![Molecular diffusion
The diffusion of molecules when the whole
bulk fluid is not moving but stationary.
Diffusion of molecules is due to a
concentration gradient.
The general Fick’s Law Equation for binary mixture of A and B
dz
dx
cD
J A
AB
AZ
*
c = total concentration of A and B [kgmol (A + B)/m3
]
xA= mole fraction of A in the mixture of A and B](https://image.slidesharecdn.com/35236lect1introductiontomas1stransfer-240802154848-3ef0dc9e/85/35236lect-1Introduction-to-Mas-1s-Transfer-ppt-3-320.jpg)
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- 1. Fick’s Law of Diffusion Molecular diffusion or molecular transport can be defined as the transfer or movement of individual molecules through a fluid by mean of the random, individual movements of the molecules. If there are greater number of A molecules near point (1) than at (2), then since molecules diffuse randomly in both direction, more A molecules will diffuse from (1) to (2) than from (2) to (1). The net diffusion of A is from high to low concentration regions. B B B B B B B B B B B A A Figure 3: Schematic diagram of molecular diffusion process (2) (1)
- 2. The two modes of mass transfer: - Molecular diffusion - Convective mass transfer
- 3. Molecular diffusion The diffusion of molecules when the whole bulk fluid is not moving but stationary. Diffusion of molecules is due to a concentration gradient. The general Fick’s Law Equation for binary mixture of A and B dz dx cD J A AB AZ * c = total concentration of A and B [kgmol (A + B)/m3 ] xA= mole fraction of A in the mixture of A and B
- 4. Example A mixture of He and N2 gas is contained in a pipe at 298 K and 1 atm total pressure which is constant throughout. At one end of the pipe at point 1 the partial pressure pA1 of He is 0.6 atm and at the other end 0.2 m pA2 = 0.2 atm. Calculate the flux of He at steady state if DAB of the He-N2 mixture is 0.687 x 10-4 m2 /s.
- 5. Solution Since a total pressure P is constant, the c is constant, where c is as follows for a gas according to the perfect gas law: Where n is kg mol A plus B, V is volume in m3 , T is temperature in K, R is 8314.3 m3 .Pa/kg mol.K or R is 82.057 x 10-3 cm3 . atm/g. mol. K, and c is kg mol A plus B/m3. For steady state the flux J*Az in Eq.(6.1-3) is constant. Also DAB for gas is constant. Rearranging Eq. (6.1-3) and integrating. (6.1-11)
- 6. Also, from the perfect gas law, pAV=nART, and Substituting Eq. (6.1-12) into (6.1-11), This is the final equation to use, which is in a form eqsily used for gases. Partial pressures are pA1 = 0.6 atm = 0.6 x 1.01325 x 105 = 6.04 x 104 Pa and pA2 = 0.2 atm = 0.2 x 1.01325 x 105 = 2.027 x 104 Pa. Then, using SI units, (6.1-13)
- 7. If pressures in atm are used with SI unit, Other driving forces (besides concentration differences) for diffusion also occur because of temperature, pressure, electrical potential, and other gradients.
- 8. Convection Mass Transfer When a fluid flowing outside a solid surface in forced convection motion, rate of convective mass transfer is given by: kc - mass transfer coefficient (m/s) cL1 - bulk fluid conc. cLi - conc of fluid near the solid surface Kc depend on: 1. system geometry 2. Fluid properties 3. Flow velocity ) ( 1 Li L c A c c k N
- 9. Principles of Mass Transfer Molecular Diffusion in Gases Molecular Diffusion in Gases
- 10. CONTENTS Mass Transfer Molecular Diffusion Convective Mass Transfer Gases Liquid Solid
- 12. Molecular Diffusion in Gases Equimolar Counterdiffussion in Gases
- 15. For a binary gas mixture of A and B, the diffusivity coefficient DAB=DBA