Question

1) As discussed briefly in class, urea removal in hemodiafiltration is due to both diffusion and actual flow of water from the blood into the dialysate. The rate of solute mass transfer from the blood into the dialysate can be expressed as the sum of these contributions as:

(m/A)= (k_m) [C_B-C_D] +vC_B

      where v is the flow velocity across the membrane.

    A) Derive an expression for the blood-side flow rate (q_B) as a function of axial position (z) in a hollow fiber membrane dialyzer with fiber radius R. You should perform a mass balance over a differential volume (from z to z+?z) to evaluate q_B. You can assume that the fluid velocity across the membrane (v) is a constant (independent of z).

    B)   Derive an expression for the solute concentration in the blood as a function z by solving the species mass balance in the dialyzer assuming that CD = 0 at all axial positions. You must take into account the variation in q_B with z. Express your results in terms of the solute concentration in the blood entering the dialyzer (C_o), the inlet blood flow rate (q_o), the dialyzer geometry, the fluid velocity v, and mass transfer coefficient k_m.

    C) Evaluate the clearance of the dialyzer in terms of v, k_m, q_Bo, and A.

Answer 1