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| '''Announcements''' ([[Archived-Announcements-2012|previous ones]]) | | '''Announcements''' ([[Archived-Announcements-2012|previous ones]]) |
| * [[Adsorption,_ion-exchange_and_chromatography_-_2012 |Notes for Tuesday are available]] | | <!-- * [[Adsorption,_ion-exchange_and_chromatography_-_2012 |Notes for Tuesday are available]] --> |
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| * '''Important''': parts of assignment 4 will be covered in class on Tuesday. Assignments must be submitted by the start of class on 6 November. | | * Grades for assignments and '''partial''' grades from the midterm will be posted this week in Avenue. |
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| | Some hints and an update for [[Assignment 4 - 2012|assignment 4]], question 5:
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| * The \(A_\text{salt}\) and \(A_\text{solv}\) terms '''''are not''''' the area of the membrane: they are the permeances of the salt and solvent respectively. This unfortunate notation is widely used though in most texts.
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| * There is a correction, the feed concentration '''should be 2.5 g NaCl per liter''' in the feed ('''not 2.5 wt% NaCl'''). I apologize for wasting your time for those of you that have been iterating with negative concentrations.
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| * And another hint. I found a way to solve question 5 that leads to faster convergence:
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| ** Specify \(C_F\) and \(\theta\)
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| ** Guess \(C_R\) instead
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| ** Calculate \(C_P\) from equation 5
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| ** If your calculated value of \(C_P\) is negative or exceeds \(C_F\), then repeat your guess for \(C_R\), until you get a \(C_P\) that lies between 0 and \(C_F\) and double check also that the rejection coefficient from this \(C_P\) is reasonable, around 90 to 99%.
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| ** This approach to estimate \(C_R\) and then \(C_P\) will get you really close to the final answer.
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| ** Now carry on with the rest of the steps in the notes. It's interesting how simply flipping what you guess first leads to much faster convergence.
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| ** If you iterate and get a negative value for \(C_P\) or \(C_R\), it simply means that you must decrease your guess for that term, since you obviously can't have a negative concentration.
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| * And a final hint: this question is much better to solve on a computer, with goal seek, than by hand. There is tremendous sensitivity to initial guesses, so solving by hand will take too long.
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| * For question 2(B), part 3: by definition, optimization implies we have excess degrees of freedom, i.e. more unknowns than equations. You should get a system of 3 unknowns (including \(A_1\) and \(A_2\)) and 2 equations. Set the 3rd unknown to various values (between its lower and upper bound), and solve for \(A_1\) and \(A_2\). Pick the solution that gives the optimum.
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| |} | | |} |
