Solving Transport Phenomena in a Steady State System

[viveklib04]

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

 

[Studiot]

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.

 

[viveklib04]

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.

 

[Studiot]

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.

 

[viveklib04]

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.

 

[Studiot]

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)

 

[viveklib04]

Thank you very much

 

[viveklib04]

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