In this problem, we examine a model for the transport of oxygen from air in the lungs to blood. First, show that, for the initial and boundary conditions c(x, t) = c(x, 0) = co (0 < x < ∞] and c(0, t) = Cs' (0 < t < ∞ ) where Co and Cs are constants, the concentration, c(x, t), of a species is given by

Where erfξ is the error function (Justification 9.4) and the concentration c(x, t) evolves by diffusion from the yz-plane of constant concentration, such as might occur if a condensed phase is absorbing a species from a gas phase. Now draw graphs of concentration profiles at several different times of your choice for the diffusion of oxygen into water at 298 K (when D = 2.10 X 10-9 m2 s-l) on a spatial scale comparable to passage of oxygen from lungs through alveoli into the blood. Use co= 0 and set Cs equal to the solubility of oxygen in water. Hint. Use mathematical software.

c(x,t) = co + (c, c,){1- erf5} (x,t) = (4Dt)\/2