Class assessment based on published paper.

1. Dynamic Model for Mass Transfer of
Solutes in Cucumber Fermentation
FredricoV. Passos, Richard M. Felder, Henry P. Fleming, Roger F.
McFeeters,David F. Ollis
Presented by
MD. WALIUL ISLAM
Oklahoma State University
Spring 2012
Course: Diffusional Mass Transport

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

3. Objective of the Study
To 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.

4. Experimental Procedure
Fruits were brined in glass jar containing 40% cucumber
and 60% brine by weight
Acetic Acid, Lactic Acid, Ethanol & Sodium
metabisulfite were also added
SO2 with trace amount was added to avoid growth of
microorganism
Brined cucumbers were held @ 30°C for 6days
(CONT’D)

5. 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
brine
NaCl concentrations were determined by titration with
standard AgNO3
Concentration of all other solutes were determined
using HPLC

6. Transport Model Development
)( bc
b
tb
CC
hV
KA
dt
dC

K= Overall Permeability
h=Thickness of Vegetable Skin (Membrane)
At= Total Skin Surface Area
Vb= Brine Volume
Cb= Concentration of Solute in Brine
Cc=Concentration of Solute at Inner Surface of Vegetable Skin

7. Similarities with Fick’s First Law
JA= -D
dz
dC
So we see, the main driving force for
mass transfer is concentration gradient

8. Fasina et al.(2002) suggested the following equation
)exp(
0
kt
CC
CC
eq
eq



The above equation provided a good fit to their data
Transient Mass Transfer
to represent the movement of solutes

9. Rate of solute permeation into or out of the cucumber
Jf(mol/s)=kfAt(Cb-Cx)
kf = film diffusivity
At =External Cucumber Surface Area
Cb= Concentration of Solute in Brine
Cx =Solute concentration @the interface between the
fluid boundary layer and the exterior cucumber surface

10. The flux through the skin
Js=(1/h)(pstAs+pecAe)(Cx-Cc)
Pst= Permeability of solute through stomata
Pec=Permeability of solute through epidermal cell
Cc=Concentration of Solute at Inner Surface of Vegetable Skin
h=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

11. Finally
Jf=Js=J where J=KAt(Cb-Cc)
ecests
t
f pApA
hA
kK 

11
And
kf, pst and pec are transport coefficients

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

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

14. 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.

15. THANK
YOU
QUESTION
S???