Mass Transfer
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The document discusses various mechanisms of mass transfer including molecular diffusion in gases and liquids, mass transfer in turbulent and laminar flow, and interphase mass transfer. Molecular diffusion is the movement of molecules due to a concentration gradient. Fick's law describes the rate of diffusion. Mass transfer in fluids occurs across a boundary layer near the surface via molecular diffusion or eddies. Interphase transfer theories include the two film theory, penetration theory, and surface renewal theory which describe mass transfer across interfaces.
Mass Transfer
- 1. Mass Transfer Presented by: Mr. E. D. Ahire M.S. PHARM Assistant Professor, Divine Collage of pharmacy
- 2. Contents 2 Introduction Molecular Diffusion In Gases In Liquid Mass Transfer in turbulent & laminar flow Interphase Mass Transfer Two film theory Penetration theory Surface Renewal Theory
- 3. Introduction 3 Transfer of material from one homogeneous phase to another with or without phase change Complex phenomenon occurs almost in all unit operations Extraction – transfer of solute Humidification – transfer of water molecule Evaporation Drying Distillation simultaneous heat & mass transfer Occurs through different mechanisms such as molecular diffusion, convection / bulk flow & turbulent mixing
- 4. Mass Transfer 4 Movement of the molecule occurs due to concentration gradient known as molecular diffusion. Molecular Diffusion LiquidsGases
- 5. Molecular diffusion in gases 5 partition Gas A moves towards chamber B and gas B movestowards chamber A Concentration of A with distance towards chamber B &B towards A, variation in concentration of component with distance in the system called concentration gradient Movement of molecule A or B occurs due to concentration gradient known as molecular diffusion Gas A Gas B dx CA decreasing CB decreasing
- 6. Fick’s law: where, DAB DBA = diffusivity of A in B & diffusivity of B in A respectively ( cm2/sec) NA & NB = rate of diffusion (gm.moles/cm2/sec) dX (negative sign, as concentration decreases with distance) NA dCA NA DAB dCA dX NB DBA dCB dX For moleculeA For molecule B 6
- 7. a) Equimolecular Counter diffusion 7 If molecular diffusion is the only mechanism of mass transfer then, NA = -NB Consider dPAand dPB are changes in partial pressure of A & B over element dx. As we assumed that there is no bulk flow, we can say , For an ideal gas, PAV= nA RTwhere, PA= partial vapor pressure nA = no. of moles in volume V at temperature T. R = gas constant dX d X dPA dPB RT PA= CA RT ( as CA = nA/ V ) CA PA
- 8. similarly for gas B BA(as DAB = D =D) where, PA1 & PA2 are partial pressures of A at distance X1 & X2 RT dX NB DBA dPBDAB dPA NA RT dX But for equimolecular counter diffusion NA = -NB, therefore, NA DA B dPA DB A dPB RT d X RT d X NA D X 2 dPA RTX 1 dX RT X2 X1 8 D PA2 PA1 NA
- 9. b) Diffusion through stationary, non- diffusing gas 9 Movement of molecules from liquid or film on drying solids, occurs to a non-diffusing gas Molecule A is moving from the surface to atmosphere due to conc. gradient in partial pressure but B is not moving towards the surface Therefore, rate of mass transfer of A takes place bymolecular diffusion & bulk flow
- 10. c) Molecular diffusion in liquids 10 where, CA1 & CA2 = concentration of A at point x1 &x2 Diffusivity of liquid are much lesser than diffusivity of gases. e.g. diffusivity of gaseous ethanol in air = 0.119 cm2/sec diffusivity of liquid ethanol in water = 1 × 10-5 cm2/sec X2 X1 CA2 CA1 NA D dX For equimolar counter diffusion, According to Fick’s law, for diffusion in liquid NA D dCA
- 11. Mass transfer in turbulent & laminar flow 11 Explained by boundary layer or film theory when fluid flows adjacent to the surface forms the boundary layer Considers two regions boundary layer bulk • If bulk flows in laminar fashion – rate of mass transfer given by molecular diffusion equation • If bulk flow is turbulent – mass transfer depends upon transfer rate across the boundary layer
