Generalization of the penetration theory for surface stretch: Application to forming and oscillating drops

Abstract

AbstractA method is developed for predicting rates of mass or heat transfer through stretching or shrinking phase boundaries of finite lifetime at low mass transfer rates. The primary result of this development, Equation (43), may be considered as a generalization of penetration theory. It includes as special cases similar expressions developed for more restricted situations, notably those of Ilkovic (7) and of Beek and Kramers (1).This general development is then used to refine the Rose‐Kintner analysis (13) of mass transfer to large oscillating liquid drops for the limitig case of all heat or mass transfer resistance in the droplet phase. It is found that convection normal to the phase boundary tends to offset the direct effect of surface stretch, and that the postulated mass transfer behavior can be expressed adequately by a very simple expression, Equation (68). This result yields slightly lower predictions of mass transfer rates than the correlation of Rose and Kintner, but available data are not sufficiently accurate to indicate which is the more reliable.The surface‐stretch model is also applied to drop formation at submerged nozzles. Experimentally it was found that the growth of surface during this process is essentially linear, which simplifies calculations. The model gives predictions of the mass transfer coefficient which are in reasonably good agreement with the predictions based on the assumption of continual formation of fresh surface first used by Groothuis and Kramers (18), and later by Beek and Kramers (1). Both models show that the mass transfer coefficient is at least fifteen times as high as predicted by boundary‐layer calculatins alone. Finally, the surface‐stretch model indicates that the mass transfer behavior druing the rise period is approximately fourteen times as important as during the formation period for the equipment used in this study.An expression was also developed for the more general situation of appreciable resistance in each phase, Equation (62), by assuming the surface‐stretch model to describe the transfer processes in both phases. The two‐resistance theory (10) is exact under such circumstances. This result was also found to correlate available data reasonably well.More data, however, are needed if meaningful tests of the above, or other, correlations are desired.