The problem of axial mixing in straight pipes is analyzed by a modification of G. I. Taylor's analysis. The treatment presented here includes the effect of both Schmidt and Reynolds numbers throughout the turbulent-flow range. All applicable data on flow of gases and liquids are found to conlirm the validity of the method.The analysis indicates that axial mixing increases rapidly as the flow approaches the laminar region, especially for liquids, and that pipe roughness causes a relatively small increase in axial mixing. Turbulent eddy diffusion in the axial direction has a negligible effect.The results of the analysis are applicable to those systems wherein the kinematic viscosity of the flowing mixture does not vary greatly from one region to another and in which the concentration region of interest is spread out along a sufllcient length of pipe. These limitations are broad enough to permit most practical problems to be treated by the method.The passage of fluid through a pipe is accompanied by mixing in the axial direction. This effect, which can be observed, for instance, by noting the dispersion of tracers, results in intermixing of products in pipe lines, in decreasing the driving force in tubular reactors, and in diminishing the sharpness of signals in tracer experiments.In unbroken straight pipes axial mixing is due to diffusion in the axial direction because of molecular or turbulent motions and to the relative axial motion of fluid elements at different radial positions. However, the effects of axial molecular and turbulent diffusion are negligible compared with the interpenetration due to relative motion. The latter depends greatly on the shape of the velocity profile and the rate of radial diffusion. The more nearly the velocity profile approaches that for plug flow, the smaller is the amount. of axial mixing. A high rate of radial diffusion tends to keep the concentration radially uniform; the different radial fluid elements then have more nearly the same composition and in moving with respect to one another, cause less severe mixing. Thus axial mixing is pronounced in the case of laminar flow, where the flow is least pluglike and where radial diffusion is small (molecular instead of turbulent).The first analysis of axial mixing based on radial variation of the velocity was made by G. I. Taylor (17 to 19), who treated first the case of laminar flow in capillary tubes and later the case of turbulent flow in pipes. His treatment of turbulent flow is valid only for high Reynolds numbers because he used a velocity profile valid only when the laminar sublayer and transition layers are negligibly small. Experimental results support this treatment for Reynolds numbers greater than 20,000.In the calculations presented here, Taylor's method is refined and extended to cover the whole range of turbulent flows. The chief differences introduced here are the inclusion of the effect of molecular diffusion and the use of experimental velocity profiles rather than a generalized profile. It was necessary to rearrange ...

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showing that reactor-product distribution is generally distorted in proportion to a reactor Peclet number. G. I. Taylor's theory of axial mixing is used to relate this Peclet number to the physical characteristics of the reactor.Although the effects of axial mixing are concluded to be negligible in most commercial or large-scale equipment, they are serious in the case of experimental or pilot-scale apparatus.Charts are drawn to illustrate design problems for these reactors. PURPOSE AND SCOPEThe successful scale-up of a process requires accurate knowledge of yields and reaction rates in the range of operation of the scaled-up process. To this end, a method is given here for designing experimental flow reactors in which good selectivity can be maintained, that is, reactors in which the products formed are characteristic of the reaction chemistry, concentrations, etc., and not characteristic of the peculiarities of the experimental reactor.Excessive axial mixing, or backmixing, in an experimental reactor makes the interpretation of results on yields and by-products highly uncertain. It is especially detrimental with integrated processes wherein recycle rates, separation procedures, etc., are based on the composition of the effluent obtained in experiments. Unrealistic amounts of by-products from a faulty experimental reactor may lead to establishment of a false optimum in operating conditions for the integrated process; and even if this mishap is later discovered, most of the experiments may involve conditions near the false optimum, thus yielding little information for the operating conditions of ultimate interest. Despite these pitfalls flow reactors are necessary in the study of certain reactions which cannot be explored with accuracy in bombs or continuous wellstirred vessels because of physical problems associated with the reaction mixture.Although there have been past studies of backmixing in homogeneous reactors ( 4 , 5,6,7,8, 9, 10) on the course of a reaction was not attempted here. Instead an approximate analysis was used which is valid for all kinds of reactions when the effect of mixing on the overall performance is not excessive. Therefore, the methods developed are useful not for interpreting data from reactors in which there has been excessive mixing, but rather for selecting reactor dimensions and operating conditions which make backmixing effects tolerably small. The product from the reactor is then substantially the same as from a batch reactor. THE EFFECT OF AXIAL MIXINGAxial mixing in an unpacked tube is caused by variation of axial velocity across the radius. Fluid elements near the center move more rapidIy than the average; thus they penetrate into downstream material near the walls and eventually mix with it. The magnitude of this effect depends greatly on the shape of the velocity profile and the rate of mixing in the radial direction. Contrary to first instinct, radial mixing inhibits axial mixing; this interrelation formed the basis for Taylor's analysis, ( I ) later extended by Tichacek,...

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