CHE2163: HEAT AND MASS TRANSFER
STEADY STATEDIFFUSION – BEYOND FICK
Learning Objectives, Readings, and Learn ChemE Videos
1. Fick’s Law with bulk motion (cont’d)
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0. Incropera p792-794; Cengel p820-824; WWWR p433-438
0. Learn ChemE video on “Deriving Differential Equations for Mass Transfer” AND derivation example PDF on Moodle
1. Stagnant Film Diffusion (NB = 0)
1. Incropera p799-802; Cengel p825-827; WWWR p452-458
1. Learn ChemE video on “Unimolecular Diffusion” and “Unimolecular Diffusion Example”
1. (NA = -NB)
2. Incropera p805-808; Cengel p827-830; WWWR p462-463
2. Learn ChemE video on “ ” and “ Example”
By the end of this week, you should be able to:
· Identify the best analytical approach for a particular problem involving mass diffusion (Fick, SFD, EMCD).
· Solve these problems using appropriate equilibrium equations.
· As previously discussed, Fick’s Law isn’t entirely accurate in practice because diffusive mass transfer will often involve some (even very small) amount of bulk motion
· This is very common in process equipment:
· Evaporation in a tank of a volatile solute in air
· Condensation of water vapour onto a cooling pipe
(a) Estimate the amount of ethanol lost to evaporation per day from a cylindrical tank….
(b) Estimate the amount of hydrogen lost through the walls of a spherical container…..
We have solved both of these types of problems using Fick’s Law to date, but does Fick’s law strictly apply to both?
3.3 stagnant film diffusion
· When a solute A is diffusing through a bulk vapour B, Fick’s law cannot easily be applied because the bulk vapour is not stationary
· If both A and B are undergoing mass transfer, then the interaction must be taken into account when calculating mass transfer rates – this is very complex!
· The “stagnant film” assumption states that while the bulk vapour B may be moving (i.e. by convective effects), there is not net mass transfer of B, i.e. ; therefore, we can ignore the mass transfer rate of the bulk vapour B
· Under the stagnant film assumption, the rate of diffusive mass transfer of solute A through stagnant phase B is:
EXAMPLE: What is the rate of evaporation of ethanol from a tank (2m diameter; 3m height) containing 5% (mole) ethanol?
3.4 EQUIMOLAR COUNTERDIFFUSION
· When a solute A is diffusing through a bulk vapour B, Fick’s law cannot easily be applied because the bulk vapour is not stationary
· If both A and B are undergoing mass transfer, then the interaction must be taken into account when calculating mass transfer rates – this is very complex!
· The “equimolar counterdiffusion” assumption states that the mass transfer rates of A and B are equal but with opposite directions, hence maintaining overall pressure, i.e. ;
· Under the equimolar counterdiffusion assumption, the rate of diffusive mass transfer of solute A through phase B is:
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