A theoretical analysis of the hydrodynamics of liquid rivulets flowing down an inclined surface is presented. Steady state solutions are developed for the laminar flow cose which relate the flow rate to the rivulet width, the physical properties of the liquid, and the contact angle. Excellent verification of the theoretical predictions was obtained in a number of experiments with various liquids on an inclined glass plate. All constants in the equations were derived from theory. These results will be useful in obtaining a better understanding and correlation of such phenomena as liquid flow over packings and catalysts and flow along walls and tube surfaces, as in condensation and evaporotion.
This communication describes experiments performed to ascertain the equivalence of pulse and step input liquid residence time data in cocurrent, downward, gas-liquid flow through packed beds (trickle-phase beds). Contrary to results in the literature, we find that data taken by the different methods are equivalent.The distribution of residence times in a piece of process equipment may be measured by injecting a pulse of tracer into the inlet stream and measuring the downstream concentration as a function of time. Alternately, a step change in inlet tracer concentration may be introduced, and the effluent analyzed to follow the approach to the new steady state. According to Laplace transform theory, the time integral of the pulse data should be equivalent to the step data if the system is linear (5) ; that is pulse decrease [I.--C2 --7 C1 step increase where CI and cz are the inlet tracer concentrations before and after the step change, respectively.Contrary to the theory, Lapidus (2) and Schiesser and Lapidus (3) report large differences between data obtained by the three methods in a trickle-phase bed of porous particles, particularly In a series of step tracer experiments in trickle-phase beds under many different conditions Hofmann ( 1 ) finds no difference between elution and saturation; he reports no pulse measurements. Since the experimental results of Schiesser and Lapidus raise doubts about the interpretation of residence time data, a repetition of their experiment seems worthwhile.Although the primary objective of this work is to test the equivalence of pulse and step residence time measurements, an important related question concerns the relation between the mean residence time and the total holdup in experiments with the air-water system. It is customary to assume that With this relation, Schiesser and Lapidus calculate the "apparent percentage of internal voids filled with liquid" as the ratio of hi calculated from t t o the value of hi for all internal voids filled.In this way they find the apparent percentage filled to be 78.8% from elution data, 48.2% from saturation, and 27.8% from the pulse run.Superficially, one might expect the mean residence time to reflect only that portion of the internal holdup which is in particles contacted by flowing liquid. But if the liquid is sufficiently nonvolatile to undergo capillary condensation in the pores, liquid will fill and remain in the interior of all particles. Since all of the particle interiors are interconnected and thus accessible to the external streams, the holdup calculated from the mean residence time should include all of the internal void volume, and the mean residence time should be independent of the method of measurement. Of course, the column must be operated long Moss transfer and contactor efficiency i n a stirred liquid-liquid reactor, Engel, A. J., and 0. A. Hougen, A.1.Ch.E. Journal, 9, No. 6, p. 724 (November, 1963).Key Words: Mixing-9, Agitation-9, Stirring-9, Reactor-1 0, Reactor Design-9, Mass Transfer-9, Liquid-Liquid Systems-8,...
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