The problem of predicting the rate of absorption for a solute gas which reacts with a non-volatile substance in the liquid film was first discussed just over half a century ago. The first case considered was that of instantaneous reaction and the solution was obtained using the comparatively simple interpretation of the Whitman "Two-Film Theory" Subsequently, progressively more difficult forms of this problem have been considered, involving reactions of various orders. Solutions for such cases have been developed using both the film theory and also the more sophisticated "Surface Renewal Theory". However, these theories are essentially concerned with transfer to stagnant pools or to deep films in plug flow. They have no terms which represent the effect of variable sub-surface velocity perpendicular to the direction of transfer. The best-known system with such velocity gradients is the thin film of Newtonian liquid, which exhibits a parabolic velocity profile between the free surface and the supporting plate. Solutions for transfer to thin Newtonian films have previously been obtained for absorption without reaction and for absorption with first order reaction. However, solutions have not previously been available for transfer to these films accompanied by instantaneous reaction. In this case a further complication arises in the form of discontinuity of concentration gradients at the reaction front. If numerical methods are employed, the effect of such discontinuity must be carefully evaluated, or serious errors may be generated. The primary aim of this research has been to develop a numerical procedure which accommodates the discontinuity at the reaction front. This has been achieved, and numerical solutions have been computed for a wide range of parameters. Their accuracy has been confirmed by comparison with analytical solutions which are known for certain limiting cases. A further aim has been to measure the absorption rate of carbon dioxide during extended exposure to such films when they contain sodium hydroxide. An apparatus was developed which enabled transfer rates to be measured for exposure times of up to one minute. The measured rates were compared with those predicted for instantaneous reaction in the film. For the initial stages of transfer to aqueous caustic soda, the measured absorption rates were about 90% of the rates predicted for instantaneous reaction. However, as transfer approached stoichiometric conversion to the carbonate, the experimental results deviated more seriously below the predicted values. The discrepancy at this stage was confirmed by separate measurements of absorption into sodium carbonate solution, where the measured rates were found to be only 47% of the rates predicted for instantaneous reaction. It is therefore concluded that to account for absorption into aqueous caustic soda beyond the point of 45% saturation, it would be necessary to develop a complex model based on instantaneous reaction's far as the carbonate stage, followed by pseudo-first order reaction to the bicarbonate stage. Although absorption into caustic soda beyond stoichiometric conversion to the carbonate was appreciably slower than the rates predicted for instantaneous reaction, the correlation between the measured and predicted results was independent of the solution strength within the range of the experiments, i.e. for solutions between 0.1 M and 1.0 M.
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