Fundamentals of Momentum, Heat and Mass Transfer by james welty 26.24 Consider a spherical gel bead containing a biocatalyst uniformly distributed within the gel. Within the gel bead, a homogeneous, first-order reaction AD is promoted by the biocatalyst. The gel bead is suspended within water containing a known, constant, dilute concentration of solute A (CA∞). a. Define the system, and identify the source and the sink for the mass-transfer process with respect to reactant A. List three reasonable assumptions for this process. Then, using the "shell balance" approach, develop the differential mate- rial balance model for the process in terms of concentration profile CA. State all boundary conditions necessary to com- pletely specify this differential equation. b. The analytical solution for the concentration profile is given by R sinh(rVk:DAn) rsinh(R√k₁/DAB) CA(r) = CAO What is the total consumption rate of solute A by one single bead in units of μmol A per hour? The bead is 6.0 mm in diameter. The diffusion coefficient of solute A within the gel is 2×106 cm²/s, k₁ is 0.019 s-¹, and CA is 0.02 μmole/cm³. Hint: Differentiate the relationship for CA(r) with respect to r, then estimate the flux NA at r = R.

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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Transcribed Image Text:Fundamentals of Momentum, Heat and Mass Transfer by james welty 26.24 Consider a spherical gel bead containing a biocatalyst uniformly distributed within the gel. Within the gel bead, a homogeneous, first-order reaction AD is promoted by the biocatalyst. The gel bead is suspended within water containing a known, constant, dilute concentration of solute A (CA∞). a. Define the system, and identify the source and the sink for the mass-transfer process with respect to reactant A. List three reasonable assumptions for this process. Then, using the "shell balance" approach, develop the differential mate- rial balance model for the process in terms of concentration profile CA. State all boundary conditions necessary to com- pletely specify this differential equation. b. The analytical solution for the concentration profile is given by R sinh(rVk:DAn) rsinh(R√k₁/DAB) CA(r) = CAO What is the total consumption rate of solute A by one single bead in units of μmol A per hour? The bead is 6.0 mm in diameter. The diffusion coefficient of solute A within the gel is 2×106 cm²/s, k₁ is 0.019 s-¹, and CA is 0.02 μmole/cm³. Hint: Differentiate the relationship for CA(r) with respect to r, then estimate the flux NA at r = R.

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