Alternating axial displacement of a fluid mixture in a column of adsorptive particles upon which an axial temperature difference is imposed leads, through coupling of oscillatory thermal and mass fields with alternating flow displacements, to a difference in limiting-condition, time-average compositions a t the column ends. The separation takes place at the expense of thermal energy; continuous operation with a fixed-bed adsorber also becomes feasible. The separation has been substantiated by experiment and b y analysis of the mathematical formulation. NTEREST in separation principles and techniques is commonI to many areas of application and research-for example, in the saline water problem, in the intercellular transport of ions in living cells, and in the separation of all manner of chemical mixtures of industry.This communication is restricted to the elements of separation by means of parametric pumping.

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Although stirred vessels are widely used in chemical technology, they have been characterized almost exclusively by empirical methods, for example power absorption per unit volume (11) The present work investigates simultaneous mixing and reaction of a basic tracer stream with a surrounding acid medium. A steady state condition is achieved by continuously introducing a tracer sodium hydroxide solution into an acid stream which flows slowly upward through the stirred vessel. Both base and acid streams contain phenolphthalein indicator; hence the distance from the impeller required for complete reaction of tracer solution is visually measurable. Any realistic and detailed description of this exceedingly complex shearing and interlarding of the reacting streams by the impeller blades would be prohibitively complicated even if the additional effects of molecular diffusion and reaction are not considered. A first-order and necessarily very crude solution is now obtained with an extremely idealized model which may even be accused of being too much of a simplification. The model assumes:1. The impeller action reduces the entering tracer stream to very thin packets. Simultaneously the shearing or other action of the blades interlards the tracer packets with the bulk circulating stream.2. The above shearing and interlarding processes OCcurs very quickly, that is before the fluid is ejected from the impeller.3. After the impeller is left, no further shearing occurs, and the acid base reaction is now controlled by molecular dihsion as outlined by Toor ( 1 2 ) .Within the impeller, effects such as flow patterns, jet mixing of the entering streams, effective eddy diffusivities, etc. are not considered separately. Their combined action is expressed in terms of packet size and subsequent reaction time. In the effluent stream only mixing on the molecular level is considered to enhance chemical reaction; larger scale eddies have little effect. If eddies in A. W. Rice is at Princeton University, Princeton, New Jersey. stirred vessels are similar to those in pipes, their dimensions are quite large, of the order of vessel diameter, impeller diameter, blade size, etc. Reaction of the basic tracer streaks in the effluent stream is now considered quantitatively. THEORYThe flat-bladed turbine impeller produces a horizontal fluid sheet that maintains its radial direction until it reaches the vessel wall. At the wall the flow divides into doughnut-shaped circulation patterns above and below the impelIer. There are two mixing processes in the vessel, the basic tracer with the acid recirculation stream at the impeller and the recirculating stream with the fresh entering acid at the bottom of the vessel.Within the confines of the impeller the tracer solution is pictured as being sheared into very thin elements (slabs, cylinders, or spheres) which are then surrounded by the recirculating stream. Reaction between these interlarded layers of acid and base then occurs when the mixture leaves the impeller and becomes part of the horizontal fluid...