Jung Han. Innovations in Food Packaging
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Mass transfer of gas and solute through packaging materials 17
Convective mass transfer
The driving force for the mass transfer of solute molecules in a medium or material is
solely the concentration difference between two positions. The concentration differ-
ence at the boundary film layer between the solution and the material is therefore per-
tinent for describing the driving force for partition of the solute between the solution
and the packaging material. In this case, the convective mass transfer coefficient A^
may need to be considered, since this coefficient is dependent on solution agitation
and
the
absorption affinity of the solute for
the
solution and for
the
material. Figure 2.3
represents the mass transfer of a solute across a membrane or a packaging material.
The convective mass transfer coefficient, h^, with dimensions of velocity
(ms~^),
is
the parameter which expresses the resistance to transfer of mass at the surface of the
material. The parameter
is
also referred
to
as the surface mass transfer coefficient. The
flux on the solution side of the boundary film layer is given by:
^H
- Ki AC = h^, (q - c/)
(2.11)
As shown in Figure
2.3,
there may be more than just resistance to mass transfer on the
solution side. On the package or membrane side at the interface, a fiirther resistance
to mass transfer may exist:
Jr, = h AC = h (C\ - C,)
h ms ms ^ si sl^
(2.12)
The absorption affinity of
the
migrating solute
across the
interface itself can be expressed
using the partition coefficient K, which is the concentration ratio for
the
solute between
Convective
mass transfer
C^
^
^
"^
Diffusional
mass transfer
^
4 C
Cso-^
OQ
•
•hH^
d L
Figure 2.3 Mass transfer of
a
solute through a membrane.
18 Innovations in Food Packaging
the two different phases (solution and packaging material). At the interface, the partition
coefficient of the solute between the solution and the material is:
^ = ^andC:, =KCi (2.13)
Similar expressions prevail for desorption. After the solute molecule has been
absorbed into the material layer, the next transfer phenomenon that follows is diffu-
sion, which can be represented by Pick's laws (equations (2.2) and (2.3)).
Overall mass transfer of gases and solutes
Gaseous difFusivity and permeability
Since the driving force for gas penetration through a packaging material is the differ-
ence in gas concentrations or partial pressures between the two sides of the packaging
material, the gas flux Jg of both permeation and diffusion can use the partial pressure
term instead of the concentration gradient. In the mass transfer situation of Figure 2.2,
the concentration can be substituted for the partial pressure/? and the solubility S from
equations (2.4) and (2.10):
^si - ^so ^ n. ^'^i~ Po^ - p. Pi~Po
V ' L V
STP ^ ^ STP
Flux^^ J = D' -^ ^ = D • ^ ^-^ = P ' — ^ n \A\
where J^ is the flux, and/^i and/7o ^^^ the partial pressures of the gas on the left- and
right-hand sides of Figure 2.2 respectively (Ci and Q sides). The partial pressure/>i
would generally be a constant at ambient conditions. However,/^o is dependent on the
diflrusion of the gas inside the food material or on its reactivity with food components.
Fast diffusion would displace the absorbed gas into the inside of the food within the
package and generate a larger
A/?
across the package material. Alternatively, in a mod-
ified atmosphere package, where the left-hand side represents the inside of the package,
Ci may vary according to the respiratory activities of the food in the package.
From equation (2.14), the permeability, the diffusivity, and the solubility of a gas
have the relationship shown in equation (2.15):
P = DS (2.15)
Therefore, the SI units of P, D and S are m^s~^ Pa~^, m^s~^ and Pa~^, respectively.
Alternatively, equation (2.14) can be rearranged using the flux definition in equation
(2.4) to retain all relevant dimensions:
P = Q^as-^STP-L ^2.16)
"^material * ^ ' (^1 PQ)
SO
that P has units of m|^^
^thickness
^arla ^~^ Pa~^, compatible with units found in
many packaging texts for permeability: cubic centimeters (or ml) of gas (under STP
Mass transfer of gas and solute through packaging materials 19
or other defined conditions) multiplied by package thickness in ml (= 0.001 inch) per
100 square inches per 24 hours per atmosphere (ASTM, 1993).
Solute mass transfer coefFicient and overall permeability
For solutes, the overall mass transfer coefficient U includes the resistances to mass
transfer at the surfaces and solute diffusivity through the membrane. The total resist-
ance {R^ is the sum of all the resistances to mass transfer:
R,
= — = R , + R.rf • =— + — + — (2.17)
t Tj surface diffusion h D h
ma md
where A^^ and
hy^^
^re the convective mass transfer coefficients associated with
absorption and desorption respectively. In the case of
a
multilayer
film,
the diffusional
resistance will be the sum of the resistances of each
layer.
