P4.11 The resistance $R$ to mass transfer in the
parallel-membrane artificial kidney is
$R = R_B + R_M + R_D$, where $R = 1/K$ and $K$ is the
overall mass transfer coefficient. Given the following
data, for the transport of urea in a specific device
involving a cellulose acetate membrane,
$\delta = 0.45$ mm
$k_B = 0.9 \times 10^{-6}$ m s$^{-1}$
$\phi = 0.28$
$k_D = 1.6 \times 10^{-6}$ m s$^{-1}$
$\mathcal{D}_M = 4 \times 10^{-7}$ cm$^2$ s$^{-1}$,
calculate the percentage of $R$ which can be attributed to
$R_B$, $R_M$, and $R_D$. As an engineer assigned to reduce $R$,
what would these results suggest to you about directions
to take in a device improvement program?
