The following problem is based on the figure below, where D is the dilution rate for the bioreactor shown in the picture, which is continuous. Prove that

a( 1) 0 F, S. (1+a) F, S, X1 D= = = u (1+a-ap) 1+a(1-B) 1-a(B-1) F, S, X H Vp Settler/ cell separator a F, S, X F, = aF; = r = X, B= = X a( 1) 0 F, S. (1+a) F, S, X1 D= = = u (1+a-ap) 1+a(1-B) 1-a(B-1) F, S, X H Vp Settler/ cell separator a F, S, X F, = aF; = r = X, B= = X