(Solved):
Please Answer correctly ASAP.
A species denoted \( A \) diffuses, having a diffusive flux \( J_{A} ...
Please Answer correctly ASAP.
A species denoted \( A \) diffuses, having a diffusive flux \( J_{A} \), through a film of stagnant species \( B \). The diffusivity is \( D_{A B} \) and the total molar concentration of all species is \( c \). On one side of the film (at a coordinate location \( z=0 \) ), species \( A \) has its mole fraction \( X_{A} \) fixed at a value \( X_{A O} \). On the other side of the film (at a coordinate location \( z=\lambda \) ) species \( A \) has a zero mole fraction. (a) Find and simplify an expression for the total flux \( N_{A} \) of species \( A \) across the film under these circumstances. The answer should involve \( D_{A B}, c, X_{A O} \) and \( \lambda \). [6 marks] (b) At location \( z=0 \), state explicitly what portion of the total flux of \( A \) is convective. Likewise state explicitly what portion of the total flux is diffusive at \( z=0 \). [4 marks] (c) For the opposite side of the film at location \( z=\lambda \), state explicitly what portion of the total flux of \( A \) is convective. Likewise state explicitly what portion of the total flux is diffusive at \( z=\lambda \). [2 marks] (d) Explain which side of the film \( z=0 \) or \( z=\lambda \) has the larger value of \( \left|d x_{A} / d z\right| \) (the magnitude of the gradient of mole fraction of \( A \) ). [4 marks] (e) Using the information obtained from part (d) sketch a diagram showing how mole fraction \( x_{A} \) varies with position \( z \) across the domain \( 0 \leq z \leq \lambda \).