Theoretical and Experimental Investigations of Transient Rayleigh-Bénard-Marangoni Convection Enhanced Mass Transfer
Convection due to the Rayleigh and Marangoni effects is known to enhance heat and/or mass transfer between two phases by as much as an order of magnitude in industrially important processes. In gas-liquid solute transfer applications this type of convection is often driven by a transient penetration type solute concentration profile. The ability to model solute transfer enhancement under such nonlinear transient concentration profiles works towards the objective of optimising such processes. In this thesis, a model of mass transfer enhancement under Rayleigh-Bénard-Marangoni convection is developed from the soluto-hydrodynamics of a gas-liquid solute transfer system. This model is developed under a penetration type base concentration profile and employing a weakly nonlinear approximation to describe slightly supercritical convection. This work improves upon recent related works by retaining a full nonlinear penetration profile throughout the development of the mass transfer enhancement model. A transient mass transfer enhancement model for roll and hexagonal convection patterns, based on the evolution of autonomous amplitude equations having spatially inhomogeneous advective terms is proposed. The model operates under a quasistatic approximation which is applicable for solute transfer in thin liquid layers. An experimental setup with the necessary sensitivity to study the weakly nonlinear mass transfer regime has been developed and used to test the proposed mass transfer enhancement model. Through numerical investigation of the convective amplitudes, it is shown that the spatially nonhomogeneous advective terms can be neglected when estimating the quasistatic amplitudes of roll and hexagonal convection, provided the planform is apriori known. When this is the case, the error introduced by neglecting the spatially nonhomogeneous terms is in the range 1 to 7%. Numerical investigations also indicate that hexagonal structures with vortex motion down the centre flow, similar to the case of Rayleigh-Bénard convection in a rotating fluid are possible with a penetration type base concentration profile. It is also found that for a large range of operating conditions, roll convection gives higher mass transfer rates over hexagonal convection. Under both roll and hexagonal convection, systems dominated by the Marangoni effect are found to produce the highest mass transfer rates. Furthermore, for any specified gas-liquid system it is possible to optimise the mass transfer enhancement by adjusting the ratio of the Marangoni number to the Rayleigh number. The proposed model of mass transfer enhancement under penetration conditions predicts an exponential-power law relationship between mass transfer enhancement and gas-liquid contact time. This is shown to be in good agreement with experimental measurements in the weakly nonlinear regime of the CO2-isobutanol system. The deviations between measured mass transfer rates and predicted mass transfer rates in this system was found to be between 3.4 and 13.5%. The variations of critical wavenumbers estimated from spectral analysis of schlieren images were found to be in agreement with quasistatic predictions in thin layers and at long critical contact times. In practice, gas-liquid solute transfer systems are finite in size and as a result, deviations from penetration theory will be observed at long times after initial gas-liquid contact. This work also explores these deviations in a linear stability analysis as well as experimentally. Under these conditions it is found that the critical Rayleigh and Marangoni numbers reach a minimum and thereafter increase with contact time. The onset of convection is then determined by the competition between system operation Rayleigh and Marangoni numbers and critical thresholds. As a result, within certain operation regimes of the system, only a limited period of convective instability is possible and a transient maximum of convective intensity is observed. This opens up the possibility of optimising gas-liquid contactors with respect to Rayleigh and Marangoni convection enhanced mass transfer. Experimental measurements are shown to support this prediction.
Advisor: Sun, Zhifa; Molteno, Tim
Degree Name: Doctor of Philosophy
Degree Discipline: Physics
Publisher: University of Otago
Keywords: Rayleigh effect; Marangoni effect; Transient interfacial convection; Fluctuating hydrodynamics; Stochastic Ginzburg-Landau equations; Heat and mass transfer enhancement
Research Type: Thesis