Using the membrane and feed conditions of and values for R_m and K₂ determined in Example 14.3 for DE microfiltration, compute and plot the permeate flux and cumulative permeate volume as a function of time. Assume a combined operation with Stage 1 at a constant permeate rate of 10 mL/minute to an upper-limit pressure drop of 25 psi, followed by Stage 2 at this pressure drop until the permeate rate drops to a lower limit of 5 mL/minute.

Example 14.3

Diluted skim milk with a protein concentration of 4.3 g/L is to undergo DEF microfiltration. Experiments have been performed using a cellulose- acetate membrane with an average pore diameter of 0.45 mm and A_M = 17.3 cm². For Stage 1 operation at a constant-permeate rate of 15 mL/minute, pressure drop across the cake and membrane increases from 0.3 psi to an upper limit of 20 psi in 400 seconds. The permeate viscosity is 1 cP. If continued in a second stage at constant ΔP at the upper limit until the permeate rate drops to 5 mL/minute, estimate the additional time of operation. Also, prepare plots of permeate volume in mL and permeate flux in mL/cm²-minute as functions of time.