A slab substrate is exposed to a solute in solution with a bulk concentration Cb. The initial concentration in the substrate is C0 and the thickness of the substrate is L. As the solute diffuses into the substrate, the concentration changes over a small distance δ through a face of area given by A. The flux at the interface is given by JA0 = F(t), where F(t) is some known function of time. A parabolic concentration profile is proposed to describe the concentration in the boundary layer. Use a boundary layer approach to fully determine the transient

Principles of Instrumental Analysis
7th Edition
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Chapter34: Particle Size Determination
Section: Chapter Questions
Problem 34.14QAP
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A slab substrate is exposed to a solute in solution with a bulk concentration Cb. The initial concentration in the substrate is C0 and the thickness of the substrate is L. As the solute diffuses into the substrate, the concentration changes over a small distance δ through a face of area given by A. The flux at the interface is given by JA0 = F(t), where F(t) is some known function of time. A parabolic concentration profile is proposed to describe the concentration in the boundary layer. Use a boundary layer approach to fully determine the transient concentration profile in the boundary layer
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