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Corrugated surfaces such as those shown schematically in the figure below are commonly encountered in chemical systems. Examples include roughness evolution in metal deposition, catalysis, and surface polishing. These systems present interesting diffusion-reaction problems wherein species diffusion into the surface cavities is coupled with reactions. Your task is to analyze the special case of steady-state diffusion and 1st order reaction following the steps below: (a) Setup a mass balance on an infinitesimally small volume element (thickness Az and width x) shown in grey color in the schematic below. Using the relationship x = a(L-z)/L (for a triangular shaped cavity) depicted in the inset below and assuming that the sidewalls are nearly vertical (0 is very small), clearly show how you can derive the differential mass balance equation: 2kL C=0 Da where C is the species concentration that varies only in the z-direction, k is the 1st order reaction

Corrugated surfaces such as those shown schematically in the figure below are commonly encountered in chemical systems. Examples include roughness evolution in metal deposition, catalysis, and surface polishing. These systems present interesting diffusion-reaction problems wherein species diffusion into the surface cavities is coupled with reactions. Your task is to analyze the special case of steady-state diffusion and 1st order reaction following the steps below: (a) Setup a mass balance on an infinitesimally small volume element (thickness Az and width x) shown in grey color in the schematic below. Using the relationship x = a(L-z)/L (for a triangular shaped cavity) depicted in the inset below and assuming that the sidewalls are nearly vertical (0 is very small), clearly show how you can derive the differential mass balance equation: 2kL C=0 Da where C is the species concentration that varies only in the z-direction, k is the 1st order reaction

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Corrugated surfaces such as those shown schematically in the figure below are commonly encountered in chemical systems. Examples include roughness evolution in metal deposition, catalysis, and surface polishing. These systems present interesting diffusion-reaction problems wherein species diffusion into the surface cavities is coupled with reactions. Your task is to analyze the special case of steady-state diffusion and 1st order reaction following the steps below: (a) Setup a mass balance on an infinitesimally small volume element (thickness Az and width x) shown in grey color in the schematic below. Using the relationship x = a(L-z)/L (for a triangular shaped cavity) depicted in the inset below and assuming that the sidewalls are nearly vertical (0 is very small), clearly show how you can derive the differential mass balance equation: 2kL C= 0 Da where C is the species concentration that varies only in the z-direction, k is the 1st order reaction rate constant, and D is the diffusion coefficient of the diffusing species. a diffusion + reaction z+Az x = a(1-/L) e is very small, so that cos 8=1
Transcribed Image Text:Corrugated surfaces such as those shown schematically in the figure below are commonly encountered in chemical systems. Examples include roughness evolution in metal deposition, catalysis, and surface polishing. These systems present interesting diffusion-reaction problems wherein species diffusion into the surface cavities is coupled with reactions. Your task is to analyze the special case of steady-state diffusion and 1st order reaction following the steps below: (a) Setup a mass balance on an infinitesimally small volume element (thickness Az and width x) shown in grey color in the schematic below. Using the relationship x = a(L-z)/L (for a triangular shaped cavity) depicted in the inset below and assuming that the sidewalls are nearly vertical (0 is very small), clearly show how you can derive the differential mass balance equation: 2kL C= 0 Da where C is the species concentration that varies only in the z-direction, k is the 1st order reaction rate constant, and D is the diffusion coefficient of the diffusing species. a diffusion + reaction z+Az x = a(1-/L) e is very small, so that cos 8=1
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