mass transport
Post on 14-Jan-2016
5 Views
Preview:
DESCRIPTION
TRANSCRIPT
EKC314:TRANSPORT PHENOMENACore Course for
B.Eng.(Hons.)-Chemical EngineeringSemester I (2014/2015)
Mohamad Hekarl Uzir, DIC.MSc.,PhD.(London)-chhekarl@usm.my
School of Chemical Engineering
Engineering Campus, Universiti Sains Malaysia
Seri Ampangan, 14300 Nibong Tebal
Seberang Perai Selatan, PenangEKC314-SCE – p. 1/57
Mass Transport
Diffusivity and the Mechanisms of Mass Transport:
The movement of one chemical species, A through abinary mixture of A and B due to a concentrationgradient of A is described by Fick’s Law of diffusion.
Fick’s Law is governed by the diffusivity constant, D inthe form given by;
mAy
A= ρDAB
xA0−0
Y
which can then be written as;
jAy = −ρDABdxA
dyEKC314-SCE – p. 2/57
Diffusivity and the Mechanisms ofMass Transport
Fick’s Law for Binary Diffusion (Molecular Mass Transport)
The term D is closely dependance on:temperature differencepressure difference
Consider a thin horizontal plate of area A andthickness Y . (to be discussed during lecture)
EKC314-SCE – p. 3/57
Diffusivity and the Mechanisms ofMass Transport
Fick’s Law for Binary Diffusion (Molecular Mass Transport)
The given equation is the 1-dimensional form ofFick’s first law of diffusion
It is valid for any binary solid, liquid or gas solution,provided that jAy is defined as the mass flux relative tothe mixture velocity, vy.
During the operation, component A (gas) moves ratherslowly with a very small concentration. thus, vy isnegligibly different from 0, which is governed by;
vy = ωAvAy + ωBvBy
EKC314-SCE – p. 4/57
Diffusivity and the Mechanisms ofMass Transport
Fick’s Law for Binary Diffusion (Molecular Mass Transport)
v is an average value with vA and vB, i.e. the massaverage velocity
The species velocity vA is not the instantaneousmolecular velocity of a molecule of A, but it is thearithmetic average velocities of all the molecules of Awithin a tiny volume element.
The mass flux is defined as;
jAy = ρωA(vAy − vy)
EKC314-SCE – p. 5/57
Diffusivity and the Mechanisms ofMass Transport
Fick’s Law for Binary Diffusion (Molecular Mass Transport)
Similarly with the mass flux of component B, whichderivation leads into a conclusion that;
DAB = DBA
For the pair A-B, there is only ONE diffusivity with thefunction of pressure, temperature and composition.
EKC314-SCE – p. 6/57
Diffusivity and the Mechanisms ofMass Transport
Fick’s Law for Binary Diffusion (Molecular Mass Transport)
The mass diffusivity can be correlated in the formsimilar to that of the momentum and thermal diffusivityas the Schmidt number;
Sc =ν
DAB=
µ
ρDAB
For gas mixture, Sc number: 0.2 to 3.0.
For liquid mixture, Sc number: ≥ 40, 000
EKC314-SCE – p. 7/57
Diffusivity and the Mechanisms ofMass Transport
Temperature and Pressure Dependence of Diffusivities
For binary gas mixture at low pressure, DAB is;1. inversely proportional to the pressure2. increased with the increase of temperature3. almost independent of the composition for the given
gas pair
An equation developed by combining the kinetic theoryand corresponding-states argument is given by;
pDAB
(pcApcB)1
3 (TcATcB)5
12
(
1MA
+ 1MB
)1
2
= a
(
T√TcATcB
)b
EKC314-SCE – p. 8/57
Diffusivity and the Mechanisms ofMass Transport
Temperature and Pressure Dependence of Diffusivities
Upon data analysis and correlation, the dimensionlessconstants obtained are:1. for non-polar gas pair: a = 2.745× 10−4 and
b = 1.823 (excluding He and H2)2. for pairs consisting of H2O and a non-polar gas:
a = 3.640× 10−4 and b = 2.334
If the gases A and B are non-polar and theirLennard-Jones parameters are known, thekinetic-theory method will give better accuracy.
EKC314-SCE – p. 9/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Gas Diffusion in Gases at Low Density
For self-diffusion, DAA∗ the correlation is given by;
(cDAA∗)c = 2.96× 10−6
(
1
MA+
1
MA∗
)1
2 p2/3cA
T1/6cA
The above equation SHOULD NOT be used for He orH2 isotopes.
