The two major models of the mechanism of mass and heat transfer between two phases are the film theory (16) and the penetration theory (2, 3). The film theory assumes that there is a region in which steady state molecular transfer is controlling; the penetration theory assumes that the interface is continuously replaced by eddies and that unsteady state molecular transfer into the eddies controls the transfer in this region.There are three classes of problems to which these theories have been applied : (1) transfer between a solid and a fluid in turbulent flow; (2) transfer between two fluids, at least one of which is in turbulent flow; and, (3) transfer between two fluids in an apparatus of discontinuous geometry such as packed column. In flow in a packed column the concept of surface renewal by eddies is replaced by that of a laminar liquid which mixes at discontinuities in the packing (2). If the flow is laminar except a t the points of mixing, neither the film theory nor the analysis developed below will apply to the liquid phase.In the absence of any other resistances the film theory predicts a first-power dependence of the transfer rate on the diffusivity or thermal conductivity, and the penetration theory predicts a square root dependence. Danckwerts (3) has shown that neither the film nor penetration theory is completely valid for a packed column, and Hanratty (6) points out that at high Schmidt numbers the penetration theory gives better results than the film theory.The purpose of this paper is to show that the film and penetration theories are not separate, unrelated concepts but rather are limiting cases of a more general model and that the two theories, rather than being mutually exclusive, are actually complementary. THEORETICAL DEVELOPMENTThe boundary layer extending from the front end of a flat plate or from the inlet to a conduit will be considered. A laminar zone is assumed to exist which is bounded by a turbulent region, and heat or mass is being transferred between the surface and the fluid. For a short distance along the plate the transfer must be by an unsteady state mechanism, for the penetration of the diffusing substance will take a finite contact time (corresponding to a finite distance along the surface) to reach the edge of the film. Some distance along the surface the transfer will reach its steady value and there will be no inore accumulation in the film. The short distance corresponds to the penetration theory, the long distance to the film theory, and for intermediate distances the transfer process has the characteristics of both mechanisms.The transfer between a gas and stirred liquid, which as postulated by Danckwerts has its surface randomly replaced by eddies of fresh fluid from the bulk of the liquid, will be considered. If the eddies remain in the surface a short period of time, each element may be assumed to absorb matter or heat at the interface by unsteady state conduction. As the life of an element increases, the penetration into the element increases and again, after a lo...

Equimolal countercurrent diffusions runs were made in a two bulb diffusion cell with the system hydrogen, nitrogen, and carbon dioxide. The initial bulb compositions were chosen so that various types of ternary interactions occurred. These interactions were well-described by the Maxwell-Stefan equations. The average deviation of the experimental mole froctions for all runs from those predicted by the Maxwell-Stefan equations was 0.45 mole %. Wilke's method 2 modified as suggested by Toor (19). Wilke's method 1 does not have the proper behavior.

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Very rapid, ropid, and slow second-order reactions were studied in an isothermal turbulent flow reactor. The two aqueous reactant solutions were separately introduced through many alternote jets and the reaction took place in the resulting nonhomogeneous mixture. Very rapid reactions were diffusion controlled and were in agreement with earlier theory. All reactions followed second-order rote laws based on time average quantities. The apparent reaction velocity constant was controlled by the mixing for very rapid reactions, by the chemical kinetics for slow reactions, ond by both mechanisms for ropid reactions.When a homogeneous chemical reaction takes place in a turbulent fluid the local instantaneous rate of reaction can be assumed to be described by the normal laws of homogeneous chemical kinetics. However, the local time average rate of reaction, r,, the mean rate, may be greater than, equal to, or less than the homogeneous rate at the local time average concentration, the homogeneous mean rate. Although the above statements are true whether or not the system is isothermal, in this paper only isothermal situations are considered.For the purposes of this discussion a homogeneous solution or mixture is one in which the RMS concentration fluctuations of all species are zero. The mean rate obviously equals the homogeneous mean rate in homogeneous solutions and this is true even in nonhomogeneous solutions if the reaction is first order.In nonhomogeneous solutions the mean rate of a type I second-order reaction, A -+ A + product, is greater than the homogeneous mean rate, while the mean rate of a type I1 second-order reaction, A + B + product, may be greater or less than the homogeneous mean rate, depending upon how the reactants are introduced; greater if the reactants are premixed, less if they are not. (The above assertions are easily justified by examining the appropriate time average expressions and noting that premixing gives a positive correlation between the fluctuating reactant concentrations. while lack of premixing gives a negative correlation. ) The deviation from the homogeneous mean rate depends upon the rate of the reaction relative to the rate of mixing. Three arbitrary divisions are convenient: very rapid reactions, rapid reactions, and slow reactions. They correspond, respectively, to reaction rates much faster than the rate of mixing, reaction rates of the same order as the rate of mixing, and reaction rates much slower than the rate of mixing. The latter case is the simplest, and most reactor design studies have been concerned with this problem. It is under reasonably good control. [It is noted that in the flow methods of studying rapid chemical reactions in solution ( 1 4 ) , the reactions are slow in the above sense, since the experiments are designed to make the mixing much faster than the reaction.]Very rapid and rapid reactions present an entirely different problem, for here the detailed turbulent motion can have a profound effect on the rate of reaction, es- pecially with type I1 second-or...

6 t coefficient, O CY1 r] = viscosity, lb./hr. ft. K = translational part of gas thermal conductivity, = B.t.u./hr. ft.' F. X = Mean free path, ft. p = symbol representnig particle size in microns 'lr = 3.1415 ... p = gas density, lb./cu. ft. 7 = coefficient relating transition thermal force to free = laminm sublayer thickness, ft. = temperature coefficient of momentum accommodation molecular thermal force DIMENSIONLESS GROUPS Kn = Knudsen number, X/r, Re = Reynolds number, Dvp/q y+ Literature CitedAmdur, I., Guildner L.,