dynamic model for mass transfer of solutes in cucumber fermentation
TRANSCRIPT
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Dynamic Model for Mass Transfer of Solutes in Cucumber Fermentation
Fredrico V. Passos, Richard M. Felder , Henry P. Fleming, Roger F. McFeeters, David F. Ollis
Presented by MD. WALIUL ISLAMOklahoma State UniversitySpring 2012Course: Diffusional Mass Transport
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“A mathematical model for transfer of solutes between whole cucumbers and brine in cucumber fermentation.”
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Objective of the StudyTo measure rates of solute movement into and out of non-fermenting brined pickling cucumbers to formulate a transport model.
To determine the controlling mechanism of solute transport.
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Experimental Procedure
Fruits were brined in glass jar containing 40% cucumber and 60% brine by weightAcetic Acid, Lactic Acid, Ethanol & Sodium metabisulfite were also addedSO2 with trace amount was added to avoid growth of microorganismBrined cucumbers were held @ 30°C for 6days
(CONT’D)
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Experimental Procedure (Cont’d)
The jars containing the material were continuously purged with N2 to prevent bloater formation.2 ml samples were taken periodically (3-12 hr) from brineNaCl concentrations were determined by titration with standard AgNO3Concentration of all other solutes were determined using HPLC
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Transport Model Development
)( bcb
tb CChV
KAdtdC
K= Overall Permeabilityh=Thickness of Vegetable Skin (Membrane)At= Total Skin Surface AreaVb= Brine VolumeCb= Concentration of Solute in BrineCc=Concentration of Solute at Inner Surface of Vegetable Skin
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Similarities with Fick’s First LawJA= -D
dzdC
So we see, the main driving force for mass transfer is concentration
gradient
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Fasina et al.(2002) suggested the following equation
)exp(0
ktCCCCeq
eq
The above equation provided a good fit to their data
Transient Mass Transfer
to represent the movement of solutes
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Rate of solute permeation into or out of the cucumber
Jf(mol/s)=kfAt(Cb-Cx)
kf = film diffusivityAt =External Cucumber Surface AreaCb= Concentration of Solute in BrineCx =Solute concentration @the interface between the fluid boundary layer and the exterior cucumber surface
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The flux through the skinJs=(1/h)(pstAs+pecAe)
(Cx-Cc)Pst= Permeability of solute through stomataPec=Permeability of solute through epidermal cellCc=Concentration of Solute at Inner Surface of Vegetable Skinh=Thickness of Vegetable Skin (Membrane)Ast=Cross sectional area of stomata (1st diffusion channel)Aec=Cross sectional area of epidermal cell (2nd diffusion channel)
Note Pec=Henry’s law solubility of solute * Diffusivity of solute
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FinallyJf=Js=J whereJ=KAt(Cb-Cc)
ecests
t
f pApAhA
kK
11And
kf, pst and pec are transport coefficients
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Plot of measured and Predicted concentrations (Cb,i/Cb0,i) vs. Time for Acetic acid (a) and Lactic acid (b) at different circulation rates.
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Plot of measured and Predicted concentrations (Cb,i/Cb0,i) vs. Time for Acetic acid (a) and Lactic acid (b) at different cucumber sizes.
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Plot of measured and Predicted concentrations (Cb,i/Cb0,i) vs. Time for Acetic acid (a) and Lactic acid (b) at different for Lactic acid , Acetic acid, Ethanol, NaCl, Glucose and Malic acid.
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THANK YOU
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