed by Sun (2006a), a critical concentration difference has been calculated for each set of experiments. It is found that the theoretically predicted critical parameters can be made close to experimentally measured parameters by a suitable estimate of the viscosity number Vi. For tests involving desorption of CO₂ from methanol, the choice of Vi = 0.43 gave a relative error between experiment and linear theory of less than 20%. It was found that a much larger viscosity number would be required to account for the discrepancy between the theory and experiment in the experiment involving absorption of CO₂ into a toluene film.