The hollow sphere model can also be used to determine the optimal edible coating thickness in some fruits such as apple and cantaloupe melons. In edible film-coated apple and cantaloupe, the flux of oxygen passing through the spherical fruit wall from the center to the interface between the film coating and the fruit surface should equal the flux of oxygen passing through the edible coating from the interface between the film coating and the fruit surface to the atmosphere, and should equal the rate of oxygen consumption of the edible film-coated apple and cantaloupe in the steady state (Carslaw and Jaeger, 1959; Chang, 1981; Crank, 1975; Doty, 1946; Jost, 1960; Solomos, 1987):
where Rc(O2) is the oxygen consumption rate of coated fruits, Dcz is the dif-fusivity of edible coatings and X is the thickness of the edible coating. Cx is oxygen concentration at the surface between the edible coating and the surface of fruits.
The optimal coating thickness which will create a desirable range of internal oxygen concentrations (CO in apples, (i.e. 2-3%) and cantaloupe melons (3-5%) can be calculated from equation [16.18]:
where b + X becomes b when X is very small. Cx is determined from equation [16.17] with C2 = Cx.
(Carslaw and Jaeger, 1959; Chang, 1981; Crank, 1975, Doty, 1946; Jost, 1960; Solomos, 1987):
on substituting u = Cr in the equation [16.13], we have: du/3t = D (d2C/dr2). In the steady state, the differential equation for this case is:
In a hollow sphere where a < r < b, if gas concentrations are kept constant at the surfaces so that they are equivalent to C1 at r = a and C2 at r = b, then C = [aCi(b - r) + bC2(r - a)]/r(b - a). By integrating with respect to time t over the surface area, the total amount of diffusing gas Qt passing through the wall can be determined by (Carslaw and Jaeger, 1959; Crank, 1975; Solomos, 1987):
where Dapp is apparent diffusivity of the hollow sphere and a and b are constants for individual fruits.
However, in the steady state the flux ofoxygenpassingthrough thespherical fruit wall should equal the rate of gas consumption, thus:
where R(O2) is respiration rate of oxygenperfruitand W isweightofthefruit.
The internal oxygen composition, C1, can be predicted using equation [16.16]. The correlation factors can be calculatedfromactualmeasurementofinternalgas composition. Also, the predicted internal gas composition of edible film-coated fruits and vegetables can be verified by measuring internal gas composition. Optimum edible coating thickness can be calculated for each produce-coating combination as shownin Box4.
Quality criteria for edible film-coated fruitsmustbedeterminedcarefullyandthe quality parameters must be monitored throughout the storage period. For example, the color change and firmness areveryimportantqualityparametersin some fruits. The color change, loss of firmness,ethanolfermentation,decayratio and weight loss of edible film-coated fruits need to be monitored (Shewfelt et al., 1987). The color change is monitored bythechangeinhueangle. Anlnstronuni-versal test machine can be used to measurefirmnessbyanon-destructivemethod (Bourne, 1982). Sensory evaluation andconsumeracceptability testsneedtobe examined duringstorage.
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