Determining diffusivitiesoffruits

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Knowledge of the diffusivities of gases inbulkyplantorgans isessentialinunder-standing physiological changes, gas exchangesandinternalgas composition.The internal gas composition of fruits is determinedbythediffusivitiesofskin,flesh and stem (Burg and Burg, 1965; Cameron and Yang, 1982). Burg and Burg (1965) designed a system to determine gas resistancefactorswhichcan beusedtoesti-mate gas diffusivities in bulky plant organsusingtheratioof internalconcentra-tion to the ratio of the production of carbon dioxide and ethylene in the steady state. The diffusivities of gases in bulkyplanttissuecanbe calculatedasshown in Box 3.

There have been several reports on determiningthediffusivitiesofbulkyplant organs. Burg and Burg (1965) defined a resistancefactor (P)whichcouldbeesti-mated for bulky plant organs, in bananaandtomato,astheratioofinternalcon-centration to the ratio of production of carbondioxideandethyleneinthesteady state. They estimated that more than 60%ofgasexchangetakes placethrough the stem scar in tomatoes. But this resistantfactorisonlyan empiricalvalue without conventional dimensions and is notconstantwithchangesinthesurface to volume ratio. Cameron and Yang (1982) measured the efflux of a metabolic inert gas, ethane, which is neither produced nor metabolized to a significant degree by the tissue. It was shown that over97%ofgasexchangeintomatofruits occurs through the stem scar. However, the measurement of ethane efflux introduces several uncertainties because they did not measure the diffusivities of exocarp, pericarp and stem scar separately.

Solomos (1987), in a review of the principles of gas exchange in bulky plant organs, considered stationary states for CO2 diffusion through spherical- and cylindrical-shaped plant organs and determined the diffusivities of flesh and skin of apple in the peeled and intact fruit. The effect of the stem in gas transfer was not considered in determining the apparent diffusivities of apple.

Wax undoubtedly serves as a gas barrier to oxygen, carbon dioxide and water vapor and other metabolic gases and also provides protective functions (for example, mechanical damage, fungal and insect attack). Therefore, it can be assumed that the primary factor which regulates the internal concentration of gases is the skin in bulky plant organs. In apple the resistance of apple skin to gas diffusion was 10- to 20-fold greater than that of the flesh, depending on the cultivar (Solomos, 1987). Chinnan and Park (1995) built such a system from Plexiglass (diffusion cell, Fig. 16.1) and used it to determine the gas diffusivities of skin, pericarp and stem scar of tomatoes (see Fig. 16.2).

The gas diffusivities of exocarp plus pericarp, pericarp and stem scar increased as the tomatoes developed from the green stage to the red stage. The oxygen and carbon dioxide diffusivities of the stem scar increased 1.2-1.3 times as the

Box 3 Diffusivity

Gas exchange in bulky plant tissue can be approximated by Fick's first law. The flux of a gas in Fick's law is dependent on the gradient of concentration and diffusivities of plant organs. However, to determine the gradient of gases, Fick's second law can be employed (Chang, 1981; Gerard, 1931; Hill, 1928; Ricciardi, 1977; Solomos, 1987, 1989). If diffusion is one-dimensional and the diffusion coefficient is constant, the rate of transfer through unit area becomes:

In the non-steady state, all the solutions can be obtained either by the method of separation of variables and Fourier series or by the Laplace transformation (Carslaw and Jaeger, 1959; Crank, 1975; Doty, 1946; Edwards and Penny, 1985; Jost, 1960; Tuwiner, 1962).

