We consider okra to be a structurally complex product. It has three constituents of different natures. As shown in Figure 1, the dark green skin constitutes an outer covering. It contains more or less spherical seeds which are attached to a spongy material constituting the central axis of the okra. Okra contains fibers that are oriented lengthwise [5] . It is therefore necessary to characterize the isotropicity of okra. For these experiments, fresh okra was purchased from a local market in Burkina Faso. They were kept in a refrigerator at 12˚C between 2 and 3 days, the time necessary to carry out these experiments.

Convective drying of okra was carried out in an oven. The temperature is set at 70˚C. As soon as thermal equilibrium is reached, the samples are introduced into the oven enclosure. On each okra, we mark with indelible ink three geometric locations where the diameter measurement will be carried out. Then, the diameter considered is the average of these three measurements. The samples are removed from the oven, at a time interval predefined by preliminary tests, for

measurements to be taken. We minimize the measurement time so as not to disturb the thermal balance already established in the product. Geometric characterization of the samples is done by initially measuring the diameters of a few sections along the entire length of the okra as well as the length of the entire okra over the drying time. For some samples, we measure the length of the sections that have been marked during drying. To do this, we use the digital micrometer (MITUTOYO, Japan, precision 2 × 10⁻⁵ m).

Contraction

During the drying of okra, the product undergoes physical deformations, as shown in (Figure 2.). In the case of drying, contraction (shrinkage) is a consequence of the loss of water from the solid matrix of the product. The models in the literature are mainly empirical and cannot be transposed from one product to another or to other experimental conditions [6] - [12] . There are nevertheless basic theories in the literature [13] . The multiplicity and diversity of products and their physical properties (density, material concentration, contraction coefficient, collapse, porosity, change in dimensions, etc. make comparisons very difficult [14] - [19] .

From experimental data, contractions are represented by the following relationships (Equations (1)-(3)):

• Volume:

V V 0 = a v X X 0 + b V (1)

• Length:

L L 0 = a L X X 0 + b L (2)

• Diameter:

d d 0 = a d X X 0 + b d (3)

where a and b are constants deduced graphically, the indices v, L and d being related respectively to the volume, length and diameter. These models have been used by certain authors for different products and applications: for carrots [20] [21] , potatoes [22] , apples [23] , grapes [24] , hammered [25] potatoes and carrots (okra [21] [26] [27] [28] [29] [30] ).

Shrinkage isotropicity.

The difficulty linked to agri-food product drying study comes from the great diversity in the field. Added to this is the structural factor, heterogeneity and anisotropicity of the agri-food product giving it, during its drying, very complex physical and mechanical characteristics. We can distinguish three main directions:

• The longitudinal direction (L), which is that of the fibers;

• The tangential direction (T), perpendicular to the plane containing the fibers;

• The radial direction (R), is perpendicular to the longitudinal and centripetal axis.

The isotropicity index makes the comparison of the contraction of samples in two directions during drying.

For drying times different from the initial time, the shrinkage isotropicity between X and Y directions was defined as the ratio of the reduction in X divided by the ratio of the reduction in Y.

For these directions, we define the isotropicity index XY by the following relation:

I X Y = X − X 0 X 0 Y − Y 0 Y 0 (4)

Thus, the radial-axial isotropicity index is defined by the following relationship, in the case of a cylindrical sample where equation 4 becomes Equation (5) [19] :

I d L = d − d 0 d 0 L − L 0 L 0 (5)

where d₀, d are respectively the initial and the current values of the sample diameter and L₀, L respectively the initial and the current values of the sample length.

During drying, the lateral dimensions of okra decrease over time. As the product loses its water it undergoes a collapse of the material which compensates for the loss of water. Consequently, its diameter decreases. Figure 3(a) indicates that for diameters 1, 2 and 3 the lateral dimensions increase from their initial value to

around 53%, 65% and 66% of this value after 530 min. We nevertheless notice that at the first moments, before the first 100 minutes, the lateral dimensions increase and slightly exceed the initial values. This is certainly due to the increase in internal pressure. Indeed, the water from the seeds and the central material that evaporates remains trapped by the skin. The water vapor increases the pressure which swells the skin. This phenomenon increases the values of the lateral dimensions. A few moments later, this water vapor escapes and the pressure drops. In addition, the skin becomes rigid and no longer swells. The variation of d/d₀ as a function of X/X₀ is quasi-linear after the first 100 minutes. Considering the overall drying time, the linear modeling has a deviation of R 2 = 0.640 , which is not satisfactory (Figure 3(b)). This poor correlation is linked to the complex structure of okra. Consequently, the lateral contraction curve which should be linear contains enormous irregularities. Lateral contraction can only be considered linear after a certain time necessary to establish a stationary transfer regime.

The loss of water from okra during convective drying results in a contraction of the longitudinal dimension. As shown in Figure 4(a), the length of these samples increases, on average, from 8.65 and 902 cm to 6.79 and 7.52 cm after 14,300 min, i.e. a variation of 78.50% and 83.37%.

The variation of L/L₀ as a function of X/X₀ is quasi-linear (Figure 4(b)). Linear modeling gives the equation:

L L 0 = − 0.0001 X X 0 + 0.9227 (6)

With R 2 = 0.5192 .

This correlation can be considered unsatisfied and highlights the complex nature of okra.

The shrinkage data obtained during convective drying were also analyzed in terms of the bulk shrinkage coefficient. Figure 5(a) shows the volume change as a function of moisture content. As shown, sampling again exhibits a linear shrink relationship with moisture content.

Considering the okra as having a cylindrical shape, the volume is calculated at each moment of drying. The results in Figure 5(a) shows that okra significantly decreases in volume during the drying process. The volume goes from 831.32 cm³

to 367.57 cm³ in min, a variation of 44.22%. Considering the relationship between V/V₀ and X/X₀ Figure 5(b) gives us a quasi-linear relationship. This linearity follows the equation:

V V 0 = 0.5443 X X 0 + 0.4621 (7)

with R 2 = 0.9923 , the linear relationship will be considered acceptable.

Examination of the lateral and longitudinal contractions of the okra during its convective drying seems to show a difference in behavior according to these directions. The samples give, on average, final lateral contractions of 53.65% and 66%, which are clearly different from the longitudinal contractions of 78.5% and 83.37%. These remarks lead us to examine the isotropicity of okra. The isotropicity index at the diametric direction versus the longitudinal one is significantly above 1 which is the isotropicity index of an isotropic product (Figure 6). However, from the first moments of drying, there is an inversion where the length

seems to contract more than the diameter. Which is characterized by a curve below the ideal Id-L = 1

Thus, the okra contracts more in diameter than in length. As can be seen in Figure 6, this isotropicity is not linear. We can explain these results by taking into account the difference in structure between the directions. Indeed, the fibers of okra are oriented in the longitudinal direction. These fibers can withstand more contraction stress, thereby reducing the decrease in length. On the other hand, these fibers parallel to each other can collapse and do not prevent the reduction in diameter.