introduction to mass transfer

Introduction to Mass Transfer

Outline

1. Mass Transfer Mechanisms1. Molecular Diffusion2. Convective Mass Transfer

2. Fick’s Law for Molecular Diffusion 3. Molecular Diffusion in Gases

3. Equimolar Counterdiffusion4. Combined Diffusion and Convection5. Uni-component Diffusion

Mass Transfer Mechanisms

1. Convective Mass Transfer 2. Diffusion

http://www.timedomaincvd.com/CVD_Fundamentals/xprt/xprt_conv_diff.html

Mass Transfer Mechanisms

3. Convective and Diffusion

http://www.timedomaincvd.com/CVD_Fundamentals/xprt/xprt_conv_diff.html

Outline




Fick’s Law for Molecular Diffusion

We’ll first consider diffusion of molecules when the bulk fluid is not moving…For a binary mixture of A and B

Molecular Transport Equations

RECALL:driving forcerate of transport = resistance

( )xyx

d vdy

( c T)y pq d

A dy

* AAy AB

dcJ Ddy

MOMENTUM HEAT MASS

Fick’s Law for Molecular Diffusion

Example

A mixture of He and N2 gas is collected 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 0.60 atm and at the other end 0.2 m pA2 = 0.20 atm. Calculate the flux of He at steady state if DAB of the He-N2 mixture is 0.687 x 10-4 m2/s.

Convective Mass Transfer Coefficient

For fluids in convective flow…

is very similar to h,

What factors influence ?

Outline




Molecular Diffusion in Gases

Equimolar Counterdiffusion

Flux of one gaseous component is equal to but in the opposite direction of the second gaseous component

A B

BA 𝐽 𝐴𝑧∗ =− 𝐽𝐵𝑧∗



A B

BA

At constant pressure,

Then,

and

Fick’s law for B,



A B

BA

Substitution of Fick’s lawinto the equation

for equimolar counter diffusion,

𝐽 𝐴𝑧∗ =− 𝐽𝐵𝑧∗

−𝐷 𝐴𝐵𝑑𝑐 𝐴

𝑑𝑧 =−(−𝐷𝐵𝐴𝑑𝑐𝐵

𝑑𝑧 )



A B

BA


𝑑𝑧 =−(−𝐷𝐵𝐴𝑑𝑐𝐵

𝑑𝑧 )


𝑑𝑧 =−(−𝐷𝐵𝐴(−𝑑𝑐 𝐴

𝑑𝑧 ))

𝐷 𝐴𝐵=𝐷𝐵𝐴



A B

BA

𝑐 𝐴1=𝑝𝐴1

𝑅𝑇 =𝑛𝐴

𝑉

𝐽 𝐴𝑧∗ =−

𝐷𝐴𝐵

𝑅𝑇𝑑𝑝𝐴

𝑑𝑧

For gases,



A B

BA

𝑐 𝐴=𝑐 𝑥𝐴

𝐽 𝐴𝑧∗ =−𝑐𝐷 𝐴𝐵

𝑑𝑥𝐴

𝑑𝑧

In terms of mole fraction,

Molecular Diffusion in GasesExample

A large tank filled with a mixture of methane and air is connected to a second tank filled with a different composition of methane and air. Both tanks are at 100 kN/m2 and 0°C. The connection between the tanks is a tube of 2 mm inside diameter and 150 mm long. Calculate the steady state rate of transport of methane through the tube when the concentration of methane is 90 mole percent in one tank and 5 mole percent in the other. Assume that transport between the tanks is by molecular diffusion. The mass diffusivity of methane in air at 0°C and 100 kN/m2 is 1.57 x 10-5 m2/s.


