5. Two gases are initially separated into two bulbs connected by a narrow diameter
capillary. Pure N2 flows from right to left, as shown below. We assume that the
system has achieved steady state and no reactions occur between N2 and O2. We
also assume that the velocity vector has only an axial component and there is
diffusion only in the axial direction.
Pure
O2
Pure
N2
z=L
z=0
The governing equation is given by below:
$\frac{dC}{dz} = D \frac{d^2C}{dz^2}$
where $v$ and $D$ are constants. The boundary conditions are:
$\cdot$ At $z = L$, $C = C_0$
$\cdot$ At $z = 0$, $C = 0$
a. Solve the differential equation to obtain C(z), the concentration profile of O2.
(20 pts)
b. BONUS: Show that in the limit of very small values of vL/D (for $\frac{vL}{D} << 1$), the
solution becomes linear ($C/C_0 = z/L$) (5 pts)
