Solving Transport Phenomena in a Steady State System

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Discussion Overview

The discussion revolves around solving a problem related to transport phenomena in a steady state system involving the dissolution of a solid sphere in a liquid and the diffusion of a gas that reacts with the solid. Participants explore the application of shell mass balance, the rates of dissolution and reaction, and the implications of these processes on the system's behavior.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how to proceed with the problem after establishing the need for a shell mass balance, indicating a lack of understanding of the basic principles of transport phenomena.
  • Another participant suggests that the key statement regarding the liquid's composition implies that the rate of solution of substance C is greater than that of substance A, which may affect the dissolution dynamics.
  • A different participant refines the earlier claim, stating that the rate of solution of C should be greater than or equal to that of A, allowing for the establishment of an equation for the dissolution rate.
  • There is a discussion about the implications of having a reaction in the system, with one participant noting that the reaction removes A completely, which could lead to a constant rate of solution, unlike a scenario without reaction where the concentration of A would increase.
  • Another participant raises the complexity introduced by the diminishing surface area of the sphere as it dissolves, which could affect the rate of solution.
  • A later reply discusses feedback received from a professor regarding the importance of comparing rates of interphase mass transfer with and without reaction, indicating a deeper exploration of the topic.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the problem, with some agreeing on the implications of the reaction while others highlight the complexities involved. The discussion remains unresolved, with multiple competing views on how to approach the problem and the effects of the reaction.

Contextual Notes

Participants mention specific textbook references and problem numbers, indicating that the discussion is grounded in academic material. There are also indications of missing assumptions and unresolved mathematical steps related to the dissolution process and the impact of the reaction.

Who May Find This Useful

This discussion may be useful for students and professionals interested in transport phenomena, chemical engineering, and reaction kinetics, particularly those grappling with similar homework problems or conceptual challenges in steady state systems.

viveklib04
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I am facing a problem on transport phenomena. Can anyone help me to solve this problem. I would really appreciate it. Its little urgent. I know that i have to use shell mass balance to start the problem but how to proceed further is what making me confused.

In a beaker, a solid sphere of substance A is suspended and dissolving in the liquid B in a steady state, isothermal flow system. Above the liquid, there is gas C, which diffuse into liquid B and reacts simultaneously and irreversibly with A: A+C-->P. The liquid consists primarily of B and C
(1) develop an expression for the dissolution rate of A and find the reaction front location
(2) Show by quasi-steady-state condition how to calculate the gradual decrease in diameter of the sphere as A dissolves
 
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Hello viveklib and welcome to Physics Forums.

Should this not be in the homework section?

The liquid consists primarily of B and C

Is this not the key statement since it means that A is removed as fast as it dissolves and that the rate of solution of C is greater than the rate of solution of A.
 


Hello Studiot,

I am new to this forum and did not exactly where to post this. Anyways, I understand your statement and agree to it but i am struggling on how to start the problem. I know i have to use the shell mass balance at the beginning and it goes as:

Acc=In-out +net gn, where acc=0 because of steady state.

but how to go further is what baffling me? I am not good at basic of transport phenomena. I tried to take help from the prof but he's not willing to help till i show something worthwhile to him.
 


I couldn't find that problem in my rather old B, S & L (1960 edition) do you have a page number? And has the reference system changed? You seem to have the problem in both chapters 18 and 19. It would seem more appropriate to my 18.

I know I said before that the rate of solution of C is greater than the rate of solution of A but in fact it should have been greater than or equal to and you can take the equality to obtain an equation for part (1) since the rate of solution of A then = rate of diffusion of C into the liquid

I remember my Chem Eng flatmate getting a First back then. He used to go everywhere muttering

Input = Output plus Accumulation

For (2) the accumulation (of the sphere of A) is negative.
 
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Thanks for the reply. I don't have the hard copy of the B, S & L book but i downloaded it online pdf. Its says 2nd edition and the problems which it is based on i.e., 18.B11 and 19.B6 are on pages 574 and 607 respectively. Thanks for the hint and with that, i can try solving part 1 of the problem. Also if you can find the problem 18.B11 in the textbook than can you do me one small favor? there's one more problem that my prof gave me. there's a reaction going on in that problem. He told me to specify the advantages of having a reaction than not having a reaction or simply "why the reaction is so important in that problem". can you specify few points on it.
 


but i downloaded it online pdf

Do you have a link?

The only thing I can think of about the reaction is that it removes A completely. If A simply went into solution without reaction its solution concentration would increase and the rate of solution gradually decrease. With removal I think you can say that the rate of solution is constant, unless you have to account for the diminishing surface area of the shrinking ball ( which would make matters really difficult)
 


Thank you very much
 


I submitted my assignment yesterday and my professor gave me feedback based on the explanation i gave regarding the importance of reaction in 18B11. Basically i had written exactly what you said and in reply he said that i am heading in the right direction but i am making the situation transient and that greatly complicates the situation (mathematically). Even without reaction there is a flow through the system. Once the absorbed species reaches the bulk fluid(z greater than delta), flow will remove it so it won't accumulate.

He told me to think in terms of comparing the rates of interphase mass transfer with and without reaction.

Can you explain this? This is not for any assignment but for my own knowledge. Thanks
 

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