BMED+3300+Lecture+6+Slides+090911

BMED+3300+Lecture+6+Slides+090911 - BMED 3300 Biotransport...

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MED 3300 Biotransport BMED 3300 Biotransport Lecture 6 eptember 9 2011 September 9, 2011. Professor Julie Babensee
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Diffusion with A Homogeneous, irst rder Chemical Reaction First-Order Chemical Reaction bsorption of a species from a gas into a liquid in which a chemical reaction occurs Absorption of a species from a gas into a liquid in which a chemical reaction occurs z Liquid urface Gas mixture and inert gas) Liquid surface composition is C A0 z Az N z=0 surface (A and inert gas) Thickness of the film is δ so that beyond this film the concentration of A is always zero, C A δ =0 Liquid B z= δ z z Az N Δ + Δ z There is very little fluid motion within the film and if the concentration of A in the film assumed small, the molar flux within the film is given by dz A dC AB D Az N = WWWR 26-38 WWWR p. 469-470
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Simplifying the equation of continuity of A for constant ρ and D AB in rectilinear oordinates A R z A C y A C x A C AB D z A C z v y A C y v x A C x v t A C + + + = + + + 2 2 2 2 2 2 coordinates ives Gives 0 2 2 = + A R A C AB D z A disappears in the liquid by a first order reaction, therefore, A C k A R 1 = 0 1 2 2 = + A C k z A C AB D he general solution to this equation is WWWR 26-42 The general solution to this equation is z AB D k C z AB D k C A C / 1 sinh 2 / 1 cosh 1 + = WWWR 26-43 The boundary conditions are B.C. 1 at z=0 C A =C A0 B.C. 2 at z= δ C A =0
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Solving for the two integration constants, A C C 0 1 = δ AB D k A C C / 1 tanh ) 0 ( 2 = Hence, the equation for the concentration profile is ,q p AB D k z AB D k A C z AB D k A C A C / 1 tanh / 1 sinh 0 / 1 cosh 0 = WWWR 26-44 The molar mass flux at the liquid surface can be determined by differentiating The concentration profile and evaluating the derivative at z=0 B B C sh AB D k z AB D k AB D k A C z AB D k AB D k A C dz A dC / 1 tanh / 1 cosh / 1 0 / 1 sinh / 1 0 + = Evaluating the derivative at z=0 C AB D k AB D k A C AB D k AB D k A C z dz A dC / 1 tanh / 1 0 / 1 tanh / 1 0 0 0 = = = So, the flux at z=0 is given by WWWR 26-45 = = AB D k AB D k A C AB D z z A N / 1 tanh / 1 0 0 , WWWR 26-46
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Biofilm for Waste Water Treatment Waste water feed stream C Ai = 0.1 mole/m 3 iofilm Biofilm cross section Biofilm Inert solid C Ao C A (z) surface
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This note was uploaded on 09/07/2011 for the course BME 3300 taught by Professor Babensee during the Spring '11 term at Georgia Tech.

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BMED+3300+Lecture+6+Slides+090911 - BMED 3300 Biotransport...

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