Assuming a
film
ofn layers
without any interfacial resistance, the diffusional resistance is:
^.^..„=^
= ^ + ^ + - + |- (2.18)
where Lj and Dj are overall thickness and overall diffusivity respectively, and
L„
and
Dn
are the thickness and the diffusivity of
the
«th layer. Vojdani and Torres (1989a)
used equation (2.18) in estimating the overall diffusivity of potassium sorbate through
methylcellulose and hydroxypropyl methylcellulose multilayer films. In their synop-
sis of permeability in multilayer
materials,
Cooksey et
al.
(1999) recommended using
a similar equation for calculating overall permeability from permeability data of
indi-
vidual layers.
The resistance to absorption of the solute into the package, and its desorption on the
low concentration side (Figure 2.3), depends on the properties of
the
solvents, pack-
age,
and solutes, and it also depends on the degree of agitation of the solvents on both
sides of
the
package material. In the case where resistances are small, such as when
agitation ensues on the solution side, and diffusion in the interface region is identical
to that through the membrane material as
a
whole,
then
C[
~
C^
and
C^i
~ Qi,
so
that
only the partition coefficient affects the rate of mass transfer across the interface.
The flux of the overall mass transfer, Jj, is the product of the overall mass transfer
coefficient,
C/,
and the concentration difference driving mass transfer, which is:
JT
= UAC = UiC, - C,) (2.19)
Equation (2.19) shows the overall mass transfer from the high concentration (Ci) side
to the low concentration (Q) side through
a
packaging
material.
In such a mass trans-
fer phenomenon, the total
flux
Jj
is
the same as the
fluxes
at the interfaces,
J^,
and the
flux of the diffusional mass transfer, J^. Therefore, the total flux
Jj^
and the overall
mass transfer coefficient U are analogous to the flux of permeation and the perme-
ation coefficient (the permeability P), respectively, in the transfer of gas through a
package given above, but in this case the driving force is a concentration difference
rather than a difference in partial pressure.
20 Innovations in Food Packaging
•^r = ha =Ja= JM = U{C, - C,) = h^^ (q - C^,)
D'(C,-C ^) (2.20)
From equations (2.13) and (2.20), where surface resistance is dominated by the parti-
tion coefficient, the diffusion flux J^ can be written by substituting Qi with K
C^
and
assuming that the partition coefficient is identical for desorption and absorption. The
convective mass transfer and the surface mass transfer coefficient /z^ are not as diffi-
cult to work with experimentally when the dimensionless partition coefficient K is
introduced, as shown in equation (2.21):
Washitake et al (1980) measured the permeability of betamethasone and salicylic acid
through eggshell membrane using equation (2.21). Smith and Haigh (1992) and Diez-
Sales et al. (1991) designed diffusion cells for drug penetrations and validated their
permeation phenomena with equation (2.21). Durrheim et al. (1980) introduced the
partition coefficient to determine the permeability of a drug through mouse skin and
human epidermal tissue. They converted the flux of equation (2.21) to a finite volume
model. The permeability was determined by equation (2.22).
y . dC/
p = -^— = ^^ (2.22)
A AC A AC
where Fis the finite volume of a drug-accepting chamber, A is the area through which
mass transfer takes place, and the flux J in this case was pertinent for their cell - i.e.
it was not expressed on a per unit area basis.
Torres and his group (Torres et al., 1985; Torres, 1987) used the partition coeffi-
cient K and equation (2.21) to estimate the transfer rates of a preservative into a maize
zein coating applied to intermediate moisture foods. However, since the late 1980s the
partition coefficient has been ignored and the definition of diffiisivity D in nP's'^ has
been used as a permeability constant P for sorbate in polysaccharide edible films
(Vojdani and
Torres,
1989a, 1989b, 1990; Rico-Pena and
Torres,
1991). Therefore, the
considerations of equation (2.21) are based on unhindered equilibration between the
concentration in the film and the concentration in the bulk solution (Torres et al.,
1985).
Keshary and Chien (1984) also used equation (2.21), with the assumption that
the partition coefficient K = 1, for a nitroglycerine patch.