For binary-diffusion, the correlation expanded into theform of;
(cDAB)c = 2.96× 10−6
(
1
MA
+1
MB
)1
2 (pcApcB)1/3
(TcATcB)1/12EKC314-SCE – p. 10/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Gas Diffusion in Gases at Low Density
Some results of the kinetic theory of gases were givenpreviously as;
the mean molecular speed relative to v;
u =
√
8κT
πm
the wall collision frequency per unit area in astationary gas;
Z =1
4nu
EKC314-SCE – p. 11/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Gas Diffusion in Gases at Low Density
Some results of the kinetic theory of gases were givenpreviously as;
the mean free path;
λ =1√
2πd2n
EKC314-SCE – p. 12/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Diffusion in Binary Liquids
The theory starts with the development of thehydrodynamic-theory from the Nernst-Einsteinequation given by;
DAB = κTuA
FA
where uA/FA is the mobility of a particle A[steady-state velocity of the particle attained under theaction of a unit force].
EKC314-SCE – p. 13/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Diffusion in Binary Liquids
By applying the creeping flow equation of motion, withA is in spherical shape and slip condition applies, thefinal equation expands into;
uA
FA
=
(
3µB +RAβAB
2µB +RAβAB
)
1
6πµBRA
at the fluid-solid interface.
EKC314-SCE – p. 14/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Diffusion in Binary Liquids
The limiting cases of βAB are of particular interest tothe system:1. βAB = ∞ (no-slip condition): At the fluid-solid
interface, the previous equation reduces intoStokes’s Law in the form given by;
DABµB
κT=
1
6πRA
EKC314-SCE – p. 15/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Diffusion in Binary Liquids
The limiting cases of βAB are of particular interest tothe system:1. OR usually called the Stokes-Einstein equation. It
can be applied to the diffusion of a very largespherical molecules in solvents of low molecularweight and to suspended particles. It has also beenused to estimate the shapes of protein molecules.
2. βAB = 0 (complete slip condition): Similarly, theequation at the fluid-solid interface reduces into;
DABµB
κT=
1
4πRA
EKC314-SCE – p. 16/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Diffusion in Binary Liquids
The limiting cases of βAB are of particular interest tothe system:2. If the molecules A and B are identical,
(self-diffusion) and they can be assumed to formcubic lattice with adjacent molecules, thus;
DAAµA
κT=
1
2π
(
NA
VA
)1
3
EKC314-SCE – p. 17/57
Diffusivity and the Mechanisms ofMass Transport
Theory of Diffusion in Binary Liquids
The formulae derived above only apply to dilutesolution of A and B.
EKC314-SCE – p. 18/57
Concentration Distributions in Solidsand in Laminar Flow
Shell Mass Balances; Boundary Conditions
1. The law of conservation of mass of species A in abinary system can be written over the volume of theshell as; (to be discussed)
2. A chemical species, ’A’ may leave or enter a system bydiffusion [molecular motion and convection], these areincluded in the term, NA.
3. Species ’A’ may also be produced or consumed byhomogeneous chemical reactions.
4. When the overall balance is complete, the shell is thenmade into an infinitesimally small thickness.
5. A system of differential equation is generated either inthe form of mass or molar flux.
EKC314-SCE – p. 19/57
Concentration Distributions in Solidsand in Laminar Flow
Shell Mass Balances; Boundary Conditions
6. The integration of the differential equation leads to anumber of constants which requires boundaryconditions for them to be determined.
(a) the concentration at surface can be specified:xA = xA0.
(b) mass flux at the surface can be specified:NAz = NA0. If the ratio of NA0/NAz is known, theconcentration gradient is already known.
(c) for diffusion occurs in a solid, at the solid surface,substance A is lost to the surrounding stream dueto;
NA0 = kc(cA0 − CAb)
EKC314-SCE – p. 20/57
Concentration Distributions in Solidsand in Laminar Flow
Shell Mass Balances; Boundary Conditions
6. The integration of the differential equation leads to anumber of constants which requires boundaryconditions for them to be determined.
(d) the rate of chemical reaction at the surface can bespecified.
EKC314-SCE – p. 21/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
Consider a diffusion system where a liquid A isevaporating into gas A. Assuming that the liquidlevel is maintained at z = z1.
At the liquid-gas interface, the gas phase concentrationof A (in mole fraction) is xA1. This is the vapour
pressure of A divided by the total pressure, pvapA
p.
