Equations involved in freezer burn Assuming a sphere with a given percentage of moist uniformly distributed through the sphere. It's surrounded by air with no humidity. How could I model the sublimation of the sphere's moist into the air? What's actually happening here? What are the equations involved? Assume the air is still and no temperature gradients. I guess there's some diffusion term to spread the humidity? Not sure about that. Thanks.
 A: Here's my educated guess: 
The first step would be to model the sphere as some kind of filamentary or foamy network with ice filling the voids. In that case, ice would only sublimate from the outer surface, and gradually this frozen surface would shrink as more and more of the dried network would be exposed. Then there'd be three parts to the problem: 


*

*sublimation from surface of frozen part

*diffusion through air in dried network

*diffusion and convection (from varying densities of humid and non-humid air) outside. 


For #1, the rate of sublimation is discussed in this web page. It's complicated, but a simple assumption is that the mass flow away from the surface is given by the Knudsen-Langmuir equation, in which the rate is proportional to the difference between the water vapor pressure and the "saturated vapor pressure", which is in turn given by the Clapeyron-Clausius equation and doesn't change in this problem. The water vapor pressure is initially zero, but we expect it to increase with time as the sublimation proceeds. My guess is that diffusion in part #2 would create a roadblock, leaving the pressure near the frozen surface to be simply very close to the saturated vapor pressure. 
For #2, I would assume that the network is dense enough to inhibit any convection, so only diffusion matters. In this case, we might solve Fick's 2nd law of diffusion in spherical coordinates, given whatever the vapor pressures are on the frozen surface and the network's outer surface. 
For #3, if this were a sphere floating space, we might end up with a diffusion gradient emanating outward, but with gravity I'd expect the buoyancy of the more humid air leaving the sphere to create convection which should leave the humidity at the sphere's surface close to zero. 
The problem, then, is just solving Fick's 2nd law, assuming diffusion between the sphere's outer surface with zero vapor pressure and the frozen inner surface with saturated vapor pressure, and connecting the mass flux you get from solving that equation to the shrinking size of the frozen part of the sphere. 
