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SURROUNDING

MASS BALANCE: WHY MASS FLOWS?. SURROUNDING. Phase a T a , P a , m i a. Phase b T b , P b , m i b. NO. NO. ISOLATED. SYSTEM. WORK. HEAT. Ideal fixed permeable membrane. a i = i th species activity. T a = T b P a = P b m i a = m i a. EQUILIBRIUM CONDITIONS

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SURROUNDING

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  1. MASS BALANCE: WHY MASS FLOWS? SURROUNDING Phase a Ta, Pa, mia Phase b Tb, Pb, mib NO NO ISOLATED SYSTEM WORK HEAT Ideal fixed permeable membrane ai = ith species activity Ta = TbPa= Pb mia = mia EQUILIBRIUM CONDITIONS dU=dUa+dUb = 0

  2. MASS BALANCE: EQ.CON. ALTERATION 1 Pa increase (>Pb) [Ta = Tb; mia = mib] Phase a T, Pa, mi Phase b T, Pb, mi MASS TRASPORT (CONVECTION) permeable membrane Mass transport represents a possible way the system has to get new equilibrium conditions once the original ones have been altered.

  3. MASS FLOW (Kg/s) =V*S*Ci V = velocity (m/s) S = cross section (m2) Ci = “i” concentration (Kg/m3) S V Ci MASS FLUX (Kg/sm2) =V*Ci V = velocity (m/s) Ci = “i” concentration (Kg/m3) S = 1 m2 V Ci

  4. mia>mib [Ta = Tb; Pa = Pb] 2 Phase a T, P, mia Phase b T, P, mib permeable membrane MASS TRASPORT (DIFFUSION) Mass transport represents a possible way the system has to get new equilibrium conditions once the original ones have been altered.

  5. FICK LAW DX CiX+DX S CiX MASS FLOW (Kg/s) =-S*D*DCi/DX S = cross section (m2) D = diffusion coefficient (m2/s) Ci = “i” concentration (Kg/m3) DCi/DX = gradient concentration (Kg/m2s) DCi/DX = (CiX+DX-CiX)/DX MASS FLUX (Kg/sm2) =-D*DCi/DX

  6. MASS BALANCE Z X Y DZ DX (X+DX, Y+ DY, Z+ DZ) G (X, Y, Z) DY (X, Y+ DY, Z) (X+DX, Y+ DY, Z)

  7. MASS BALANCE: EXPRESSION DX DZ (X, Y, Z) G DY Ci = f(X, Y, Z, t)

  8. DX DZ (X, Y, Z) G DY DIVIDING FOR DV

  9. FLUXES EXPRESSIONS Ideal solution Diffusion Diffusion Diffusion Convection Convection Convection Bi = mobility of the diffusing components

  10. Remembering that:

  11. MASS BALANCE: CYLINDRICAL COORDINATES Jir+dr Jir+dr Jiz Jiz+dz Jir Jir Jir Jiz Jiz+dz Jir+dr r dr dz TWO DIMENSIONS r z

  12. Ci = f(z, r, t) r dr dz Dividing by 2prdrdz

  13. Remembering the derivativedefinition

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