Mass Transfer as you have learned it. Diffusion with Drift. Classic - in Gases 1. Three Gases (1) Appendix. Mass transfer in

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1 to ourse mterl for ÅA TF ourse 44 / 8 Mss trnsfer nd seprton tehnology Mssöverf verförng rng oh seprtonsten ( MÖF-ST ) See lso Krshn & Wesselngh Chem. Eng. S. 5(6) Appendx. Mss trnsfer n mult-omponent mxtures A. Old-shool Ron Zevenhoven Åbo Adem Unversty t Engneerng Lbortory tel. ; ron.zevenhoven@bo.f februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 /4 februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 /4 Mss Trnsfer s you hve lerned t Dffuson wth Drft J : flux of wth respet to the mxture J D d F s Δ lw Δ D J D Δ Δ z dffusvty oeffent : flux wth respet to n nterfe dfferentl equton D d x dfferene equton Δ x { dffuson flux drft flux flux of mxture sδ Stefn or drft orreton Clss - n Gses J D d gs: onstnt fluxes wth respet to mxture J D d J J D d only one bnry D whh s ndependent of omposton D ( ) x Three Gses () A H begnnng: x 46. x H 54. del gses P 98 K CO x 5. x CO 48. Queston: Does trnsfer () from A to B? (b) from B to A? () not t ll? (d) or does t do () (b) nd ()? B pge of

2 to ourse mterl for ÅA TF ourse 44 / 8 mole frton x A B H B A B A CO Three Gses () tme h reverse dffuson Two Ctons hgh onentrton H Cl - H moves rpdly H so n move gnst ts onentrton grdent! ton permeble membrne Cl - low onentrton exess hrge nd eletrl feld Gses n Porous Plug () 98 K P 98 K P M M frton ( / plug) < frton ( / plug) the plug mtrx or membrne s (pseudo)omponent! Gses n Porous Plug () 98 K P Δp 98 K P(for exmple) mn reson: vsous flow retrds elertes Grvty - smple Potentl the potentl dfferene s the wor requred to hnge the ondton of the weght A. Drvng fores m here: Δψ mg 98. J ( 98. m) g or per mole Δψ Mg g F the drvng fore s the negtve potentl grdent: dψ F Mg the fore s downwrds februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 /4 pge of

3 to ourse mterl for ÅA TF ourse 44 / 8 x γ mxture wor requred: hnge n the heml potentl pure (one mole) Cheml Potentl heml potentl μ onst γ x tvty μ ( p T ) RTln ( ) onst p T Δμ μ μ RTln tvty oeffent μ n n Idel Soluton heml potentl n n del soluton n n del gs μ onst ( p T ) RT ln x p μ onst( p T ) RT ln p prtl pressure februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 4/4 Momentum Blne Movng Through Eh Other momentum n ( m & v ) hnge of momentum n fores F momentum out ( m & v ) d( mv ) ( mv & ) n ( mv & ) out F dt out H z z CO () () u u spees velotes februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 5/4 februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 6/4 Fores on Hydrogen () drvng dp fore A z p re A z z frton p ( ) p u u fore p A z volume A dp Fore blne: pp(u u ) fore per volume p RT dp wth gves RTp(u u ) foreper mole RT p Drvng foref RTp (u u ) ζ x (u u ) RT RT wth frton oeffent ζ ζ D D ote: often x nd u Gses: u ~ - m/s Lquds: u ~ -4 m/s Drvng Fore (per Mole of ) dμ d ln F RT for gven T nd p RT d RT dx x n del solutons februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 7/4 pge of

to ourse mterl for ÅA TF ourse 44 / 8 Mxwell-Stefn Equton drvng fore on frton oeffent between nd ( ) F ζ x u u mole frton of (dffusve) spees velotes Flm Theory Thness of Flms two thn one dmensonl

4 to ourse mterl for ÅA TF ourse 44 / 8 Mxwell-Stefn Equton drvng fore on frton oeffent between nd ( ) F ζ x u u mole frton of (dffusve) spees velotes Flm Theory Thness of Flms two thn one dmensonl flms next to the phse boundry eddes & lrge sle onveton flm : no eddes gses 4 m lquds 5 m phse boundry K membrne n sold prtle 7 4 m d d Dfferene Form of Fore Δμ Δln RT Δ F RT for gven T nd p RT Δx x n del solutons Δμ RT - - Approxmton ext ln pproxmte Δ.5 ( ) pproxmte wors out better n dfferene equtons februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 /4 Fores n Glss of Beer growng bubble of CO x. ote: u 5 m mole frton of CO RT dx RT Δx F x x x. Exmple (. from boo) Exmple februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 4/4 pge 4 of

5 to ourse mterl for ÅA TF ourse 44 / 8 Exmple (. from boo): Exmple ): nswer A. Frton februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 5/4 februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 6/4 Frton Coeffents of Spheres oeffent of sngle sphere ( ) ζ A πηd mol ms spheres lqud See PTG 6.7: Stoes Lw A 6 moleules mol - F Dffuson nd Frton Coeffents Ð RT Ð A πη d RT ζ (.4 ) s Mxwell-Stefn dffusvty of lrge moleules n dlute lquds (not gses) ζ RT Ð eh others nverse we use both 9 m One Equton Mssng omponents: reltve veloty ndependent equton Bootstrp () only reltve velotes omponents: reltve velotes ndependent equtons n omponents: n - reltve velotes n - ndependent equtons bootstrp F ζ x ( u u ) flotng trnsport reltons: hve to be ted to surroundngs pge 5 of