If surface concentrations are constant, the following boundary and initial conditions may apply:

C = Cu x = 0, t > 0 C = 0, x = L, t > 0 C = 0, 0 < x < L, t = 0

The solution in the form of a trigonometrical series is:

C(x,t) = C1 (1 - x/L)-2/p jj Cjnsin(nx/L)exp(-Dn2p2 t/L2) [16.9]

As t approaches infinity the terms involving the exponential vanish and we simply have the linear concentration distribution. The rate at which the gas emerges from unit area of the surface x = L of the test sample is given by -D(dC/3X)x=l, which is easily deduced from equation [16.9]. By integrating with respect to t, we obtain the total amount of diffusing substance Qt which has passed through the membrane in time t as follows:

QjLCi = Dt/L2 -1/6 - 2pjj(-1)exp(-Dn2p2 t/L2) [16.10]

As t approaches infinity, equation [16.10] approaches the line:

This has a intercept L on the t-axis given by:

The intercept Lt is referred to as the 'time lag'. Thus, the measured values of concentration of the diffusion constant can be determined from the linear portion of the plot (Floros and Chinnan, 1989).

Fig. 16.1 Diffusion cell is constructed from Plexiglass™ to determine diffusivities. The cell is composed of three main parts: the sample holder, the supplying chamber and the sampling chamber. The face of each part is tooled for an O-ring which provides a tight connection. Chinnan and Park (1995) modified and reconstructed the apparatus for this gas diffusion study. (1) Sample holder, (2) gas chamber, (3) sample, (4) sample retainers, (5) threaded bush, (6) sealing O-ring, (7) tubing adapters, (8) thumb nuts, (9) thread rods.

Fig. 16.1 Diffusion cell is constructed from Plexiglass™ to determine diffusivities. The cell is composed of three main parts: the sample holder, the supplying chamber and the sampling chamber. The face of each part is tooled for an O-ring which provides a tight connection. Chinnan and Park (1995) modified and reconstructed the apparatus for this gas diffusion study. (1) Sample holder, (2) gas chamber, (3) sample, (4) sample retainers, (5) threaded bush, (6) sealing O-ring, (7) tubing adapters, (8) thumb nuts, (9) thread rods.

Fig. 16.2 Diffusivity can be measured by the following procedures (Chinnan and Park, 1995). Each of the cored and sliced samples prepared for the study is placed in the diffusion cell and a premixed gas (9.9% O2, 10.1% CO2, 80.0% N2) is introduced to the supplying chamber. The amount of CO2 and O2 diffusing through the sample in time t into the sampling chamber can be measured by gas chromatography. The sampling interval is 5 min, and the total sampling period is 2h. The diffusion cell is immersed in a water bath maintained at 21°C. All equipment for determining gas diffusivities is placed in a heat insulated chamber and the temperatures at several places inside the chamber are monitored. (1) Diffusion cell, (2) water bath, (3) flask, (4) mineral oil, (5) test gas inlet, (6) nitrogen inlet, (7) three-way valve, (8) three-way connector, (9) two-way valve, (10) sampling chamber, (11) silicone septum, (12) gas flowmeter, (13) brass tubing.

Fig. 16.2 Diffusivity can be measured by the following procedures (Chinnan and Park, 1995). Each of the cored and sliced samples prepared for the study is placed in the diffusion cell and a premixed gas (9.9% O2, 10.1% CO2, 80.0% N2) is introduced to the supplying chamber. The amount of CO2 and O2 diffusing through the sample in time t into the sampling chamber can be measured by gas chromatography. The sampling interval is 5 min, and the total sampling period is 2h. The diffusion cell is immersed in a water bath maintained at 21°C. All equipment for determining gas diffusivities is placed in a heat insulated chamber and the temperatures at several places inside the chamber are monitored. (1) Diffusion cell, (2) water bath, (3) flask, (4) mineral oil, (5) test gas inlet, (6) nitrogen inlet, (7) three-way valve, (8) three-way connector, (9) two-way valve, (10) sampling chamber, (11) silicone septum, (12) gas flowmeter, (13) brass tubing.

tomatoes developed from green to red. The extent of increase in gas diffusivities for exocarp plus pericarp and pericarp were greater than that of the stem scar during the ripening process. Progressive loss of firmness during the ripening process is the result of a gradual transformation of protopectin into pectin which is degraded by the enzyme polygalacturonase in the cell wall (Hobson and Davies, 1971). This enzymatic degradation of pectin can probably be attributed to greater diffusion of gases in the bulky organs of tomato.

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