The climbing of Marangani films up vertical solid surfaces was investigated experimental ly and theoretically. The system considered was a nonisothermal plate with i t s warm end partially immersed i n a nonvolatile liquid. Observed f i l m thicknesses and rates of climb were i n agreement with an approximate hydrodynamic model obtained by assuming the supply capacity of the f i l m to be rate Itmiting.The results of this study confirm the hypothesis that previously observed liquid films formed against gravitational forces above equilibrium menisci are produced by surface-tension inequalities. It i s pointed out that hydrodynamic processes cannot allow for the advancement of the leoding edge of Marangoni films and a sepamte physicochemical process i s required to explain spontaneous spreading of these films. Evidence i s presented for the formation of much thinner primary films ahead of the secondary bulk films described by hydrodynamics. These primary films appear t o be produced by a combination of multilayer adsorption and/or surface diffusion. The kinetics of these diffusional processes may l i m i t spreading rates when surface-tens ion gradients become sufficiently large.Finally, the Marangoni films were found to be unstable i n a manner hitherto not considered.
Fig. 2. Interference apporatus for observing thin films. AlChE Journal PT az a@ t Equation (8) is the solution to the differential equation Vt--= Drwith Equations (1) and ( 2 ) as boundary conditions. Vol. 14, No. 4 AlChE Journal Poge 621 Boundary Condition 3 at 71 = 1, VY(T) = 0 (35) Boundary Condition 4 at The third and fourth boundary conditions come from the kinematic condition, Equation (17), and the normal component of the surfaoe equation of motion, Equation Fig. 4. Qualitative picture of vertical roll cell disturbances.
This paper is concerned with the mechanism of formation of stable super‐meniscus electrolyte films, observed on gas diffusion electrodes. The Marangoni effect associated with surface tension gradients in liquids is considered and found to give film characteristics which are in agreement with many observations made to date. By numerical example it is shown that a temperature gradient of −0.4 C/cm in water or a concentration gradient of 0.035 mole/liter·cm in aqueous KOH solution each can produce a typical liquid film, 1μ thick and unlimited in height. This mechanism is shown to provide more vigorous water recirculation in films than vapor phase transport, and a preliminary unsteady‐state analysis is shown to give the right magnitude for the climbing rates observed for the spreading of many hydrocarbons on vertical surfaces. The mechanism is unable to explain effects observed in the absence of concentration or temperature gradients, but apparently could have a pronounced effect under operating conditions of gas diffusion electrodes.
The stability of vertical laminar falling films sobjected to interphase mass transfer ond surface-tension gradients in the direction of flow is investigated by linear perturbation analysis. The perturbations considered are vertical waves or rivulets as described by Ludviksson and Lightfoot for nonisothermal films. Perturbations of this type are thought to lead to the maldistribution of flow observed in distillation and gas absorption by Zuiderweg and Harmens and by Francis and Berg.Three unstable regions are predicted, one corresponding closely to that found by Ludviksson and Lightfoot, and two new ones, previously unreported, resulting from interphase mass transfer across the free surface.These predictions confirm the conclusions of Zuiderweg ond Harmens for situations in which surface tension increases upward, and they provide a means of estimating the range of unstable gradients. Experimental evidence for instability predicted when the surface tension increases downward is inconclusive, Further investigation of this region, which is of considerable importance, is recommended.
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