6 to ourse mterl for ÅA TF ourse 44 / 8 februr 8 H Bootstrps () H Cl - CO no net volume flow Cl - plug does not move membrne does not move (lmost) no hrge trnsfer Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 /4 februr 8 Fluxes n prtl problems we use fluxes: F x ζ x x ( u u ) f ζ ( x x ) u ux flux form of MS-equton: fore on per unt volume of mxture F / V ; x / Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 /4 x From Dfferentl to Dfferene x postve dreton x RT d RT bnry: x ( u u ) u Ð nfntesml d ( u u ) x lyer ( Ð ) fnte lyer (pproxmte) Δ x ( u u ) Ð 6 flm 78 u verge onentrton u Averge Veloty spees veloty (depends on poston n flm) spees veloty t the verge omposton postve veloty februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 4/4 Dfferenes wth Fluxes Multomponent Equtons Δ x( u u) x Δ x ( x x ) usng velotes Δ ( u u ) x for del solutons usng fluxes Δ x Δx ( x x ) februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 5/4 februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 6/4 pge 6 of

7 to ourse mterl for ÅA TF ourse 44 / 8 Trnsfer Coeffents Ð Δ z m s gses m s n pores lquds 4 m s n pores februr 8 Temperture Effets MS-equton F ζ x (u u ) (therml dffuson terms) smll drvng fore dμ RT dx F T x dfferene t onstnt form: temperture hnges re not RT Δx F very mportnt x verge flm temperture Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 8/4 A.4 Bnry exmples drops on try gs: tre of H () bul of () trnsport relton Strppng - dlute x x Δx x bootstrp x x flux Δx..s you lredy new.. februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 9/4 Strppng - onentrted Vporsng Droplet x het x 5. x Δx Δx x benzene () voltle toluene () y Kx x x x x y K x vpour removed by onveton bootstrp: y ν y pge 7 of

8 to ourse mterl for ÅA TF ourse 44 / 8 Fluxes from Vporsng Droplet Crbon Gsfton ν x x Δx x x Δx x x x ν Δ x x x ν Δ exmple ν x x. Δx < Δx > 5 4 Δ x ( ) Δx Stefn (drft) orretons O () CO( ) O C CO C both omponents re movng nd hve hgh onentrton bootstrp: ms mol m lulte nd Fluxes n Gsfton x x ( x x ) Δx Δx 6. x x 7.. ( ) ( ext ) ( :.94 ) mol m 46. : 47. mol m s.9 ext s lmost the sme Bnry Dstllton x x trnsport relton heptne () x x Δx x x hexne () bootstrp (equmolr exhnge) Δx ( x ) x Δx Δx Some Bootstrps membrne stgnnt bul stgnnt (bsorpton) tre stgnnt (polrston) equmolr exhnge (dstllton) nterfe determned (vporston) reton stohometry u M u y y ν ν A.5 Ternry exmples februr 8 Åbo Adem - TF - Värmeten - Bsopsgtn 8 5 Åbo MÖF-ST RZ 8 48/4 pge 8 of

9 to ourse mterl for ÅA TF ourse 44 / 8 Ternry - per mole of Ternry - per mole of Mxture dμ ζ x u u x u u dμ ζ x u u x u u ( ) ζ ( ) ( ) ζ ( ) fores per mole of fores per mole of x d μ ζ xx ( u u) ζ xx ( u u) x d μ xx ( u u) xx ( u u ) ζ ζ fores per mole of mxture these should nel: ζ ζ Ð Ð More Components Condensor oolng wter vpour bnry x x Δx x x x x x x Δx ternry quternry Mx: H H O H H () nd H O () ondense on tube H () does not ondense ms fnd the velotes n the gs flm ms lqud H O H H Condenser () trnsport (MS) reltons: H : H O : ( ) ( ) ( ) ( ) bootstrp three lner equtons three unnowns.5.45 mol m ext solutons:..49 mol m s s Condenser () H O moves down ts grdent H drgged gnst ts grdent H does not move t ll mxture veloty HO H H pge 9 of

10 to ourse mterl for ÅA TF ourse 44 / 8 Ternry Dstllton () ethnol wter tre of butnol lrge frton between nd 8 ms m s - bootstrp: equmolr exhnge uy uy uy n whh dreton does move? vpour.5.45 lqud Butnol - whh dreton? y y u 75. u 58. no moton u 8. H () () Ammon reton H H H () trnsport reltons: x x x x Δx x x x x Δx x x x x Δx When s:? ternry n be pproxmted s bnry when Δx x u u x u u L x u u eff eff x eff tlyt surfe bootstrp: one frton term domntes: x x x u u x eff x << eff (exmple: moble spees n mny membrnes) equl veloty of two spees: x x x x x eff u u ( u u) eff (exmple: nd Cl - n wter) equl dffusvtes ( n m- nd p-xylene) xeff x x ( x x ) u ( x u x u ) u eff x u x x u x Effetve Bnry n Retve System smplfyng trnsport equton of n mmon formton: elmnte nd wth x x x x effδx wth eff smlrly for H nd H If ll fluxes re relted v the sme reton stohometry pseudo - bnry pge of

Mass transfer in multi-component mixtures

Mass transfer in multi-component mixtures Chapters -0 ex. 7, of 5 of boo See also Krshna & Wesselngh Chem. Eng. Sc. 5(6) 997 86-9 Mass transfer n mult-component mxtures Ron Zevenhoven Åbo Aadem Unversty Thermal and Flow Engneerng Laboratory tel.