4217011(1).ppt

Introduction to Mass Transfer

Introduction to Mass Transfer

OutlineMass Transfer MechanismsMolecular DiffusionConvective Mass Transfer 2. Ficks Law for Molecular Diffusion 3. Molecular Diffusion in GasesEquimolar CounterdiffusionCombined Diffusion and ConvectionUni-component Diffusion

Mass Transfer Mechanisms

1. Convective Mass Transfer

2. Diffusionhttp://www.timedomaincvd.com/CVD_Fundamentals/xprt/xprt_conv_diff.htmlAnalogous to heat convection and conduction3

Mass Transfer Mechanisms3. Convective and Diffusionhttp://www.timedomaincvd.com/CVD_Fundamentals/xprt/xprt_conv_diff.html


Ficks Law for Molecular DiffusionFor a binary mixture of A and B

J = molar diffusivityC = total concentrationXa = mole fraction of A in the mixture

Other driving forces for diffusion: temperature, pressure, electrical potential, etc. (Will not be discussed in 131)6

Molecular Transport EquationsRECALL:

MOMENTUMHEATMASS

Ficks Law for Molecular DiffusionExample

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. Steady state diffusionConcentration at the boundaries are constantDiffusion is limited to molecular motionDiffusivity is independent from concentrationNo temperature gradientAssume ideal gas, calculate c values from the P given.Answer: J = 5.63 x 10-6 kg mol of A/s-m28

Convective Mass Transfer CoefficientTo have a fluid in convective flow usually requires the fluid to be flowing past another immiscible fluid or a solid surface.Na = convective molar flux, k = MTC with different units depending on the units of the driving force*MTC is a function of system geometry, fluid properties, and flow velocity.

We will discuss convective mass transfer in more detail LATER9


Molecular Diffusion in GasesEquimolar Counterdiffusion

Flux of one gaseous component is equal to but in the opposite direction of the second gaseous componentABBAConsider 2 gases A and B in a chamber, initially separated by a partition. At some instant in time, the partition is removed, and A and B diffuse in opposite direction as a result of the concentration gradients.

Examples: distillation, alcohol/H2O, HOAc/H2O

11


ABBAConsider 2 gases A and B in a chamber, initially separated by a partition. At some instant in time, the partition is removed, and A and B diffuse in opposite direction as a result of the concentration gradients. 12


ABBASubstitution of Ficks lawinto the equation for equimolar counter diffusion,Consider 2 gases A and B in a chamber, initially separated by a partition. At some instant in time, the partition is removed, and A and B diffuse in opposite direction as a result of the concentration gradients. 13


ABBAFor a binary mixture of A and B the diffusivity coefficient DAB for A diffusing in B is the same as DBA for B diffusing into A.14


ABBAFor gases, 15


ABBAIn terms of mole fraction, 16

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 0C. 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 0C and 100 kN/m2 is 1.57 x 10-5 m2/s.17

Molecular Diffusion in GasesDiffusion plus Convection

Va= velocity of A relative to a stationary point, sum of diffusion velocity and the average or convective velocityVad = diffusion velocity of A, measured relative to the moving fluidVm = molar average velocity of the whole fluid relative to a stationary point18


Total convective flux of A wrt stationary ptDiffusion flux wrt moving fluidConvective flux wrt to stationary pointVa= velocity of A relative to a stationary point, sum of diffusion velocity and the average or convective velocityVad = diffusion velocity of A, measured relative to the moving fluid19


Va= velocity of A relative to a stationary point, sum of diffusion velocity and the average or convective velocityVad = diffusion velocity of A, measured relative to the moving fluid20


General equation for diffusion plus convectionFor equimolar counterdiffusion, Na = -Nb and the convective term becomes zero.21

Molecular Diffusion in GasesUni-component Diffusion

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

http://sst-web.tees.ac.uk/external/U0000504/Notes/ProcessPrinciples/Diffusion/Default.htmA special case wherein, one boundary at the end of the diffusion path is impermeable to component B, so it cannot pass through.

Example: Gas Absorption, evaporation of organic solvent in air22








http://sst-web.tees.ac.uk/external/U0000504/Notes/ProcessPrinciples/Diffusion/Default.htmWhen P is constant,

A special case wherein, one boundary at the end of the diffusion path is impermeable to component B, so it cannot pass through.


Molecular Diffusion in GasesExample

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.

26Long Exam ResultsLE 1LE 2Mean33.3236.55Median32.0030.75Mode39.0025.50Passing Rate0.009.09QuizzesMachine ProblemsTarget Average ScoresStudent No.TotalQ 5/5Total*M 15/15LE3L 60/60FinalF 20/202011-18077301.50240128230.48216.42011-57319462.30240129027.89018.02010-04141361.802401282318216.42010-01283261.30240128929.18917.82010-31873472.352401285298517.02011-07217261.30240126733.36713.42011-03676502.50240129326.99318.62010-36588231.15240129228.79218.42011-18143311.55240127331.97314.62011-18147311.55240127731.37715.42011-09522331.65240121022610220.42011-30507231.15240128829.68817.62011-09270190.95240128130.98116.22010-53270361.80240127431.67414.82011-14930613.052401251355110.22009-2111980.40240129928.19919.82011-21884482.40240127032.17014.02011-1928090.45240129229.59218.42011-267901045.20240124534.1459.02010-21409140.702401210027.310020.02011-01530572.85240126532.56513.02011-30255211.05240129128.99118.2

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