Diffusion plus Convection

𝑣𝑀❑

𝑣𝐴❑

𝑣𝐴=𝑣𝐴 𝑑+𝑣𝑀

𝐽 𝐴∗=𝑣𝐴𝑑𝑐𝐴

Multiplying by ,



𝑣𝑀❑

𝑣𝐴❑

𝑣𝐴=𝑣𝐴 𝑑+𝑣𝑀

𝐽 𝐴∗=𝑣𝐴𝑑𝑐𝐴

𝑁 𝐴= 𝐽 𝐴∗+𝑐𝐴𝑣𝑀

Total convective flux of A

wrt stationary pt

Diffusion flux wrt moving fluid

Convective flux wrt to stationary point

𝑁 𝐴

𝐽 𝐴∗

𝑐𝐴𝑣𝑀



𝑁=𝑐𝑣𝑀=𝑁 𝐴+𝑁𝐵

Solving for , Replacing and ,

)



)


Uni-component Diffusion

One component (A)diffuses, while the other (B) remains stagnant

http://sst-web.tees.ac.uk/external/U0000504/Notes/ProcessPrinciples/Diffusion/Default.htm

Since B cannot diffuse,




Since B cannot diffuse,

)




𝑁 𝐴=−𝑐𝐷𝐴𝐵𝑑𝑥𝐴

𝑑𝑧 +𝑐𝐴𝑁 𝐴

𝑐

𝑁 𝐴=−𝑐𝐷 𝐴𝐵

𝑥𝐵

𝑑𝑥𝐴

𝑑𝑧




𝑁 𝐴=−𝐷 𝐴𝐵𝑃𝑅𝑇

𝑑𝑝𝐴

𝑑𝑧 +𝑁 𝐴𝑝𝐴

𝑃

When P is constant,

𝑁 𝐴=−𝐷 𝐴𝐵𝑃𝑅𝑇 𝑃𝐵

𝑑𝑝𝐴

𝑑𝑧


Example

Water in the bottom of a narrow metal tune is held a t a constant temperature of 293 K. The total pressure of air (assumed dry) is 1.01325 105 Pa and the temperature is 293 K.

Water evaporates and diffuses through the air in the tube, and the diffusion path z2-z1 is 0.1524m long. Calculate the rate of evaporation of water vapor at 293 K and 1 atm pressure. The diffusivity of water in air is 0.250 x 10-4 m2/s. Assume that the system is isothermal.

Long Exam Results

LE 1 LE 2

Mean 33.32 36.55

Median 32.00 30.75

Mode 39.00 25.50

Passing Rate 0.00 9.09

Quizzes Machine Problems Target Average ScoresStudent No. Total Q 5/5 Total* M 15/15 LE3 L 60/60 Final F 20/202011-18077 30 1.50 240 12 82 30.4 82 16.42011-57319 46 2.30 240 12 90 27.8 90 18.02010-04141 36 1.80 240 12 82 31 82 16.42010-01283 26 1.30 240 12 89 29.1 89 17.82010-31873 47 2.35 240 12 85 29 85 17.02011-07217 26 1.30 240 12 67 33.3 67 13.42011-03676 50 2.50 240 12 93 26.9 93 18.62010-36588 23 1.15 240 12 92 28.7 92 18.42011-18143 31 1.55 240 12 73 31.9 73 14.62011-18147 31 1.55 240 12 77 31.3 77 15.42011-09522 33 1.65 240 12 102 26 102 20.42011-30507 23 1.15 240 12 88 29.6 88 17.62011-09270 19 0.95 240 12 81 30.9 81 16.22010-53270 36 1.80 240 12 74 31.6 74 14.82011-14930 61 3.05 240 12 51 35 51 10.22009-21119 8 0.40 240 12 99 28.1 99 19.82011-21884 48 2.40 240 12 70 32.1 70 14.02011-19280 9 0.45 240 12 92 29.5 92 18.42011-26790 104 5.20 240 12 45 34.1 45 9.02010-21409 14 0.70 240 12 100 27.3 100 20.02011-01530 57 2.85 240 12 65 32.5 65 13.02011-30255 21 1.05 240 12 91 28.9 91 18.2

introduction to mass transfer

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