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Co-Current and Counter-Current Exchange in Dialysis

Co-Current and Counter-Current Exchange in Dialysis. Steven A. Jones BIEN 501 Monday, May 5, 2008. Co-Current Exchange. Conservation of Mass. Membrane Diffusion:. Different Notation.

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Co-Current and Counter-Current Exchange in Dialysis

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  1. Co-Current and Counter-Current Exchange in Dialysis Steven A. Jones BIEN 501 Monday, May 5, 2008 Louisiana Tech University Ruston, LA 71272

  2. Co-Current Exchange Conservation of Mass Membrane Diffusion: Louisiana Tech University Ruston, LA 71272

  3. Different Notation I personally do not find the notation to be completely intuitive. For me, a better way is to talk about the mass flux per unit area along the z-direction. The conservation of mass then becomes: Louisiana Tech University Ruston, LA 71272

  4. Definitions Louisiana Tech University Ruston, LA 71272

  5. The Differential Equation With: Divide through bydz Take the limit as dz goes to 0. Louisiana Tech University Ruston, LA 71272

  6. Interpretation Consider: This equation has the simple interpretation that concentration decreases along the length of the membrane as a result of mass loss through the membrane. Because it uses well-defined derivatives, its meaning is much more clear than the equation in the book: Louisiana Tech University Ruston, LA 71272

  7. Dialysate Side, Mass Conservation On the dialysate side, the amount of mass coming in is equal to the amount of mass leaving the blood. Thus, And these two equations can be combined to obtain: Louisiana Tech University Ruston, LA 71272

  8. The Two Basic Equations Conservation of Mass is then: And Membrane Diffusion is: Where: Louisiana Tech University Ruston, LA 71272

  9. Compare to the Book’s Notation A comparison of our membrane equation: To the equation in the book: Clarifies what the book means by , for if we divide by dAm: Thus, is the rate of change of total mass flux with membrane area, and it is equivalent to the mass flux per unit area as we have defined it. Louisiana Tech University Ruston, LA 71272

  10. Combine the Two Equations Blood Side Dialysate Side Divide the blood side by Qbh and divide the dialysate side by Qdh Louisiana Tech University Ruston, LA 71272

  11. Subtract With: So: Louisiana Tech University Ruston, LA 71272

  12. Combine the Two Equations From We need to determine the transport across the membrane. We will integrate the equation below with respect to z: Louisiana Tech University Ruston, LA 71272

  13. Combine the Two Equations Louisiana Tech University Ruston, LA 71272

  14. Eq. 7.8.10 In our notation, the book’s equation is: Louisiana Tech University Ruston, LA 71272

  15. Compare Co- and Counter-Current Co-Current Counter-Current The concentration differences (inlet vs. outlet) are closer to one another for counter-current exchange. What about the net mass transfer? Louisiana Tech University Ruston, LA 71272

  16. Total Mass Transfer From Equations 7.8.1 and 7.8.2: Note sign change. And similarly: Louisiana Tech University Ruston, LA 71272

  17. Total Mass Transfer Combine to eliminate flow rates (co-exchange): Louisiana Tech University Ruston, LA 71272

  18. Total Mass Transfer Louisiana Tech University Ruston, LA 71272

  19. Total Mass Transfer Combine to eliminate flow rates (counter-exchange): Louisiana Tech University Ruston, LA 71272

  20. Total Mass Transfer Sort of a cross-difference w.r.t 0 and L. Louisiana Tech University Ruston, LA 71272

  21. Look at the Plots Look at z=L z=L z=0 z=0 Louisiana Tech University Ruston, LA 71272

  22. Clearance (K) Louisiana Tech University Ruston, LA 71272

  23. Efficiency Co-current Counter-current Are the same for co- and counter-current. Where Louisiana Tech University Ruston, LA 71272

  24. Questions Co-current Counter-current Where What do these functions look like? If QB = QD, do you get infinite efficiency? For what value of Z is E a maximum? Louisiana Tech University Ruston, LA 71272

  25. Efficiency as a function of Z Louisiana Tech University Ruston, LA 71272

  26. Question Does it help to have a large QD? Louisiana Tech University Ruston, LA 71272

  27. Counter-Current Exchange Conservation of Mass Louisiana Tech University Ruston, LA 71272

  28. Compare Co- and Counter-Current Co-Current Counter-Current Louisiana Tech University Ruston, LA 71272

  29. Integrate w.r.t. z Louisiana Tech University Ruston, LA 71272

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