Your company manufactures hemodialyzers that have the characteristics described in Example 8.3. A colleague in the company has proposed replacing the membranes with better ones, which have the same thickness, area, and porosity but for which the urea diffusivity in the membrane is 2.7×10⁻⁵ cm²/s. Assuming that the average concentrations of urea in the blood and dialysate are the same as with the old membranes, by what percentage would the new membranes increase the urea removal rate? In terms of resistances, explain why this turns out to be such a small improvement.

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EXAMPLE 8.3 SOLUTION In patients with severe kidney disease, urea must be removed from the blood with a "hemodialyzer." In that device, the blood passes by special membranes through which urea can pass. A salt solution ("dialysate") flows on the other side of the membrane to collect the urea and to maintain the de- sired concentrations of vital salts in the blood. One geometry for hemodialyzer design is with flat membranes in a rectangular system. For such a geometry, consider the following typical values: Blood side: mass-transfer coefficient for the urea average urea concentration within the dialyzer Dialysate side: mass-transfer coefficient for the urea average urea concentration within the dialyzer Membrane: thickness diffusivity of urea in the membrane total membrane area porosity a. From Equation 8.5, the initial removal rate is Cureablood Nurea = a. Based on these values, what is the initial removal rate of urea? (Note: This rate will decrease as the urea concentration in the blood decreases.) 1 hm.blood-sideA b. One might be tempted to try to increase the removal rate of urea by developing better hemodi- alyzer membranes. Based on analysis of these characteristics, is such an effort justified? (0.0019 cm/s) (1.2m²) 1000L Axmem Durea, memAE pore :) (₁ b. The three resistances of importance are + m³ 1 hm.blood-side Axmem Durea mema Epore Cureadialyse 1m 100 cm 0.02 0.0016 cm + (1.8 x 10-5 cm²/s) (1.2m²)(0.2) + 0.003 gmol /L 0.0019 cm/s 0.020 gmol/L 60s - min 0.0011 cm/s 0.003 gmol/L 0.0016 cm 1.8 x 10-5 cm²/s 1.2 m² 20% hm.dialysate-sideA 1 (0.0019 cm/s) (12,000 cm²) + = 0.0658mol min 1 1 hm.dialysate-sideA (0.0011 cm/s) (12,000 cm²) (0.0011 cm/s) (1.2m²) 0.0016 cm (1.9 x 10-5cm²/s) (12,000 cm²) (0.2) 0.0439 S cm- = 0.0370 S = 0.0758 cm³ S cm Improvement of the membranes would increase the transfer somewhat, since its resistance is significant relative to the other resistances. But the greatest potential to increase the removal rate is on the dialysate side, which has the largest resistance.