BMED+3300+Lecture+5+Slides+090711

BMED+3300+Lecture+5+Slides+090711 - BMED 3300 Biotransport...

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MED 3300 Biotransport BMED 3300 Biotransport Lecture 5 eptember 7 2011 September 7, 2011. Professor Melissa Kemp for Professor Julie Babensee
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Mass-Transfer Controlled by xternal Diffusion Resistance External Diffusion Resistance sa t • Liquid drop contains a supersaturated solution of some species C A,sat p A,sat • Solute exists as either solid or as liquid immiscible phase • Liquid concentration of solute is C A,sat olute species is volatile and has a vapor pressure N A,r • Solute species is volatile and has a vapor pressure p A,sat • Saturated drop is surrounded by a stagnant gas Problem: Analyze the steady diffusion into the gas Assume: No bulk flow, v =0 No reaction, R A =0 Steady state, 0 = A C Middleman, Example 3.2.1 t
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Simplifying the Equation of continuity of A for constant ρ and D AB A C r v A C r v r A C r v t A C = + + + sin 1 1 φ θ A R A C r A C r r A C r r r AB D + + + 2 2 2 sin 2 1 sin sin 2 1 2 2 1 esults in Results in 0 2 2 1 = dr A dC r dr d r Integrating with respect to r C a dr A dC r = 2 Integrating with respect to r b r a A C + =
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eed two boundary conditions to solve C quation for integration constants, Need two boundary conditions to solve C A equation for integration constants, a and b Diffusion is occurring at the outer surface of the sphere, at the semi-infinite Region, r R. At r=R - , C = C sa t . This is inside the sphere, not the domain g, , A A,sat p, In which diffusion is occuring. Need the concentration at r=R +, where p A = P A, sat . Need concentration in terms of molar units, so use ideal gas law. + = = = R r at , R C RT sat A p A C B.C.1 B.C.2 = = r at 0 A C Solving for integration constants, b=0, a=-RC R R r R C A C
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Rate of mass transfer (evaporation of A) for the system? C R r dr A dC AB D R r r A N = = = , R RC A dC 2 R R r dr = = R C AB D R R r r A = , Rate of evaporation? roduct of the flux N nd the mass transfer area Product of the flux N A and the mass transfer area AB D R RC R r r A N R A W π 4 , 2 4 = = = What is the definition of a surface mass transfer coefficient , k, which Is the proportionality constant between the flux and the concentration Difference between the surface and the surroundings. = R AB D R C A N k R kC R C k C k A N = = Δ ) 0 (
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Respiration of a Spherical Cell Spherical particle within which a homogeneous reaction, involving a single species A, is occurring.
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BMED+3300+Lecture+5+Slides+090711 - BMED 3300 Biotransport...

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