Problem $12\mathrm{.}6$ from our textbook $($Oxygen Diffusion and Consumption in the Cornea$).$ The Cornea of the mammalian eye can be considered, as a first approximation, to be a membrane $0\mathrm{.}05cm$ thick. Assume the thickness of the cornea is much smaller than its surface area so it can be treated as a slab. The inside of the cornea is bathed by a dilute salt solution, the aqueous humor. The aqueous humor maintains a small oxygen concentration at the corneal inner surface which we assume for this problem to be zero. The cornea uses up oxygen at the rate of $8\mathrm{.}045{10}^{-10}$mol$\frac{O_2}{c}{m}^3$ cornea per second. This oxygen consumption follows a Oth$-$order reaction. The diffusivity of oxygen in the cornea is $1\mathrm{.}08{10}^{-9}\frac{m^2}{s}.1)$ Assume the eye is open and the outer surface of the cornea is in equilibrium with the oxygen concentration $(21\%)$ in the air. The equilibrium Henry's law constant between oxygen at the corneal surface and that in the air is $47,000at\frac{m}{m}$ole fraction of $O_2.$ For conversion, use $1$ mole fraction of $O_2$ in the cornea as approximately equal to $55\mathrm{.}56{10}^{-3}$ moles of $\frac{O_2}{c}{m}^3$ of cornea. Calculate the concentration of oxygen in the corneal outer surface in $mo\frac{l}{c}{m}^3.2)$ Calculate the oxygen concentration profile as a function of depth in the cornea under steady$-$state conditions $($plug in numbers and simplify$).3)$ Roughly sketch the oxygen concentration profile calculated in part $2.4)$ Calculate the oxygen flux at the corneal outer surface.

Flow$/$length $=k^{\text{'}\text{'}}(r_o^2-r_i^2)$

$12\mathrm{.}61)$ At outer surface, concentration $=2\mathrm{.}482{10}^{-7}mo\frac{l}{c}{m}^3$ cornea; $2)c(x)=3\mathrm{.}725{10}^{-5}{x}^2+3\mathrm{.}103$

Problem $12\mathrm{.}6$ from our textbook $($Oxygen Diffusion and Consumption in the Cornea$).$ The Cornea of the mammalian eye can be considered, as a first approximation, to be a membrane $0\mathrm{.}05cm$ thick. Assume the thickness of the cornea is much smaller than its surface area so it can be treated as a slab. The inside of the cornea is bathed by a dilute salt solution, the aqueous humor. The aqueous humor maintains a small oxygen concentration at the corneal inner surface which we assume for this problem to be zero. The cornea uses up oxygen at the rate of $8\mathrm{.}045{10}^{-10}$mol$\frac{O_2}{c}{m}^3$ cornea per second. This oxygen consumption follows a Oth$-$order reaction. The diffusivity of oxygen in the cornea is $1\mathrm{.}08{10}^{-9}\frac{m^2}{s}.1)$ Assume the eye is open and the outer surface of the cornea is in equilibrium with the oxygen concentration $(21\%)$ in the air. The equilibrium Henry's law constant between oxygen at the corneal surface and that in the air is $47,000at\frac{m}{m}$ole fraction of $O_2.$ For conversion, use $1$ mole fraction of $O_2$ in the cornea as approximately equal to $55\mathrm{.}56{10}^{-3}$ moles of $\frac{O_2}{c}{m}^3$ of cornea. Calculate the concentration of oxygen in the corneal outer surface in $mo\frac{l}{c}{m}^3.2)$ Calculate the oxygen concentration profile as a function of depth in the cornea under steady$-$state conditions $($plug in numbers and simplify$).3)$ Roughly sketch the oxygen concentration profile calculated in part $2.4)$ Calculate the oxygen flux at the corneal outer surface.

$**$ANSWERS:

$1)$ At outer surface, concentration $=2\mathrm{.}482{10}^{-7}mo\frac{l}{c}{m}^3$ cornea; $2)c(x)=3\mathrm{.}725{10}^{-5}{x}^2+3\mathrm{.}103{10}^{-6}$xmo$\frac{l}{c}{m}^3$

$4)N_{\text{o}\text{u}\text{t}}=-7\mathrm{.}373mo\frac{l}{c}{m}^2*s$