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Introduction to Mass Transfer. Outline. Mass Transfer Mechanisms Molecular Diffusion Convective Mass Transfer 2. Fick’s Law for Molecular Diffusion 3. Molecular Diffusion in Gases Equimolar Counterdiffusion Combined Diffusion and Convection Uni -component Diffusion.
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Outline • Mass Transfer Mechanisms • Molecular Diffusion • Convective Mass Transfer 2. Fick’s Law for Molecular Diffusion 3. Molecular Diffusion in Gases • EquimolarCounterdiffusion • Combined Diffusion and Convection • 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 • Mass Transfer Mechanisms • Molecular Diffusion • Convective Mass Transfer 2. Fick’s Law for Molecular Diffusion 3. Molecular Diffusion in Gases • EquimolarCounterdiffusion • Combined Diffusion and Convection • Uni-component Diffusion
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: HEAT MOMENTUM 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 • Mass Transfer Mechanisms • Molecular Diffusion • Convective Mass Transfer 2. Fick’s Law for Molecular Diffusion 3. Molecular Diffusion in Gases • EquimolarCounterdiffusion • Combined Diffusion and Convection • Uni-component Diffusion
Molecular Diffusion in Gases EquimolarCounterdiffusion Flux of one gaseous component is equal to but in the opposite direction of the second gaseous component B A A B
Molecular Diffusion in Gases EquimolarCounterdiffusion At constant pressure, Then, and Fick’s law for B, B A A B
Molecular Diffusion in Gases EquimolarCounterdiffusion Substitution of Fick’s law into the equation for equimolar counter diffusion, B A A B
Molecular Diffusion in Gases EquimolarCounterdiffusion B A A B
Molecular Diffusion in Gases EquimolarCounterdiffusion For gases, B A A B
Molecular Diffusion in Gases EquimolarCounterdiffusion In terms of mole fraction, B A A B
Molecular Diffusion in Gases Example 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.
Molecular Diffusion in Gases Diffusion plus Convection Multiplying by ,
Molecular Diffusion in Gases Diffusion plus Convection Total convective flux of A wrt stationary pt Diffusion flux wrt moving fluid Convective flux wrt to stationary point
Molecular Diffusion in Gases Diffusion plus Convection Replacing and , ) Solving for ,
Molecular Diffusion in Gases Diffusion plus Convection )
Molecular Diffusion in Gases Uni-component Diffusion One component (A)diffuses, while the other (B) remains stagnant Since B cannot diffuse, http://sst-web.tees.ac.uk/external/U0000504/Notes/ProcessPrinciples/Diffusion/Default.htm
Molecular Diffusion in Gases Uni-component Diffusion Since B cannot diffuse, ) http://sst-web.tees.ac.uk/external/U0000504/Notes/ProcessPrinciples/Diffusion/Default.htm
Molecular Diffusion in Gases Uni-component Diffusion http://sst-web.tees.ac.uk/external/U0000504/Notes/ProcessPrinciples/Diffusion/Default.htm
Molecular Diffusion in Gases Uni-component Diffusion When P is constant, http://sst-web.tees.ac.uk/external/U0000504/Notes/ProcessPrinciples/Diffusion/Default.htm
Molecular Diffusion in Gases 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-z1is 0.1524m long. Calculate the rate of evaporation of water vapor at 293 K and 1 atmpressure. The diffusivity of water in air is 0.250 x 10-4m2/s. Assume that the system is isothermal.
