1.30b, d. Steady-state molecular diffusion in gases.
Water evaporating from a pond at 300 K does so by molecular diffusion across an air film 1.5 mm thick. If the relative humidity of the air at the outer edge of the film is 20%, and the total pressure is 1 bar, estimate the drop in the water level per day, assuming that conditions in the film remain constant. The vapor pressure of water as a function of temperature can be accurately estimated from the Wagner equation (Reid, et al., 1987)
Solution
From Appendix A
1.31b, d. Steady-state molecular diffusion in a ternary gas system.
Calculate the fluxes and concentration profiles for the ternary system hydrogen (1), nitrogen (2), and carbon dioxide (3) under the following conditions. The temperature is 308 K and the pressure is 1 atm. The diffusion path length is 86 mm. At one end of the diffusion path the concentration is 20 mole% H2, 40% N2, 40% CO2; at the other end, the concentration is 50% H2, 20% N2, 30% CO2. The total molar flux is zero, N = 0. The MS diffusion coefficients are D12 = 83.8 mm2/s, D13 = 68.0 mm2/s, D23 = 16.8 mm2/s.
Solution
Appendix C-1: Solution of the Maxwell-Stefan equations for a multicomponent mixture of ideal gases by orthogonal collocation (NC = 3).
Orthogonal collocation matrices
The pressure and temperature in the vapour phase are
The Maxwell-Stefan diffusion coefficicients are
The length of the diffusion path is
The density of the gas phase follows from the ideal gas law
Initial estimates of the fluxes
Initial estimates of the concentrations