One approach to the development of newistresnis to grow the cells in a porous polymer

matrix. The matrix provides support for the cells to adhere to$,$ divide, and synthesize new

tissue. One concern in the design of these tissue constructs is the optimum size that can be

grown in culture. The size is determined, in part, by oxygen delivery to the cells.

Consider a polymer implant of thickness $L$ filled with cells at density $x(cell\frac{s}{m}l).$ The cells

consume $O_2$ at a constant rate of moles $\frac{O_2}{{10}^6}$ cells $.\{$:$s).$ The oxygen consumption rate

equals $Q_{O_2}x.$ The oxygen concentration at the surface of the polymeric material is

maintained uniformly at the value $C_0.$ The diffusion coefficient of oxygen in cell$-$free

polymers is the same as in water.

For these conditions, an oxygen consumption rate of $4{10}^{-7}mo\frac{l}{c}{m}^3.$s was obtained for

tissue$-$engineered matrices $200m$ thick. The following data are applicable:

$D_{O_2}=2{10}^{-5}c{m}^2{s}^{-1}$

$Q_{O_2}=1\mathrm{.}1{10}^{-9}mo{l}^{-1}({10}^6$ cells ${)}^{-1}{s}^{-1}$

$C_0=1{10}^{-7}molm{L}^{-1}$

Cell diameter $=10m$

Determine

$($a$)$ Whether oxygen consumption is diffusion or reaction limited $1$ mark

$($b$)$ The intrinsic reaction rate if all cells were exposed to $C_0.($Hint: You can assume a worst$-$case

scenario for the effectiveness factor, which is the reaction to be first order.$)1$ mark

$*$Solve part B please