CE20095 - Mass Transfer Models Flashcards
(41 cards)
How is convective diffusion found?
Na = -DdCa/dz + vCa
Where v = (Na + Nb) / Ctot
Convective diffusion considers bulk movement of particles (via convection) as well as random diffusivity motion
What occurs in equimolar counter diffusion?
N a = - N b
What is diffusion and convection?
Diffusion – mass transfer of individual molecules by random molecular motion and associated with a driving force such as a concentration gradient.
Example: dissolving sugar in water
Convection – is the collective motion of particles in a fluid
Example: Flow of fluid in a pipe
- Convection also includes diffusion and that is why we use the term convective diffusion
How is convective mass transport calculated?
N = v*C
Mass flux of comp. A = fluid velocity * conc A
What occurs in diffusion in stagnant components?
N.B = 0
How can the equation for convective diffusion be simplified when considering equimolar diffusion?
N.A = D/RT * ((PA1 - PA2)/ z2 - z1))
! Derive
How is the equation for stagnant diffusion simplified for stagnant diffusion?
N.A = D/RT * PT/(z2-z1) * ln ((PT - PA2 / PT - PA1 ))
! Derive
What are the three main mass transfer models, used to represent conditions near a boundary?
Two film theory
Penetration theory (Higbie)
Surface renewal theory (Higbie-Danckwerts)
What’s the (Two-) film theory?
A model to represent conditions near the boundary.
Basic concept – the resistance to diffusion can be considered equivalent to that in hypothetical film of a certain thickness.
It postulates that near the interface there exists a laminar film . This laminar film is hypothetical since we really don’t know the details of the velocity profile near the interface.
How does film theory take place?
Basic concept – the resistance to diffusion can be considered equivalent to that in hypothetical film of a certain thickness.
Mass transfer occurs by molecular diffusion through a fluid layer at phase boundary
- The theory assumes that for equimolar counter diffusion (EMCD) there is no turbulence at the interface, and a laminar layer exists in two films.
- In reality, the concentration gradient is linear close to the interface, and becomes less as one moves away from it.
It assumes that the resistance to mass transfer lies in 2 layers (one either side of the interface).
Inside these layers, the model assumes that the concentration gradient is linear; the thickness of the films are shown by Zg and ZL.
- It is assumed that equilibrium exists at the interface and therefore the relative position of points are determined by the equilibrium between the two phases (hence the ‘jump’ from point a to b).
How is the rate of mass transfer per unit area in terms of the two-film theory for EMCD given?
From liquid film:
N(A.l) = (D.l/z.l)*(C.Ai - C.A)
= k.l * (C.Ai - C.A)
Where k.l is liquid film mass transfer coefficient
From gas film:
N(A.g) = (D.g/Z.g*RT) * (P.A - P.Ai)
= k.g(P.A - P.Ai)
Where k.g is gas film mass transfer coefficient
k.l/k.g = (P.A - P.Ai) / (C.Ai - CA)
It’s assumed there is no accumulation.
What’s Henry’s law?
P.A = H * C.A
Where H is Henry’s constant
What does the penetration theory suggest?
It’s a model to represent conditions near the boundary.
It assumes that eddies bring an element of the fluid (e.g. liquid) to the interface, the fluid is exposed to the second phase (e.g. gas) for a set time interval; after this time interval the surface element (liq) is remixed with the bulk.
What are basic assumptions of the penetration theory?
1) Unsteady state mass transfer (by diffusion) occurs to a liquid element as long as it is in contact with the bubbles or other phase
2) Equilibrium exists at the gas-liquid interface
3) Each if the liquid elements stays in contact with the gas for a fixed period of time
What is Fick’s 2nd law?
Law for unsteady state concentration gradient:
dC.A/dt = DA.B * d2C.A/dy2
It is true for equimolar counter diffusion.
It is only true for absorption when concentrations of the diffusing material are low.
From this, surface flux and average flux can be found.
Fick’s first law considers changes in concentration with distance WHEREAS Fick’s second law considers this with time.
What is surface flux?
The mass transfer rate per unit area of surface
What is the mass transfer coefficient in penetration theory?
k = (D.AB / pi*t )^0.5
Average k = double the above
What are the drawbacks of penetration theory?
It assumes the same contact time for all liquid elements (however different sized particles would have different contact times)
Some elements may be quickly swept away by the eddies or some element may stay at the gas liquid interface for longer time. (age distribution)
It assumes constant time period
What are the assumptions of the surface renewal theory?
Liquid elements at the gas liquid interface are being randomly replaced by fresh liquid (random distribution of ages)
Unsteady state mass transfer occurs at the gas liquid interface
It takes place over a time distribution (whereas penetration occurs over a fixed period of time)
What is S in the surface renewal theory equations?
Danckwerts parameter
S is an age distribution parameter (independent of the age of the element) or fractional rate of surface renewal. (S ≈ 1/tm) ; mean residence time (tm).
What does the size of the k value for mass transfer coefficients suggest?
Larger k means more effective mass transfer.
As k increases, film resistance decreases (film theory).
What are the boundary conditions for penetration theory?
At t=0, for all values of y, Ca = Ca0 (bulk value)
At t>0, if y=0, Ca = Cai (interface value)
if y = infinity, Ca = Ca0
Ca0 constant as it’s so far from the interface
What’s the inverse of mass transfer coefficient equal to?
Resistance (1 / K)
Overall resistance is equal to the sum of individual resistances
The term (gas film control) refers to the resistance lie in the gas film.
The term (liquid film control) refers to the resistance lie in the liquid film.
What problems does the use of an overall mass transfer coefficient solve?
Problem 1 is the difference of concentration at different heights in the column
Problem 2 is that the interfacial area is unknown.
Incorporate the area into the M.T.C. and calculate K multiplied by a (a is the interfacial area).
