Bubble Entrainment and Enhanced Mass Transfer

Mass transfer in polymeric solutions by molecular diffusion is a comparatively slow process, and in extraction equipment where mass transfer occurs through a thin wiped film, inordinately large equipment surface areas are often required in order to obtain substantial rates of mass transfer. In commercial practice when this situation occurs, the required surface areas may, instead, be obtained by either one of two methods, both of which involve reducing the pressure in the extraction zone. In one approach the extraction pressure is fixed at a value which is less than the equilibrium partial pressure of the monomer or solvent in the polymeric solution fed to the extraction zone. In these circumstances gas bubbles 

The net effect of this reduction, of course, is to increase the driving force for mass transfer in the liquid phase. 

The beneficial effect that the introduction of water has on the extraction of ethylene from low-density polyethylene is shown in Fig. 18. The reduction in the exit concentration of ethylene is substantial, especially at the higher pressures, and dramatically illustrates the increase in mass transfer rates which results from the introduction of an immiscible stripping agent. 

Consider a situation in which a concentrated polymeric solution enters the extraction zone of, say, an extruder in circumstances when the pressure in the extraction zone. Pa, is less than the equilibrium partial pressure of the volatile component in the feed solution. Under these conditions the solution will be supersaturated at the extraction pressure, flashing of the volatile component will occur, gas bubbles of radius Rq will be formed, and the concentration will immediately fall from Wi to wq. If bubble formation occurs by homogeneous nucleation, the rate at which these bubbles will be formed per unit volume of solution should depend on the difference between the equilibrium partial pressure of the volatile component and the devolatilization pressure. Since this pressure difference is greatest when the solution first enters the extraction zone, the rate of formation of bubbles will at first be high but as devolatilization pro- 

When it is assumed that the pressure inside the gas bubbles at the time they are formed is the equilibrium pressure, then 

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