Study of Water Diffusion through Raffia Vinifera fibres of the Stem from Bandjoun-Cameroon : Case of Drying Kinetics

The objective of this study is to determine some physic-chemical properties of raffia Vinifera fibres resulting from the stem. The moisture content rate of these fibres was evaluated along the stem and varies in the intervals [12-6] % and [19-107] % for dry and fresh fibres respectively. Thermo gravimetric method using the temperatures 60, 70 and 80°C respectively, enables us, through Fick’s 2 law, to find other parameters. Owing to the data on the moisture content, the different curves were plotted. Fourteen models were tested to predict the drying kinetics of fibres with cylindrical form. It comes out that the models “Diffusion approach” and “Verma et al. (1985)” models fitted well with the phenomenon. The effective diffusion coefficient of the initial phase varies in the intervals [6.32×10-3.00×10] m/s and [1.76×10-4.47×10] m/s for dry and fresh fibres respectively. We notice that the moisture content and the effective diffusion coefficient grow from the periphery towards the centre in each cross-section. Owing to the relation of Arrhenius, the activation energy was evaluated only in the initial phase and oscillates respectively in [4.72 – 22.86] KJ/mol.K and [4.65 – 12.13] KJ/mol.K for dry and fresh fibres.


INTRODUCTION
The raffia is a plant which generally grows in the tropical zones of Africa, Asia and South America (Musset, 1933;Obahiagbon, 2009).This plant belongs to the family of palm trees monocotyledons called arecacea.There are about twenty species of raffia in the world among which the raffia vinifera (Sandy and Bacon, 2001).This variety of raffia does not have a trunk (Ndenecho, 2007) and grows essentially in the swamp and at the bottom of the mountainous areas.The raffia vinifera is a plant which has several parts, namely: the stump, the stem, sheets and the fruits (Ndenecho, 2007).
The use of the raffia vinifera as basic materials in the realization of art and craft products such as the baskets, stools, hats, clothing, braces, beds, etc. becomes increasingly intense.In fact, since few years, there is a strong demand by the population.So, the raffia forests are frequently solicited and therefore disappear progressively, since the time of regeneration is long.
In order to understand the physical behaviour of this biodegradable material, the study of dehydration is carried out.
Many researches have been carrying out for an understanding of the behaviour of raphia.We can enumerate the use of the bamboo raffia as reinforcement in the concrete by Kankam (1997), the physicochemical characterization of oils coming from the raffia sese and laurenti by Silou et al. (2000), the study of the thermal properties of the trunk of raffia hookeri used like material of ceiling by Etuk et al. (2003).For the raffia textilis, reflections were carried out on the microstructure and the physical properties of fibres resulting from the sheets on the one hand and on the other hand on the drying kinetics of these fibres whose sheets are used as materials of roof by villagers (Elenga et al., 2009(Elenga et al., , 2011a, b), b).In addition, for the raffia viniféra, we can indicate the biochemical characterization of the sap (wine of palm) and its effect on the rats by Tiepma et al. (2010).The study on the long-term behaviour of the stem of raffia viniféra in compression or in flexion was approached by Talla et al., 2004Talla et al., , 2005Talla et al., , 2007Talla et al., and 2010)).The toxicity of the fruits of raffia viniféra also was the subject of an attention carried out by Fafioye et al. (2004) and Fafioye et al. (2005).Also on the determination of some mechanical properties of raffia Vinifera fibres resulting from the stem, were evaluated like some ∑ parameters related to those as the Young modulus and the density by Njeugna et al. (2012).
The knowledge of other parameters related to the raffia Vinifera fibres is important for the realization of composite with those fibres as reinforcement.We are proposed to study the drying kinetics of these fibres.The aim of this study is to propose a drying kinetic model, the determination of the moisture content, the effective diffusion coefficient and the activation energy the fibres along the stem of raffia vinifera during drying.

Materials:
The fibres come from raffia vinifera stem of the swamp located around of the University Institute of Technology Fotso Victor of Bandjoun in the west region of Cameroon.We obtained these fibres using the mechanical or direct method as described by Njeugna et al. (2012) on the methods of extraction.This study is undertaken on two varieties of stems classified according to the moisture content.
The tools used, are a numerical balance whose precision is about 0.01 g for the weighing of the various samples and a drying oven.

Methods:
The fibres used are characterized by a length of 150 mm and the mass ranging between 0.50g and 1g per package.The packages of raffia fibres were taken in the twelve extraction zones along the stem and according to the cross-section as shown in the Fig. 1a and b below.Namely 4 longitudinal positions (PL-1/4; PL-2/4; PL-3/4; PL-4/4) and 3 radial positions (R1; R2; R3).
To choose a mathematical model for the fibres, we carried out the tests of the various existing models in a precise zone of the stem.Thus, the choice of the suitable model to describe this phenomenon with a good accuracy will be the one that presents a higher correlation coefficient (R 2 ); a lower Root Means Square Error (RMSE) and a chi-square (χ 2 ).These statistical parameters are defined by the following relations:

and
(1) where, ݉ , , ݉ , , N and n are respectively the ith experimental masses, the ith theoretical masses, the number of observations and the number of constants.These selection criteria were applied to the drying of the sheets of Mint or waste of Olive by Akgun and Doymaz (2005) and Doymaz (2006Doymaz ( , 2005)).
We chose three temperatures 60, 70 and 80°C to undertake this study.The air velocity in the laboratory is 1.5 m 2 /s and remains constant for the various temperatures (Arumuganathan et al., 2009;Kongdej, 2011;Chien et al., 2008).
When the drying oven is started, we regulate the temperature that we need.We introduce the prepared package of fibres into the drying oven and after each three minutes, we carry out the various weighing until reaching a noted constant mass m ∞ .The interval time between the exit and the introduction of the package of fibres is supposed to be negligible.Because this duration is evaluated approximately at 20s.The studies of the drying kinetics of the fruit of chempedak (Chien et al., 2008) and of the effects of the sun on onions (Arlan and Özcan, 2010) were made in the same direction.

