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Lecture 2 - Intro to Mass Transfer - Fick's Law

# Lecture 2 - Intro to Mass Transfer - Fick's Law - Lecture 2...

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2/16/2012 1 Lecture 2: Introduction to Fick’s Law and Mass Transfer • Fick’s First Law describing the Diffusive Flux • The Diffusion Coefficient - Gases - Liquids - Solids • Expressions for Concentration and the Diffusive Flux • Total flux in the presence of diffusion and convection • The Continuity Equation - Derivation of… - Simplifications of… The Diffusion Coefficient • D AB describes the rate at which molecules of “A” randomly migrate through solid, liquid, or gas “B” “Species A” “Species B” D AB ~ (length) 2 time cm 2 /s, m 2 /s, ft 2 /s • D AB units:

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2/16/2012 2 The Diffusion Coefficient for Gases • D AB describes the rate at which gaseous molecules of “A” randomly migrate through gas “B”. • Typically, in a gas, molecules are not packed closely together. • So, molecules of “A” experience few collisions with molecules of “B”. • As a result, molecules of “A” can traverse a set distance (point 1 to point 2) relatively quickly--they collide infrequently and take a straighter path through gas “B”. • Put differently, molecules of “A” diffuse rapidly through gases. “B” “A” 1 2 D AB Gases: 10 -4 – 10 -6 m 2 /s @ RT D AB for a gas mixture: Table 6.2-1, Perry’s In which of the following ways would you expect the diffusion coefficient of species “A” in gas “B” (D AB ) to vary when the pressure of the system is increased? a. D AB will increase. b. D AB will decrease. c. D AB will not change. “B” “A” 1 2
2/16/2012 3 In which of the following ways would you expect the diffusion coefficient of species “A” in gas “B” (D AB ) to vary when the Temperature the system is increased (P=constant)? a. D AB will increase. b. D AB will decrease. c. D AB will not change. In gases, D ~ T n , where “n” = 1.5 - 1.75 “B” “A” 1 2 The Diffusion Coefficient for Liquids D AB describes the rate at which solute molecules of “A” randomly migrate through liquid “B” Relative to a gas: • Molecules of “A” experience more collisions with molecules of “B” • Takes LONGER to diffuse • Molecules of “A” diffuse more slowly in liquids • On average D AB liquid: 10 -8 – 10 -10 m 2 /s • Liquids: molecules are packed more closely together 1 2 • D AB for a liquid mixture: Table 6.3-1, 6-4.1, Perry’s

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Lecture 2 - Intro to Mass Transfer - Fick's Law - Lecture 2...

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