Answered: Consider a fluid layer A surrounded on…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Transcribed Image Text:Consider a fluid layer A surrounded on both sides by a fluid, B. The fluid layer can be thought of as a membrane. A species S is diffusing across this membrane, and has concentrations c and c (in the fluid B) on the two sides of the membrane, as shown in Fig. 7.28. It often happens that the solubility of material S inside the membrane is different than its solubility in bulk solution B. We therefore define a partition coefficient k as concentration of S in material A (at equilibrium) (7.30) concentration of S in material B Hence k < 1 means that S is less soluble in the membrane, and k> 1 means S is more soluble. Write down an expression for the flux across the membrane in terms of c, c, DA (diffusion coefficient of S in A) and Aya. Sketch the concentration profile. What is the effective diffusion coefficient value with partitioning, De?

Fluid A
Fluid B
Fluid B
Concentration
Concentration
дуА
Figure 7.28

Expert Solution

Step 1

From Fick's first law of diffusion which states that diffusion flux of concentration goes from higher concentration to the lower concentration which can be written as

J= - D dc/dy

Here J is the diffusion flux

D is the diffusion coefficient or diffusivity and dc/dy is concentration gradient .

Step 2

Draw the diagram of the conentration profile for k<1 as,