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  3. chapter 23 problem 7p bookmark show all steps on consider...

Question: chapter 23 problem 7p bookmark show all steps on consider...

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Chapter 23, Problem 7P Bookmark Show all steps ON Consider the diffusion of solute A into the single cylindrical pore shown in the figure below. The end of the pore at z = L is sealed. The pore space is initially filled with inert fluid B. As solute A diffuses into the quiescent fluid space inside the pore space, it adsorbs onto the inner walls of the pore. The adsorption isotherm of solute A onto the solid surface of the pore is described by the Langmuir equation, given by K +CA where qA is the amount adsorbed on the surface (moles A/cm2 surface area), CA is the local concentration of solute A right above the surface (moles A/cm3), and K is the equilibrium constant (moles/cm3), and qA,max is the maximum amount of solute A, which can be adsorbed on the surface (moles A/cm2 surface area). At high concentrations where cA > K, qA qA,max, and at low concentrations where K>CA, the adsorption isothermbecomes linear, so that Cylindrical pore Adsorbont surtace Buk fluid barrier t Solute Ain pore fluid Solute A adsorbed on pore wall a. Think of a specific physical system-ie., propose specific materials for solute A, the fluid B and the solid surface from an outside literature reference. What does the plot of the Langmuir isotherm (qA vs. CA) look like for this specific physical system? Develop an algebraic expression that describes the maximum amount of solute A, which can be adsorbed within a single pore. b. You may now consider that the concentration profiles of solute A is only in the axial direction, not in the radial direction. You may also assume that the process is dilute with respect to solute A, the linear adsorption isotherm is valid, and the rate processes of adsorption are extremely fast. Using the shell balance approach, develop the differential forms of the general differential equation for mass transfer and Ficks flux equation, taking into account the adsorption of solute A onto the surface of pore in the differential mass balance. Then combine the simplified forms of the general differential equation of mass transfer and Ficks flux equation to arrive at a single differential equation for the transfer of solute A within the pore in terms of concentration cA. State all assumptions and boundaryinitial conditions as part of the analysis

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