We analyse iterations of maps on an interval with an added noise term, in the neighbourhood of an intermittency threshold. We rigorously derive a universal scaling function for the laminar time expressed as a function of the distance from the threshold and the variance of the noise.

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The surface rejuvenation model of the turbulent burst process, already developed for the momentum and heat transfer processes, is applied to the field of mass transfer. The range of applicability of the theory, previously shown to be valid for the Prandtl number range 0.7 to 64 is extended to Schmidt numbers of 6,500 without introducing any new parameters. Concentration and temperature profiles for high Schmidt and Prandtl numbers are in agreement with experimental data. Theoretical expressions for Sherwood and Stanton numbers are calculated and shown to be in agreement with experimental data over five orders of magnitude. CONCLUSIONS AND SIGNIFICANCEA turbulent burst or surface rejuvenation model has been developed in this study for mass or heat transfer to fluids with values of Sc or Pr up to lo4. In this approach, the actual unsteady process that occurs between inrush and ejection phases of a burst event is modeled, with the approach distance distri- which is in agreement with experimental data for Sc from 0.5 to 10,000. The analysis indicates that the thickness of the unrepIenished layer of fluid existing at the surface is significant for values of Sc much greater than 5. For values of Sc less than about 5, this layer occupies less than 10% of the molecular wall region, such that the simple surface renewal model can be used.Based on the results of this analysis and on earlier work, it is concluded that the surface rejuvenation model provides a useful Page 1614October, 1985 AlChE Journal (Vol. 31, No. 10) alternative approach to characterizing the wall region for moderate to high values of Sc and Pr. Because of the strong physical basis for the surface rejuvenation model, and as this approach involves a minimum level of empiricism, the theory is believed to provide a fundamental basis for generalization to other transport processes involving wall turbulence.

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To = maximum temperature to which char has been exposed previous to gasification in IGT kinetic scheme 2 Superscript o c = condition in the bulk phase = condition at the core surface = condition at the transition between gasification = condition at the top of the reactor = condition at the gas inlet = condition at the core surface and combustion zone This paper presents a simplified formulation for Elf for low to moderate Prandtl number fluids and for E, , , that utilizes the surface renewal model, but which also accounts for the fact that eddies do not reach the surface. The predicted trend in Prt obtained on the basis of the present analysis suggests an opposite dependency on Pr to that predicted by many of the other analyses.The primary objective of this paper is to demonstrate to turbulence and the classical eddy diffusivity concept. the relationship between the surface renewal approachThe compatibility between these two approaches to turbulence has been previously demonstrated in the context Akron, Ohio.of a comprehensive but complicated surface rejuvenation formulation. A simpler development is presented in this Chemical Engineers.paper for moderate Prandtl numbers (0.5 Pr 5.0)L. C. Thomas is presently on leave from the University of Akron,