SUITABILITY OF CRANK’S SOLUTIONS TO FICK’S SECOND
LAW FORWATER DIFFUSIVITY CALCULATION AND
MOISTURE LOSS PREDICTION IN OSMOTIC DEHYDRATION
OF FRUITS
C.I. OCHOA-MARTÍNEZ
1,2
, H.S. RAMASWAMY
1,3
and A.A. AYALA-APONTE
2
1
Department of Food Science
Macdonald Campus of McGill University
Ste. Anne de Bellevue, PQ, Canada H9X 3V9
2
Department of Food Engineering
Universidad del Valle
Apartado 25360, Cali, Colombia
Accepted for Publication January 9, 2008
ABSTRACT
Various solutions (Crank’s) of Fick’s law of diffusion have been used to
predict moisture loss (ML) in osmotic dehydration, by correlating experimen-
tal data. Selection of a particular solution should depend on the sample
geometry and the fulfillment of a number of assumptions made to obtain that
solution. Crank developed solutions for long-time, short-time, and a solution
for diffusion into a sample from a well-stirred tank for sheets, cylinders and
spheres. This work was carried out to find the most suitable Crank’s solution
to predict ML for a wide range of published data. The long-time solution and
the solution for a well-agitated tank, for plane sheets, satisfactorily predicted
ML of semi-infinite sheets and semi-infinite cylinders.
PRACTICAL APPLICATIONS
Crank’s solutions of Fick’s law for various geometric shapes are used in
practice to determine the diffusivity from experimental data for unit operations
governed by mass transfer. Once the diffusivity is known, those solutions can
be used to predict the kinetics of mass transfer. One of the specific cases where
this information is useful is in determining the loss of water for the process of
osmotic dehydration. Crank developed solutions for several sets of initial and
3
Corresponding author. TEL: 514-398-7919; FAX: 514-398-7977; EMAIL: hosahalli.ramaswamy@
mcgill.ca
Journal of Food Process Engineering 32 (2009) 933–943. All Rights Reserved.
© Copyright the Authors
Journal Compilation © 2008 Wiley Periodicals, Inc.
DOI: 10.1111/j.1745-4530.2008.00254.x
933