(Assuming that gas A and liquid B obey the idealgas mixture and that the solubility of gas B inliquid A is negligible)
A stream of gas mixture A-B with concentration xA2
flows past the top of the tube, maintaining the molefraction of A at xA2 for z = z2. EKC314-SCE – p. 22/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
System must be kept at constant pressure andtemperature and both gases A and B are assumed tobe ideal.
Neglecting the effect of dependency of gas velocity (ofthe z-component) with respect to the radius of thecontainer/cylinder.
At the steady state a balance equation of the formbelow is obtained;
NAz = −cDAB∂xA
∂z+ xA(NAz +NBz)
EKC314-SCE – p. 23/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
When NBz = 0, solving for NAz resulted into;
NAz = − cDAB
1− xA
dxA
dz
At a steady-state condition, for every increment of ∆z,the amount of A entering at plane z equals to theamount of A leaving at plane z +∆z, which leads to;
SNAz|z − SNAz|z+∆z = 0
where S is the cross-sectional area of thecolumn/cylinder.
EKC314-SCE – p. 24/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
Division by S∆z and taking limit as ∆z → 0 leads to;
−dNAz
dz= 0
Combining with the previous equation gives;
d
dz
(
cDAB
1− xA
dxA
dz
)
= 0
EKC314-SCE – p. 25/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
For an ideal gas mixture;
p = cRT
and for gases, DAB is nearly independent of thecomposition, thus;
d
dz
(
1
1− xA
dxA
dz
)
= 0
Upon integration gives;
1
1− xA
dxA
dz= C1
EKC314-SCE – p. 26/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
With further integration leads to;
− ln (1− xA) = C1z + C2
By replacing C1 with − lnK1 and C2 with − lnK2,reduces the equation into;
1− xA = Kz1K2
EKC314-SCE – p. 27/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
Using boundary conditions:i. B.C. 1: at z = z1, xA = xA1
ii. B.C. 2: at z = z2, xA = xA2
the equation becomes;
(
1− xA
1− xA1
)
=
(
1− xA2
1− xA1
)
z−z1z2−z1
The profile for gas B can be determined usingxB = 1− xA
The slope of the profile, dxA/dz is not constantalthough NAz is.
EKC314-SCE – p. 28/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
The equation determined above can be used to obtainthe average values and mass fluxes at surfaces.
The average concentration of B in the region betweenz1 and z2 can be found using;
xB,avg
xB1
=
∫ z2z1( xB
xB1
)dz∫ z2z1
dz=
∫ 1
0(xB2
xB1
)ζdζ∫ 1
0dζ
=(xB2
xB1
)ζ
ln (xB2
xB1
)
∣
∣
∣
∣
∣
1
0
where ζ = (z − z1)/(z2 − z1) or can be rewritten as;
xB,avg =xB2 − xB1
ln xB2
xB1
EKC314-SCE – p. 29/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
With the previous equation, the mass transfer at theliquid-gas interface (rate of evaporation) can beobtained using;
NAz
∣
∣
∣
∣
∣
z=z1
=cDAB
1− xA1
dxA
dz
∣
∣
∣
∣
∣
z=z1
=cDAB
xB1
dxB
dz
∣
∣
∣
∣
∣
z=z1
=cDAB
z2 − z1ln
(
xB2
xB1
)
EKC314-SCE – p. 30/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion Through a Stagnant Gas Film
By combining the mass transfer equation with that ofthe logarithmic mean given by, xB,avg leads to;
NAz
∣
∣
∣
z=z1=
cDAB
(z2 − z1)(xB)ln(xA1 − xA2)
EKC314-SCE – p. 31/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Heterogeneous Chemical Reaction
Involved solid catalyst with either gas or liquid phasereactant.
Reaction only occurs at the catalyst surface whenreactant(s) diffuses towards the surface (externaldiffusion) OR diffuses into the porous catalyst (forinternal diffusion)
For a reaction involving a component A (reactant)producing component B (product), component A needsto diffuse into the surface of the catalyst at which thereaction will occur and the product B formed from thereaction will diffuse back out. The reaction is assumedto occur instantaneously.
EKC314-SCE – p. 32/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Heterogeneous Chemical Reaction
Also assuming that the gas film is isothermal at thispoint.
