What is Fick’s Law?
governing equation for mass transport in STAGNANT gas (ie. diffusion ONLY)
N(A) = - D C(tot) dy(A)/dz
What is the governing equation for diffusion in a moving gas (ie. the Mass Transfer Eqn)? what are the two components?
N(A) = convective flux + diffusive flux (Fick’s)
convective = N(tot) y(A)
Diffusivity constant relationship with T and P in a gas
D proportional to T^1.75
proportional to 1/P (ie. inversely proportional)
What law is used for diffusion of liquid molecules (solute A in solvent B)?
Stokes-Einstein eqn
assumes molecules are perfect spheres
Name the type of diffusion of fluids in a porous medium. How do pores affect diffusion?
Knudsen Diffusion
diffusion is FASTER with pores
eqn for Kn in knudsen diffusion
Kn = L(FP) / d(pore)
where L(FP) = mean free path length
and d(pore) is pore diameter.
LARGE Kn means significant pore influence
Diffusivity constant relationship with T when Kn is high
D(Kn) proportional to d(pore)*√T
Mass transfer coefficient - what is the eqn in which it appears
N(A) = km * ∆C(A)
km is the mass transfer coefficient, parallels h in HT.
Define the Sherwood number
Nu equivalent for MT.
Sh = km * a / D
(vs Nu = h * a / k)
Define Qm. what are two general equations for Qm?
Qm is the total flow of moles per second.
Qm = d/dt (V * C(T) * y(A))
ie. change in number of moles of A wrt time
Qm = A * N(A)
similar to Q = A * q in HT.
mass transfer coefficient km and Sh for binary equimolar counter diffusion in a capillary
km = D / L
(similar to h = k/L)
Sh = 1
Purpose of Stefan tube - describe set up and how D is found
measuring D for the vapour of a volatile liquid, F
liquid in cylinder, gas blown across the top so that y(F) = 0
Slow inflow of air so assume N(A) stagnant hence simplify MTE –> integrate for eqn.
measure N(F) by loss of weight of liquid to find D
km and Sh for dilute gases
similar to conduction in slab
km = D / L
Sh = 1
km = D/L for rich gases - how appropriate?
km = D/L appropriate for dilute gases.
UNDERPREDICTS mass transfer rate for rich gases, as y–>1 by up to 50%
Eqns for diffusion with reaction
Rate per SA = N(A) = km ∆C(A)
ROR (kinetics) = kr * C(A,S)
where ∆C(A) is difference in conc A at bulk and at surface (where the rxn is occurring)
C(A,S) being conc A at surface
SSA: equate the two rates.
eqn for effective rate constant when there is diffusion and a first order reaction taking place
1 / Kr = 1/kr + 1/km
for effective rate constant Kr
inequality condition for PURE mass transfer (ie. diffusion controlled, ignore reaction, sufficiently fast)
D «_space;a * kr
where a is characteristic length, eg. radius
ie. kr is large, rxn is fast
Kr = km
inequality condition for reaction/kinetic controlled
D»_space; a * kr
ie, kr is small so it is the slowest thing here.
Kr = kr
