PRACTICAL 9: Diffusion
(A few data tables are available at the end of the question sheet.)
1. Draw a table of equations for 1D diffusion Fick’s law diffusion in the following circumstances (hint – consider Fourier’s law for conduction):
a) Mass transfer through a flat wall, concentration units are in partial pressure
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b) Mass transfer through a flat wall, concentration units are in molar concentration
c) Mass transfer through a flat wall, concentration units are in molar fraction
d) Mass transfer through a cylindrical wall, concentration units are in partial pressure
e) Mass transfer through a cylindrical wall, concentration units are in molar concentration
f) Mass transfer through a cylindrical wall, concentration units are in molar fraction
g) Mass transfer through a spherical wall, concentration units are in partial pressure
h) Mass transfer through a spherical wall, concentration units are in molar concentration
i) Mass transfer through a spherical wall, concentration units are in molar fraction
j) Do you think we can extend Fick’s law using the simple concept of resistances in series? Why/Why not?
2. Estimate the mass diffusivity DAB at 25 oC for:
a) ethanol in air (very low concentration, total pressure 1 atm);
b) ethanol in air (very low concentration, total pressure 2 atm);
c) ethanol in water (0.05 kmol m-3 );
d) ethanol in water (4 kmol m-3 );
e) comment on the diffusivity of ethanol in water compared to air. Would the values ever be equal?
3. A thin cylindrical membrane is used to separate H2 from a gas stream. The concentration of H2 is 0.01 kmol m-3 and 0.08 kmol m-3 at the inner and outer surfaces of the membrane respectively, the cylinder is 10 cm long, with a 1 cm internal diameter and the membrane is 1 mm thick. If the diffusivity of H2 through the membrane is 10-9 m2s-1, what is the diffusive molar flux of H2 through the membrane?
4. Consider the interface between atmospheric air and a body of water, both at 25 oC.
a) What is the mole fraction of water on the air side of the interface?
b) What are the mole and mass fractions of O2 on the water side of the interface, assuming air contains 21 % O2 by volume?
c) What is the mass transfer flux of water into the air if the relative humidity is 50% and the boundary is 1cm thick?
d) What is the mass transfer flux of oxygen between the air and the water if the boundary is 1cm thick ?
5. The thermal conductivity of insulation increases if water vapour condenses within it. This generally occurs in cold weather, when water vapour in a humidified room diffuses through a dry wall (plaster board) and condenses in the adjoining insulation.
a) If the vapour pressure for water is 0.03 bar in the room and 0.0 bar in the insulation, the dry wall is 10 mm thick, the solubility of water vapour in the wall material is approximately 5 x 10-3 kmol m-3 bar-1 and the binary diffusion coefficient for water vapour in the dry wall is approximately 10-9 m2s-1, estimate the mass diffusion rate for a 3 m by 5 m plasterboard wall.
b) Comment on your confidence in your answer and the validity of your assumptions; how will the diffusive flux and the water content of the insulation change over time? What will happen in summer? (consider both heat and mass transfer processes in your answer)
6. One of your friends recently told you that he uses compressed N2 rather than compressed air to fill his car tyres because it keeps the tyre pressure higher for longer. High tyre pressure means less surface area in contact with the road, lower friction and hence lower fuel consumption for a motorist, or faster speed for the same effort on a bicycle.
Cycling home from uni one day you notice a servo which has both compressed N2 and compressed air available for filling tyres; the air is free, the N2 will cost you $ 10 to fill your bike tyres. You would like your tyres to hold their pressure for longer, but $ 10 is a lot of money, and your friend hasn’t studied mass transfer. You decide to calculate if it is worth the money to put N2 in your bike tyres.
Your tyres are made of rubber 1 mm thick and are typically at 25 oC. You live near sea level, where atmospheric air pressure is 14.7 psi. You assume that gas is lost only through diffusion through the rubber (none through the valve or rim), and you model this as diffusion through stationary medium. The volume of gas in each tyre is constant at 0.01 m3 and the surface are through which gas diffuses is also constant: 0.3 m2. Determine the following:
a. what are the concentrations of N2 and O2 on the inside edge of the rubber tyre when the tyre has been filled to 55 psi (gauge pressure) with compressed air (79 % N2, 21 % O2 by volume)?
b. what are the rates of loss of N2 and O2 from the tyre due to diffusion when the tyre has been filled to 55 psi (gauge pressure) with compressed air? what is the rate of pressure loss from the tyre?
c. what is the concentration of N2 on the inside edge of the rubber tyre when the tyre has been filled to 55 psi (gauge pressure) with compressed N2?
d. what is the rate of loss of N2 from the tyre due to diffusion when the tyre has been filled to 55 psi (gauge pressure) with compressed N2? what is the rate of pressure loss from the tyre?
e. develop a general equation for the tyre pressure as a function of time, after it has been filled to 55 psi (gauge pressure) initially. Compare these expressions for compressed air and compressed N2
f. how long will it take until the tyre pressure falls to 25 psi (gauge pressure) under each scenario?
g. will you fill your tyres with air or N2 next time? Why? Comment also on the validity of your assumptions and your confidence in your calculations.
A FEW DATA TABLES
Incropera and de 1
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