For a reaction given by;
2A → B
at steady-state condition;
NBz = −1
2NAz
EKC314-SCE – p. 33/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Heterogeneous Chemical Reaction
The substituted equations give;
NAz = − cDAB
1− 12xA
dxA
dz
Consider a thin slab of thickness ∆z in the gas film.The balanced equation gives;
dNAz
dz
EKC314-SCE – p. 34/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Heterogeneous Chemical Reaction
Substitute with the above equation leads to;
d
dz
(
1
1− 12xA
dxA
dz
)
= 0
Upon integration w.r.t z resulted into;
−2 ln (1− 1
2xA) = C1z + C2 = −(2 lnK1)z − (2 lnK2)
EKC314-SCE – p. 35/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Heterogeneous Chemical Reaction
Using boundary conditions of:1. B.C. 1: at z = 0 and xA = xA0
2. B.C. 2: at z = δ and xA = 0
Leads into;
(1− 1
2xA) = (1− 1
2xA0)
1− zδ
which then gives the molar flux of reactant through thefilm;
NAz =2cDAB
δln
(
1
1− 12xA0
)
EKC314-SCE – p. 36/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Homogeneous Chemical Reaction
Consider a reaction involving component A (gasphase) and B (liquid phase) with reaction following,A(g) + B(l) → AB(l)
Assuming that the formation of AB does not affect thediffusion process (pseudo-binary assumption) andupon mass balance on species A over a thickness ∆zof the liquid phase;
NAz
∣
∣
zS −NAz
∣
∣
z+∆zS − k
′′′
1 cAS∆z = 0
where k′′′
1 is the first order rate constant for thedecomposition of A, with S as the cross-sectional areaof the liquid. EKC314-SCE – p. 37/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Homogeneous Chemical Reaction
The division by S∆z and taking limit ∆z → 0 gives;
dNAz
dz+ k
′′′
1 cA = 0
For a very small concentration of A, the byapproximation,
NAz = −DABdcAdz
EKC314-SCE – p. 38/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Homogeneous Chemical Reaction
And therefore leads to;
DABd2cAdz2
− k′′′
1 cA = 0
The above equation can be solved using the boundaryconditions:1. B.C. 1: at z = 0 and cA = cA0
2. B.C. 2: at z = L and NAz = 0 OR dcAdz
= 0
EKC314-SCE – p. 39/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Homogeneous Chemical Reaction
With the dimensionless variable as;
d2Γ
dζ2− φ2Γ = 0
the dimensionless variables include:1. dimensionless concentration: Γ = cA
cA0
2. dimensionless length: ζ = zL
3. dimensionless Thiele Modulus: φ =
√
k′′′
1L2
DAB
EKC314-SCE – p. 40/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Homogeneous Chemical Reaction
Using the necessary boundary conditions:1. B.C. 1: at ζ = 0, Γ = 1
2. B.C. 2: at ζ = 1, dΓdζ
= 0
which then gives the solution of the form of;
Γ = C1 coshφζ + C2 sinhφζ
Solving for the constants leads to;
Γ =coshφ coshφζ − sinhφ sinhφζ
coshφ=
cosh [φ(1− ζ)]
coshφ
EKC314-SCE – p. 41/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Homogeneous Chemical Reaction
Substitute back to the original notation resulted into;
cAcA0
=cosh
√
k′′′
1L2
DAB(1− z
L)
cosh
√
k′′′
1L2
DAB
The above equation can be used to determine theaverage concentration in the liquid phase;
cA,avg
cA0
=
∫ L
0( cAcA0
)dz∫ L
0dz
=tanhφ
φ
EKC314-SCE – p. 42/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion with a Homogeneous Chemical Reaction
The molar flux at the plane z = 0 can also be foundusing;
NAz
∣
∣
∣
z=0= −DAB
dcAdz
∣
∣
∣
z=0=
(
cA0DAB
L
)
φ tanhφ
EKC314-SCE – p. 43/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
Consider a system of forced-convection mass transferin which viscous flow and diffusion occur under suchconditions that the velocity field can be considered asvirtually unaffected by the diffusion.
Specifically, consider consider the absorbtion of gas Aby a laminar falling film of liquid B.
Material A is only slightly soluble in B, so that theviscosity of the liquid is unaffected.
The diffusion also takes place very slowly in the liquidfilm that component A (gas) will not penetrate very farinto the film (the penetration distance will be small incomparison with the film thickness)
EKC314-SCE – p. 44/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
Let the system is the absorption of O2 in H2O.
