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

“A mathematical model for transfer of solutes between whole cucumbers and brine in cucumber fermentation.”

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.

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)

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

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

Similarities with Fick’s First LawJA= -D

dzdC

So we see, the main driving force for mass transfer is concentration

gradient

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

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

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

FinallyJf=Js=J whereJ=KAt(Cb-Cc)

ecests

t

f pApAhA

kK

11And

kf, pst and pec are transport coefficients

Plot of measured and Predicted concentrations (Cb,i/Cb0,i) vs. Time for Acetic acid (a) and Lactic acid (b) at different circulation rates.

Plot of measured and Predicted concentrations (Cb,i/Cb0,i) vs. Time for Acetic acid (a) and Lactic acid (b) at different cucumber sizes.

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.

THANK YOU

QUESTIONS???