- 12. Boundary layer consist of 3 sub layers Laminar sub layer adjacent to surface Buffer / transient sub layer Turbulent region towards the bulk of fluid Turbulent layer : eddies move under inertial forces causing mass transfer. The rate of mass transfer is high and conc. gradient is low Buffer layer : Combination of eddy and molecular diffusion responsible for mass transfer Laminar sub layer : molecular diffusion is the only mechanism of mass transfer. Concentration gradient is high and rate of mass transfer is low The rate of mass transfer can be estimated by considering a film which offers the resistance equivalent to boundary layer.12
- 13. Let, PAi = partial pressure of A at surface PAl = partial pressure of A at laminar sub layer According to Fick’s law for diffusion, We know, therefore where, CAi & CAb concentration of A on either side of the film. X' of thickness X PAb= partial pressure of A at the edge of boundary layer. conc.gradient= PAi – PAb . 13 RT X' D PAi – PAb NA X’ is not known , hence kg constant known as mass transfer coefficient isintroduced. RT CA PA NA kg.CAi CAb
- 14. Interphase Mass Transfer 14 Involves two phase mass transfer e.g. distillation, liquid-liquid extraction Different theories involved Two film theory Penetration theory Surface Renewal theory
- 15. Two film theory 15 Theory has been developed by Nernst, Lewis and Whitman Postulates that two non-turbulent fictitious films are present on either side of the interface between the film Mass transfer across these films purely occurs molecular diffusion Total resistance for mass transfer is summation of resistance of two films
- 16. Let, pAg = partial pressure of A in the bulk of gas pAi = partial pressure of A in gas at the interface CAi = concentration of A in liquid at interface CAl = concentration of A in the bulk of liquid kg & kl = mass transfer coefficients of individual films of gas & liquid respectively But difficult to know pAi and CAi. Hence concept of overall mass transfer coefficient is used. pAe = gas phase partial pressure of A equilibrium with conc. of A in the bulk of liquid (CAl) CAe = conc. Of A in the liquid phase equillibrium with partial pressure of A bulk gas (pAg ) 16 KG and KL are overall mass transfer coefficient , by applying Fick’slaw, or pA = H CA + b where, H & b are constant. NA KGpAg pAe NA KLCAe CAl Equilibrium between two phases ,
- 17. and process becomes liquid phase controlled. If A is highly soluble in liquid ( i.e. H is very low ) then KG ≈ kg and process is gas phase controlled According to this theory, mass transfer is directly proportional to molecular diffusivity of solute in the phase into which it is going and inversely proportional to thickness of films By considering individual film transfer equations and overall mass transfer equations, equilibrium equations can be developed between overall and individual phase mass transfer coefficients 1 1 H KG kg kl KL HKG Hkg kl 1 1 1 1 kl 17 If A is less soluble in liquid ( i.e. H is very large ) then KG H
- 18. Penetration theory 18 This theory proposed by Higbie considers unsteady state at interface Fluid eddies travel from bulk to interface by convection & remain there for equal but limited period of time When eddies comes at interface, solute moves into it by molecular diffusion & get penetrated into bulk when eddies moves to bulk According to this theory, rate of mass transfer directly proportional to square root of molecular diffusion and inversely proportional to exopsure time of eddies at interface.
- 19. Surface renewal theory 19 This theory proposed by Dankwort Each eddies gets equal exposure time at interface Continuous renewal of interface by fresh eddies which have composition of that bulk Turbulent eddies remain at interface for time varying from 0 to ∞ and taken back into bulk phase by convection current According to this theory, rate of mass transfer is directly proportional to square root of molecular diffusivity.
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