A common process for increasing the moisture content of air is to bubble it through a column of water. The air bubbles are assumed to be spheres having an initial radius of 1.0 mm, and are in thermal equilibrium with the surrounding water. The saturation or equilibrium vapor pressure of water is temperature dependent, ranging from about 0.03 atm at 298 K to 1.0 atm at 373 K. The total pressure of the gas inside the air bubble is 1.0 atm, and will not change even as water evaporates into it. The bubbles initially contain some water vapor (along with the other components of air).
a. How will the final bubble radius vary i) with initial water vapor concentration in the bubble and ii) with bubble/water temperature?
b. Draw a picture of the physical system, and state at least five reasonable assumptions for the mass-transfer aspect of the water evaporation process. What coordinate system should be used?
c. What are the simplified differential forms of Fick's flux equation for water vapor (species A), the general differential equation for mass transfer in terms of concentration CA, and a resulting expression that combines the two (don't worry if it can't be too simplified).
d. Propose reasonable boundary and initial conditions