The definitions of permeation, diffusion and absorption have been reviewed with sep-
arate considerations for gas and solute penetration. Permeation is the mass transfer
phenomenon that occurs when a molecule passes through a material or membrane from
an area of high concentration to an area of low concentration. Diffusion is the movement
Mass transfer of gas and solute through packaging materials 21
Table 2.1 Summaty
of
mass transfer through packaging material
Permeation
P
Diffusion
Gas transmission
Flux7
Ap
VsTP-L
L
Absorption
•^
./ .
Mass transfer coefficient
Permeability P(w
Diffusivity
Q
s
^s-'Pa-')
^las
' ^
m^
• s •
Pa
Solubility
S
{Pa'^)
'^laterial
' ^^
Solute permeation
Flux J Mass transfer coefficient
P AC Permeability
P
AC
D
Diffusivity
Q
h^AC Surface mass transfer coefficient
h
of molecules within
a
material caused by a concentration difference. Absorption is the
surface sorption
of
the molecules from the surroundings
to
the material. The mass
transfer coefficients of permeation, diffiision, and absorption are the permeability (P),
the diffusivity (D), and the solubility (5) in the case
of
a gas, or the partition coeffi-
cient (K) for a solute, respectively. Table 2.1 summarizes the definitions and the units
of the coefficients.
The units and definition of the diffiisivity of
a
molecule are identical regardless of
whether the diflfiisant is a gas or a solute. The diffusivity defines the transfer rate of an
amount of the diffiisant across
a
known distance in the material. In both gas and solute
diffusion, the diffusion has
a
driving force
of
the difference
in
concentration
of
the
molecule within the material.
The permeation of gas and solute molecules has the same physical phenomenon of
penetration
as a
permeant through
a
material. However,
gas and
solute permeation
usually have their flux defined differently. Henry's law is applied to relate the surface
concentration of a gas component with the partial pressure in the atmosphere in which
the packaging material
is in
contact.
On the
other hand, solute permeants
do not
follow Henry's
law.
The permeability of a solute is directly related to the overall mass
transfer coefficient, which includes the surface mass transfer coefficient
(Z^^)
and the
diffusional resistance
(L/D).
Often, the surface mass transfer coefficient is dictated by
the partition
of
the solute between solvent and membrane. The partition coefficient
(K)
relates the concentration of solute at the surface (Q) with the concentration of the
solute in the solution.
Most permeable substances that affect the quality
of
food products are gases such as
oxygen, carbon
dioxide,
noble gases, nitrogen and water
vapor.
These gases affect ranci-
dity, ripening, and hydration/dehydration of a food
product,
and generally determine the
length of a product's shelf
hfe.
Therefore, the oxygen transmission rate OTR
{OP
Ap/L,
where OP
is
oxygen permeability) and water vapor transmission rate WVTR {WVP
[Ap/L,
where
WVP
is water vapor permeability) are commonly used
for
quantifying the
performance of packaging materials in industry. Because OTR and WVTR are common
practical examples for the passage
of
a
substance (oxygen and water vapor) through
a
material (the package), solute permeation has not been considered as extensively
as
22 Innovations in Food Packaging
gas permeation. However, in the case of drug delivery and active packaging systems
solute permeation is theoretically important in order to explain active ingredient transfer,
and its experimental determination is reasonably straightforward. This warrants study-
ing all the factors that affect how fast solutes will permeate through given materials.
References
ASTM (1993). D 1434: Standard test method for determining gas permeability character-
istics of plastic film and sheeting. In: Annual Book of ASTM Standards, Vol. 15.09,
pp.
274-283. ASTM, Philadelphia, PA.
Carslaw, H. S. and Jaeger, J. C. (1959). Conduction of Heat in Solids. Oxford University
Press,
London, UK.
Cooksey, K., Marsh, K. S. and Doar, L. H. (1999). Predicting permeability and transmission
rate for multilayer materials. Food
Technol.
53(9),
60-63.
Crank, J. (1975). The Mathematics of Diffusion. Oxford University Press, London, UK.
Diez-Sales, O., Copovi, A., Casabo, V G. and Herraez, M. (1991). A modehstic approach
showing the importance of the stagnant aqueous layers in in vito diffusion studies,
and in vitro-in vivo correlations.
IntlJ.
Pharmaceutics 77, 1-11.
Durrheim, H., Flynn, G. L., Higuchi,
W.
L and Behl, C. R. (1980). Permeation of hairless
mouse skin I: Experimental methods and comparison with human epidermal perme-
ation by alkanols. J. Pharm. Sci. 69(7), 781-786.
Geankophs, C. J. (1993).
Transport Processes
and Unit
Operations,
3rd edn., pp. 408-413.
