Homework 4
1. Name two types of glassy polymers for gas separation
2. Show typical plots for permeability, diffusivity, and solubility to illustrate the effects
of temperature on them for both rubbery and glassy polymers.
3. The diffusion (D) and solubility (S) coefficients for oxygen and nitrogen in a silicone
rubber membrane at 20°C are:
DO2 = 3 x 10-5 cm2/s SO2 = 17 x 10-4 cm3 (STP)/(cm3-cm Hg)
DN2 = 2.2 x 10-5 cm2/s SN2 = 11 x 10-4 cm3 (STP)/(cm3-cm Hg)
Calculate
1) Oxygen permeability in Barrer [10-10 cm3 (STP).cm/(cm2.s.cm Hg)],
2) Oxygen flux,
3) Nitrogen permeability in Barrer,
4) Nitrogen flux
5) Oxygen/nitrogen separation factor through the 10-micron thick silicone rubber
membrane with air (21% oxygen and 79% nitrogen) at this temperature and 1
atm as feed and vacuum (p’’ = 0) at the permeate side.
4. Membrane-based oxygenators are frequently used as a heart-lung device in medical
applications. The partial pressure of oxygen in venous blood is 53 mbar.
1) Estimate the driving force with air as feed gas at 1 atm.
2) In a heart-lung device, generally higher partial oxygen feed pressures are
supplied, i.e., partial oxygen feed pressure = 0.9 atm. A 100-micron silicone
membrane with an oxygen permeability of 550 Barrers and a carbon dioxide
permeability of 3000 Barrers is used for the oxygen and carbon dioxide
transfer. Calculate the oxygen flux.
3) Calculate the membrane area if 250 cm3 (STP) of oxygen is required per
minute.
4) The carbon dioxide pressure in the supply gas is negligible, and the venous
carbon dioxide pressure is 60 mbar. The carbon dioxide production rate is
200 cm3 (STP)/min. Is the area calculated in (3) above sufficient to remove
the carbon dioxide from the blood?
, 5. Gas solubility in glassy polymers can be described by the dual-mode sorption model:
c = cD + c H
cH' b p
c = kD p +
1+ b p
The companion transport model to the dual-mode sorption model expresses the flux
in terms of a two-part contribution as follows:
dc dc
j = − DD D − DH H
dx dx
For the case in which the permeate is effectively zero, derive the following
expression for the permeability P:
FK
P = kD DD (1 + )
1+ b p
DH
Where F = and K = cH' b / kD
DD
1. Name two types of glassy polymers for gas separation
2. Show typical plots for permeability, diffusivity, and solubility to illustrate the effects
of temperature on them for both rubbery and glassy polymers.
3. The diffusion (D) and solubility (S) coefficients for oxygen and nitrogen in a silicone
rubber membrane at 20°C are:
DO2 = 3 x 10-5 cm2/s SO2 = 17 x 10-4 cm3 (STP)/(cm3-cm Hg)
DN2 = 2.2 x 10-5 cm2/s SN2 = 11 x 10-4 cm3 (STP)/(cm3-cm Hg)
Calculate
1) Oxygen permeability in Barrer [10-10 cm3 (STP).cm/(cm2.s.cm Hg)],
2) Oxygen flux,
3) Nitrogen permeability in Barrer,
4) Nitrogen flux
5) Oxygen/nitrogen separation factor through the 10-micron thick silicone rubber
membrane with air (21% oxygen and 79% nitrogen) at this temperature and 1
atm as feed and vacuum (p’’ = 0) at the permeate side.
4. Membrane-based oxygenators are frequently used as a heart-lung device in medical
applications. The partial pressure of oxygen in venous blood is 53 mbar.
1) Estimate the driving force with air as feed gas at 1 atm.
2) In a heart-lung device, generally higher partial oxygen feed pressures are
supplied, i.e., partial oxygen feed pressure = 0.9 atm. A 100-micron silicone
membrane with an oxygen permeability of 550 Barrers and a carbon dioxide
permeability of 3000 Barrers is used for the oxygen and carbon dioxide
transfer. Calculate the oxygen flux.
3) Calculate the membrane area if 250 cm3 (STP) of oxygen is required per
minute.
4) The carbon dioxide pressure in the supply gas is negligible, and the venous
carbon dioxide pressure is 60 mbar. The carbon dioxide production rate is
200 cm3 (STP)/min. Is the area calculated in (3) above sufficient to remove
the carbon dioxide from the blood?
, 5. Gas solubility in glassy polymers can be described by the dual-mode sorption model:
c = cD + c H
cH' b p
c = kD p +
1+ b p
The companion transport model to the dual-mode sorption model expresses the flux
in terms of a two-part contribution as follows:
dc dc
j = − DD D − DH H
dx dx
For the case in which the permeate is effectively zero, derive the following
expression for the permeability P:
FK
P = kD DD (1 + )
1+ b p
DH
Where F = and K = cH' b / kD
DD
