conditions the antifoam promotes localized thinning and rupture of the bubble walls which cause coalescence to precede disengagement from the frit. Once formed, however, air bubbles rising through the antifoam-containing liquid show a high degree of resistance to agglomeration even after repeated collisions.In general, antifoams are employed to break up stable surface foams and it is suggested that they function by rapidly spreading on the bubble surface, sweeping away surfactant, and thereby rupturing the bubble. They appear to be most effective against thin-walled, well-drained foams. Our experiments suggest that similar conditions exist on the frit surface where substantial drainage can occur between bubbles while they are still held in contact by attachment to the frit. In contrast, in the bulk liquid colliding bubbles can separate from each other faster than interfacial drainage can occur and the relatively thick liquid film maintains bubble integrity even when antifoam is present.3. Hydrophobic frits modify the flow regime primarily by increasing the average bubble size prior to disengagement and not by promoting agglomeration during bubble formation. In this respect they behave much more like perforated plates than their hydrophilic counterparts and may be more appropriate to use in modeling studies.
ACKNOWLEDGMENTThe authors are much indebted to J. L. Henkes for his expertise in obtaining the photographs. NOTATION Q = void fraction y = surface tension p = liquid density g = gravitational constant J B
A combination of Happel's free surface model and variational principles is used to obtain bounds on the drag offered by the creeping flow of a power law fluid past an assemblage of solid spheres. The theoretical predictions of the product of the Fanning friction factor f and Reynolds number Re, are in close agreement with available experimental data on non-Newtonian flow through porous media. The product (f Re,) reduces for the Newtonian case to that of Happel and Brenner.
SCOPEThe flow of a Newtonian fluid through packed and fluidized beds has received considerable attention in the chemical engineering literature. A free surface model developed by Happel is widely used to predict the friction factor for ~~~~~~i~~ fluids. H~~~~~~, the analogou9 problem of flow of a non-Newtonian fluid through packed and fluidized beds has not been analyzed so far with this model. This paper extends the Happel's free surface model to the flow of power law fluids by making use of variational principles and presents an analysis for the friction factor in packed and fluidized beds. CONCLUSIONS A N D SIGNIFICANCE A combination of Happel's free surface model and variational principles yields numerical values for the product of the Fanning friction factor f and the Reynolds number Re, for various values of bed porosities and flow behavior indexes. An expression for the product (f Re,) in terms of the porosity and flow behavior index is developed which well predicts experimental values of friction factor for power law flow through packed and fluidized beds. A correlating equation was developed which provides a continuous STUART W. CHURCHILL representation f
Terminal velocities of drops of organic liquids of diameter 0.0726 to 0.7256 cm in polymer solutions are determined. The Reynolds number range covered is 0.1 to 103. Visual observations on the shapes and oscillations of drops are reported. A correlation for the terminal velocity data is presented.
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