Allyn and Bacon, Newton, MA.
Keshary, P. R. and Chien,
Y.
W. (1984). Mechanisms of transdermal controlled nitroglyc-
erin administration. (1): Development of a finite-dosing skin permeation system.
Drug
Develop.
Ind. Pharmacy 10(6), 883-913.
Miller, D. G. (1960). Thermodynamics of irreversible processes. Chemical Reviews 60,
15-37.
Moore,
W.
J. (1972). Physical Chemistry, 5th edn. Longman Group Limited, London, UK.
Rico-Pena, D. C. and
Torres,
J.
A. (1991). Sorbic acid and potassium sorbate permeability
of an edible methylcellulose-palmitic acid film: Water activity and pH effects.
J.
Food
Sci. 56(2), 497^99.
Robertson, G. L. (1993). Permeability of thermoplastic polymer. In: Food Packaging,
Principles and Practice, pp. 73-110. Marcel Dekker, New
York,
NY.
Schwartzberg, H. G. and Chao, R. Y. (1982). Solute diffusivities in leaching processes.
Food
Technol.
36(2), 73-86.
Segall, K. L and Scanlon, M. G. (1996). Design and analysis of a modified-atmosphere
package for minimally processed romaine lettuce. J. Am. Soc. Hort. Sci. 121,
722-729.
Smith, E. W. and Haigh, J. M. (1992). In vitro diffusion cell design and validation. II.
Temperature, agitation and membrane effects on betamethasone 17-valerate perme-
ation. Acta Pharm. Nordica 4(3), 171-178.
Torres, J. A. (1987). Microbial stabilization of intermediate moisture food surfaces. In:
Water
Activity (Proceedings of the Tenth Basic Symposium by the Institute of Food
Technologists and the International Union of Food Science and Technology),
pp.
329-368. lUFoST
Mass transfer of gas and solute through packaging materials 23
Torres, J. A., Motoki, M. and Karel, M. (1985). Microbial stabilization of intermediate
moisture food surfaces. I. Control of surface preservative concentration. J. Food
Process. Preserv. 9, 75-92.
Vojdani, F. and Torres, J. A. (1989a). Potassium sorbate permeability of methylcellulose
and hydroxypropyl methylcellulose multilayer films. J. Food Process. Preserv. 13,
417^30.
Vojdani, F. and Torres, J. A. (1989b). Potassium sorbate permeability of polysaccharide
films: chitosan, methylcellulose and hydroxypropyl methylcellulose. J.
Food
Process.
Eng. 12, 33-48.
Vojdani, F. and Torres, J. A. (1990). Potassium sorbate permeability of methylcellulose
and hydroxypropyl methylcellulose coatings: effect of fatty acid. J. Food Sci. 55(3),
841-846.
Washitake, M., Takashima, Y., Tanaka, S., Anmo, T. and Tanaka, I. (1980). Drug perme-
ation through egg shell membranes. Chem. Pharm. Bull. 28(10), 2855-2861.
Quality of packaged
foods
Rakesh
K.
Singh
and Nepal
Singh
Introduction 24
Kinetics 25
Shelflifb 28
Aseptic packaging 36
Conclusions 40
References 40
Introduction
The quality of packaged foods is a combination of attributes that determine their
value as human food. These quality factors include visual appearance (freshness,
color, defects, and decay), texture (crispness, turgidity, juiciness, toughness, and
tis-
sue integrity), flavor (taste and smell), nutritive value (vitamins A and C, minerals,
and dietary
fiber),
and safety (absence of chemical residues and microbial contamina-
tion) (Robertson, 1993). "Keeping quality" is used more commonly than "shelf hfe"
because of consumer demand for product
fi*eshness.
The deterioration of foods that
occurs progressively during storage may result from physical or chemical changes in
the food
itself,
or
fi*om
the activity of micro-organisms growing in or on the product.
Eventually, the cumulative effect of the changes reaches a point at which the con-
sumer rejects the product. Rejection is based on the sensory expectations and percep-
tions of consumers. Shelf life depends on
a
multiplicity of variables and their changes,
including the product, the environmental conditions, and the packaging. Depending
on the product and its intended application, shelf life may be dictated by microbiol-
ogy, enzymology, and/or physical effects (Brody, 2003). The combined knowledge
and experience of processors and those involved in the storage, distribution and retail-
ing of foods enable estimates to be made of
the
likely shelf life of the product under
specific storage conditions. In practice, however, the influencing variables that accel-
erate or retard shelf life are temperature, pH, water content, water activity, relative
humidity, radiation, gas concentration, redox potential, the presence of metal ions,
and pressure.
