Balance

(Na2 ( pi ) rLI r−Na2 (pi ) rLI r+r−Ra2 (pi )RL=dCadt

(2 ( pi ) rLr )) /(2 (pi ) rLr )

Ra=−m

dCadt

=0

( 1r ) dNa (r )dr

+m=0

Na=Ja+vzCa

Ja=−Dab( dCadr )

( 1r )(−Dab( dCadr ) ddr )+m=0

( 1r ) d2Cadr2

(−Dab ) (r )+m=0

∫ d ( dCadr )¿¿

( dCadr )(−Dab(r))=−mr2

2+C1

(−Dab(r ))∫dCa=−∫ mr22

+C 1¿dr ¿

−Dab(r )(Ca)=−mr3

6+C1 r+C2

Condiciones

1- r=R2 por flujos identicos dCadr

=0

2- r=R1Ca=Ca1

( dCadr )(−Dab(r))=−mr2

2+C1

Usando 1

C1=mR2

2

−Dab(r )(Ca)=−mr3

6+(mR22 )r+C2

C2=−Dab (r 1 ) (Ca1 )+(m )r 1[3 ]

6+(mR22 )r 1

El perfil de concentracion

Ca=(−mr36

+(mR22 )r−Dab (r 1 ) (Ca1 )+ (m )r 1[3 ]

6+(m R22 )r1)

−Dab (r )