Four stages of the simultaneous mass and heat transfer during bubble formation and rise in a bubbly absorber

We studied nonisothermal absorption of a solvable gas from growing at an orifice and rising bubble when the concentration level of the absorbate in the absorbent is finite (finite dilution of absorbate approximation). It is shown that simultaneous heat and mass transfer at all stages of bubble growth and rise in a bubbly absorber can be described by a system of generalized equations of nonstationary convective diffusion and energy balance. Solutions of diffusion and energy balance equations are obtained in the exact analytical form. Coupled thermal effects during absorption and absorbate concentration level effect on the rate of mass transfer are investigated. It is found that the rate of mass transfer between a bubble and a fluid increases with the increase of the absorbate concentration level. The suggested approach is valid for high Peclet, Prandtl and Schmidt numbers. It is shown that for the positive dimensionless heat of absorption K thermal effects cause the increase of the mass transfer rate in comparison with the isothermal case. On the contrary, for negative K thermal effects cause the decrease of the mass transfer rate in comparison with the isothermal case. The latter effect becomes more pronounced with the increase of the concentration level of the absorbate in the absorbent. Theoretical results are consistent with the experiments of Kang et al. (Int. J. Refrigeration 25 (2002) 127) for absorption from ammonia gas bubbles rising in water and aqueous ammonia solutions.