Innovations in Food Packaging
ISBN: 0-12-311632-5
Copyright © 2005 Elsevier Ltd
All rights of reproduction in any form reserved
Quality of packaged foods 25
Table 3.1 Undesirable changes that can occur in foods
|
Attribute Undesirable change
Texture a. Loss of solubility
b. Loss of water holding capacity
c. Toughening
d.
Softening
Flavor Development of:
e. Rancidity (hydrolytic or oxidative)
f Cooked or caramel flavor
g.
Other off-flavors
Color h. Darkening
i. Bleaching
j.
Development of other off-colors
Appearance k. Increase in particle size
I. Decrease in particle size
m. Non-uniformity of particle size
Nutritive value Loss or degradation of:
n. Vitamins
o. Minerals
p. Proteins
q.
Lipids
Reprinted from Robertson (1993), p. 254, courtesy of Marcel Dekkerlnc.
There
is no
simple, generally accepted definition of shelf life
in the
food technology lit-
erature. Li 1978 the National Food Processors Association in the USA recommended, as
a working professional definition for internal industry, the following (Hotchner, 1981):
A product is within its shelf life when it is neither misbranded nor adulterated; when the product
quality is generally accepted for its purported use by a consumer; and so long as the container
retains its integrity with respect to leakage and protection of the contents.
The histitute of Food Technologists in the USA (Anon, 1974) has defined shelf Hfe as
the
period between manufacture and retail purchase of a food product, during which time
the product is in a state of satisfactory quality in terms of nutritional value, taste, texture
and appearance. An alternative definition is that shelf life is the duration of that period
between packing of
a
product and its use for which the quality of
the
product remains
acceptable
to the
product
user.
Packaging can affect
the rate
and magnitude of many of the
quality changes shown in Table
3.1.
As
examples, development of oxidative rancidity can
ofl:en be minimized if the packaging is an effective oxygen barrier, and the particle size
of many food powders can increase if the package is
a
poor moisture barrier. Thus pack-
aging is commonly used
to
maintain the quality and improve the shelf life of foodstuffs.
Kinetics
Rates of deteriorative reactions
Quality attributes that define shelf life gradually deteriorate over time. The rates of
these deteriorative chemical, biochemical and microbiological reactions depend on
26 Innovations in Food Packaging
both intrinsic and extrinsic factors. The general equation describing quahty loss may
be written as:
-dc/dt = f(I,E) (3.1)
where c is the index of deterioration, t is the time, /is intrinsic variables,
and
E is extrin-
sic variables. A negative sign is used if the concentration of c decreases with
time.
Since
the quality of foods and the rate of quality changes during processing and storage
depend on intrinsic factors, it is possible in many cases to correlate quality losses with
the loss of a particular component. Hence, the quality loss can also be represented as
being proportional to the power of the concentration of the reactant or product:
dA/dt = -k{AY (3.2)
where n is the order of reaction, dA/dt is the change in concentration of ^ with respect
to time (rate of reaction), and k is the rate constant. The negative sign indicates that at
a constant temperature, the magnitude of the quality parameter decreases with time.
In some cases the opposite is true, as in case of formation of chemicals rather than its
disappearance, and the rate should be designated as an activation or formation rate
rather than an inactivation or destruction rate. It is important to know the concentra-
tion of the reactant or the product so as to determine the acceptability of the final
product from the packaging point of view.
Zero-order reactions
In zero-order reactions, such as non-enzymatic browning in certain situations, which
follow a linear rate independent of the concentration of reactants, the rate of loss of ^
is constant with time and independent of the concentration of
^4:
^e/4 = -K (3.3)
or
A M = kt
(3.4)
where A^ is the initial value (time zero),
AQ
is the value of attribute A at the end of its
shelf life,
t^
is the length of shelf life, and k is the rate constant. For a zero-order reac-
tion, the concentration of ^ remaining with respect to time yields a straight line as
shown in Figure 3.1. The slope of this straight line represents the rate constant k hav-
ing the units of (concentration) (time~^). When « = 0, the reaction is said to be
pseudo-zero-order with respect to A. These types of reactions include non-enzymatic
browning, lipid oxidation, enzymic degradation, etc.
First-order reactions
First-order reactions, n = \, such as microbiological growth, follow a non-linear rate
dependent on reactant concentration. In this case:
A^
=
A^
Q-
(3.5)