Consider the momentum transfer of the falling film(refer to momentum transfer example), which resultedinto the velocity profile in z-direction given by;
vz(x) = vmax
[
1−(x
δ
)2]
ignoring the end effect
EKC314-SCE – p. 45/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
Consider mass balance on component A that changesw.r.t thickness ∆x as well as ∆z which resulted into;
NAz
∣
∣
∣
zW∆x−NAz
∣
∣
∣
z+∆zW∆x
+NAx
∣
∣
∣
xW∆z −NAx
∣
∣
∣
x+∆xW∆z = 0
Dividing the above equation with W∆x∆z and theusual limiting process as volume element becomes→ 0 gives;
∂NAz
∂z+
∂NAx
∂x= 0
EKC314-SCE – p. 46/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
But, NAz and NAx are given by;
NAz = −DAB∂cA∂z
+ xA(NAz +NBz) ≈ cAvz(x)
and
NAx = −DAB∂cA∂x
+ xA(NAx +NBx) ≈ DAB∂cA∂x
respectively.
EKC314-SCE – p. 47/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
Upon substitution gives;
vmax
[
1−(x
δ
)2]
∂cA∂z
= DAB∂2cA∂x2
with boundary conditions;1. B.C. 1: at z = 0, cA = 0
2. B.C. 2: at x = 0, cA = CA0
3. B.C. 3: at x = δ, ∂cA∂x
= 0
EKC314-SCE – p. 48/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
The first B.C.: the film consists of pure B at the top(z = 0)
The second B.C.: at the liquid-gas interface, theconcentration of A is determined by the solubility of Ain B (that is cA0)
The third B.C.: A cannot diffuse through the solid wall
Due to this reasons, the equation needs to be modifiedsuch that the B.C. is valid thus the new equationbecomes;
vmax
∂cA∂z
= DAB∂2cA∂x2
EKC314-SCE – p. 49/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
With the new boundary conditions;1. B.C. 1: at z = 0, cA = 0
2. B.C. 2: at x = 0, cA = CA0
3. B.C. 3: at x = ∞, cA = 0
By applying the method of combination of variablesleads to;
cAcA0
= 1− 2√π
∫
x√
4DABzvmax
0
exp (−ξ)2dξ
EKC314-SCE – p. 50/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
Or it can also be written in the form of;
cAcA0
= 1− erfx
√
4DABzvmax
= erfcx
√
4DABzvmax
This will give the local mass flux at the gas-liquidinterface using;
NAx
∣
∣
∣
x=0= −DAB
∂cA∂x
∣
∣
∣
x=0= cA0
√
DABvmax
πz
EKC314-SCE – p. 51/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Gas Absorption)
Then the total molar flow of A across the surface atx = 0 is given by;
WA =
∫ W
0
∫ L
0
NAx
∣
∣
∣
x=0dzdy
= WLcA0
√
4DABvmax
πL
EKC314-SCE – p. 52/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Solid Dissolution)
Consider a liquid B flowing in laminar motion down avertical wall.
The film begins far enough up the wall such that vzdepends only on y for z ≥ 0.
For 0 ≤ 0 ≤ L, the wall is made of a species A that isslightly soluble in B.
For a short distances downwards, species A will notdiffuse very far into the falling film.
A is present only in a very thin boundary layers nearthe solid surface.
EKC314-SCE – p. 53/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Solid Dissolution)
The diffusing A molecules will experience a velocitydistribution similar to that of the falling film next to thewall at y = 0 where;
vz =ρgδ2 cos β
2µ
[
1−(x
δ
)2]
When cosβ = 1 and x = δ − y, thus;
vz =ρgδ2
2µ
[
1−(y
δ
)2]
=ρgδ2
2µ
[
2(y
δ
)
−(y
δ
)2]
EKC314-SCE – p. 54/57
Concentration Distributions in Solidsand in Laminar Flow
Diffusion into a Falling Liquid Film (Solid Dissolution)
At and adjacent to the wall;
(y
δ
)2
≪(y
δ
)
therefore, the velocity vz ca be approximated to;
vz =(ρ)
EKC314-SCE – p. 55/57
Equations of Change forMulticomponent Systems
Equation of Continuity for a Multicomponent Mixture:
To establish the equation of continuity for variousspecies in a multicomponent mixture (using massbalance)
To obtain diffusion equations (in various forms) byinserting the mass flux equation of continuity
To combine all equations of change for mixture forproblem solving.
EKC314-SCE – p. 56/57
Equations of Change forMulticomponent Systems
Equation of Continuity for a Multicomponent Mixture:
i. rate of increase of mass, α in the volume element,(
∂ρα∂t
)
∆x∆y∆z
ii. rate of addition of mass, α across face at x, nαx|x∆y∆z
iii. rate of removal of mass, α across face at x+∆x,nαx|x+∆x∆y∆z
iv. rate of production of mass, α by chemical reaction,rα∆x∆y∆z
EKC314-SCE – p. 57/57
top related