3.3 Comparación entre resultados obtenidos
3.3.1 Resultados ensayo – modelo matemático simplificado
Moisture loss from a product can be considered as the result of two phenomena: ( 1 ) migration
of moisture within the body to its surface; and (2) transfer of the vapour at the surface to the
surrounding air (Bonacina & Comini, 197 1 ). The moisture transfer mechanisms within a
(2) vapour diffusion in air-filled pores caused by a partial pressure gradient; and
(3) molecular diffusion due to a concentration gradient.
Where it occurs, capillary action is the dominant mechanism for products with higher moisture content «((fischer & Mahler, 1959; Van Arsdel, 1963; Luikov, 1966; King, 1968), because water transport is in the liquid phase only and relatively rapid. Vapour diffusion is usually significant only with lower product moisture contents. Molecular diffusion would, usually, be limited to capillaries with molecular dimensions and because it is slow, its contribution to the total moisture migration within the body would be small if capillary action also occurs to any significant extent. Since many food materials are solids with capillary structure, capillary action is often the leading mechanism (Bonacina & Comini, 197 1). In contrast, diffusion is slow and typically all the water is lost from the outside few millimetres of the product (Lovett et ai., 1976; Fulton et ai., 1987).
At the surface, heat is required to provide the latent heat of evaporation for the water. The rate of heat flow and the rate of moisture loss depend on a variety of conditions. The evaporation rate also relates to the transport of water inside the product. Radford et ai. (1976) found that the rate of evaporation from slabs of meat was initially the same as that from a fully wetted surface, but that the surface dried rapidly. The evaporation declined progressively until equilibrium was reached between the evaporation rate and the rate of movement of water to the surface from the underlying tissues. As cooling proceeded, the partial pressure driving force for evaporation diminished until the diffusion transport rate exceeded the evaporation. The surface progessively re-wetted and the evaporation rate then once more approached that for a wetted surface. Surface fat or skin acts as an effective barrier to the water diffusion and therefore restricts weight loss (Gigiel et aI., 1989).
2.5.2 Modelling of Evaporative Heat Transfer at the Product Surface
When evaporation is considered in the boundary condition for heat transfer, it is often necessary to include the mass transfer of water by diffusion or capillary action within the product as part of the model (Comini & Lewis, 1976; Radford et ai., 1976; Cleland, 1989). For regular shapes this can be accomplished by linking finite difference calculations for diffusion with finite difference calculations for heat conduction (Cleland, 1989).
Weight loss in a horticultural product is a combination of the rate of carbon loss due to the evolution of carbon dioxide arising from respiration particularly during storage and the rate of moisture loss. In cooling, the carbon loss is usually an insignificant part of the total weight loss, except in cases where moisture loss rates are very low. The rate of water vapour flow
(the rate of moisture loss from the product) can be described as follows (Chau et al., 1985; Cleland, 1989): m -
K A (pJ - P, J
(2.27) where m =K
= = =PwJ
=Pa
=Pwa
=Hr
= (2.28) (2.29) evaporation rate (kg S-1 m-2)overall mass transfer coefficient (kg S-1 m-2 Pa-1)
surface water activity (vapour pressure lowering effect due to the presence of solute in the product moisture)
partial pressure of water vapour at evaporating surface (Pa)
(saturation) vapour pressure of pure water at the evaporating surface temperature (Pa)
partial pressure of water vapour in the surrounding air (Pa)
(saturation) vapour pressure of pure water at the surrounding air
temperature (Pa)
air relative humidity
The evaporation rate is normally numerically small in size (Lutz & Hardenberg, 1968;
Bonacina & Comini, 197 1). The partial pressure exerted by water vapour in the surrounding
air is a direct function of the dry bulb temperature and relative humidity of the air. The partial pressure of water vapour in the boundary layer at the evaporating surface is a function of temperature at the product surface and the surface water activity.
If the ambient temperature is below the product temperature, a large vapour pressure difference exists, and the moisture loss may be expected to be rapid. In the early stages of chilling, air relative humidity has little effect on weight loss, and the temperature difference
during the later stages of cooling and in subsequent storage, the effect of humidity can be substantial (Brown & James, 1992; Pham & Willix, 1985).
An alternative description is a dew point model. If product temperaure is the same as the air dew point temperature then there is no driving force for either water condensation or
evaporation. If product temperature is below the air dew point, condensation occurs, whereas
if it is above the air dew point, evaporation occurs (Patel et ai., 1988).
Water activity is closely related to physical, chemical and biological properties of products but also depends on moisture content (Troller & Christian, 1978; Chirife & Fontan, 1982). The water activity can be used to describe the variation of surface dryness throughout the cooling process. As evaporation proceeds the surface moisture becomes depleted, so the water activity changes with time (Comini & Lewis, 1976; Radford et al., 1976; Sastry et ai.,1985; Balaban,
1989; Cleland, 1989). In modelling, the major difficulty is knowing how the product water activity varies with water concentration at the product surface and in obtaining accurate data for water movement through the solid (Cleland, 1989).
Van Beek (1983, 1985) stated that the mass transfer coefficient could not be considered as a constant product property. In his experience it changed with temperature and in circumstances with little air movement, it could vary with position on a surface. Since the skin of horticultural products is permeable to water vapour, Chau et al. (1985) proposed that the mass transfer coefficient (K) be determined from two variables, the skin coefficient
(Ks)
and the air film coefficient(Kg)
as follows:1
K
1 + -1K s
K g
= = (2.30) skin mass transfer coefficient (kg S-1 m-2 Pa-1)air film mass transfer coefficient (kg S-1 m-2 Pa-1)
It would be more general to include a packaging mass transfer coefficient,
Kp'
as well:1
K
where
Kp
1 + - + -1 1