Consider a capillary completely filled with red blood cells $($RBCs$)$ as shown in the figure

below. We wish to derive an expression for the effective viscosity $({}_{\text{e}\text{f}\text{f}})$ of the RBC

suspension passing through this capillary compared with that of plasma $($of viscosity ${}_p)$

along passing through this capillary. You may assume that the small amount of fluid between

two adjacent RBCs moves at the same velocity as that of the RBCs$.$

$($a$)$ Let the velocity of each $RBC$ be given a $v,$ and let the average pressure gradient $(-$

$d\frac{P}{d}x)$ driving the flow be G$.$ Can you find the velocity profile of the fluid in the gap

$v2h$

$(b)$ Next $do$ a force balance $on$ the column $ofRBCs$ and find the velocity $vas$ a function

$ofG.$