Theory on the diffusion of mass through a solid:
The equation of mass transfer through solid results in the Fick's 2 nd law.This law is given by the Eq. ( 2): with C (mol/m 3 ) concentration in diffusing molecule and D (m 2 /s) the diffusion coefficient.Taking into consideration the geometry of raffia fibre which has an elliptic cross-section (Njeugna et al., 2012), we approximate as a full cylinder.
The Eq. (2) will be written only in cylindrical coordinates.We have: Considering the ratio of length on the diameter which is very high and by neglecting the diffusion along z axis, the Eq. ( 3) is reduced to: Considering the boundary conditions, we have: The solution to the Eq. ( 4) can be written according to Crank (1975) as follows: with J 0 and J 1 being respectively Bessel functions of zero and first order.
Let us note M t and ‫ܯ‬ moisture content of water diffused through raffia fibre respectively at the moment t and initial time.The Eq. ( 5) can be rewritten for the water mass rate rejected in terms of effective diffusion coefficient (D eff ).
According to Crank (1975), the Eq. ( 5) becomes: With ܽߙ being the positive roots of the Bessel function of zero order, a radius of fibres and D eff the effective diffusion coefficient.The Eq. ( 6) was used by Rastogi et al. (1997Rastogi et al. ( , 2002) ) in the study of the phenomenon of dehydration during the mass transfer.
The ratio of the moisture content noted MR, is defined by relation: with m 0 , m t and ݉ ∞ the mass of fibres samples respectively at the beginning, a time t and the end.From the Eq. ( 6), we can say that the Moisture Ratio (MR) can take the expression: This consideration was done for the case of the study on the influence of the shape of the crop products during drying by Senadeera et al. (2003) or for the thermo gravimetric analysis of the pasta products by Takenobu et al. (2012).
Taking the first term of the series as presented by Senadeera et al. (2003), Chien et al. (2008) and Schössler et al. (2012).The relation (8) becomes: మ and k = ‫ܦ‬ ߙ ଵ ଶ , Eq. ( 9) take the form: With (aα 1 ) first root of the Bessel function of zero order, a radius of the cross-section of fibre, D eff the effective diffusion coefficient.

Moisture content:
The Moisture Content (MC) of raffia Vinifera fibres resulting from the various zones of sampling will be given by the formula: This equation was used for the study of the drying kinetics of pumpkin (Kongdej, 2011) and also during the modelling of drying kinetics of the plates of kiwifruit (Mohammed et al., 2009). 1 gives the different models used during the description of the drying kinetics of some vegetable products.

Evaluation of the effective diffusion coefficient:
Applying the logarithmic function to the Eq. ( 10), we obtain: To determine the effective diffusion coefficient of raffia vinifera fibres, we plot the curve of ln MR. according to time t.This curve will be a line referring to the Eq. ( 12), the slope of this straight line to deduce the effective diffusion coefficient (Senadeera et al., 2003;Chien et al., 2008;Arumuganathan et al., 2009;Kongdej, 2011;Duygu, 2012;Ngankham and Pandey, 2012).

Determination of the activation energy:
The equation of Arrehenius is used to describe activation energy in chemical process (Senadeera et al., 2003;Arumuganathan et al., 2009;Ngankham and Pandey, 2012): Its general expression is given by: where D 0 is the constant in the Arrhenius equation expressed in (m 2 /s), E a the activation energy in (KJ/mol), R the constant of perfect gases which is in 8.314 J/mol/K and T the absolute temperature of the air of drying in (°K).
Applying the logarithmic function to the Eq. ( 13), we have: The variation of ln D eff with 1/T is plotted using Matlab R2009b and enables us to obtain the slope m = ( ா ೌ ோ ) of the straight line and to deduce the activation energy.

RESULTS AND DISCUSSION
Moisture content: According to the use of the raffia vinifera stem by the populations, two varieties were the subject of our study.By using the formula of the Eq. ( 11), the moisture content of fibres resulting from the stems of raffia was evaluated according to the zones along these.
It comes out that the moisture content rate of one variety is between 12% and 16% as shown in Fig. 2.
We observe that the variation of the moisture content on an unspecified cross-section along the stem is not significant.A similar analysis can be made in the longitudinal direction.The interval of moisture content obtained is comparable with the values found in study on agricultural waste like the bark and the cork of the raffia hookeri which have respectively as water content 10.70% and 14.20% (Israel et al., 2008).It will be called dry raffia vinifera fibre.
Figure 3 shows us a variation of moisture content included between 19% and 107%.We notice that for each cross-section specified along the stem, the moisture content of raffia fibres increases from the periphery towards the center.We also note that the moisture content of fibres located on the cross-section near the sheet at PL-4/4 of the stem is around 20%.It is very low compared to the values located in the interval [65%-107%] obtained in other zones PL-1/4, PL-2/4 and PL-3/4.Such a difference comes from a probable variation of the microstructure of raffia fibres in the cross-section along the stem and also by the feeding system of the sheets in sap.We will name this other fresh raffia vinifera fibre in the following development.It is also the case of raffia vinifera fibres resulting from the fresh stem.The same curves were obtained during the study of the drying of some vegetable products (Taheri-Garavand et al., 2011;Elenga et al., 2011a, b;Ngankham and Pandey, 2012;Duygu, 2012).

Drying kinetics:
Choice of a mathematical model: Table 1 illustrates the different parameters of the proposed models of the  Table 2: Different existing models for the study of the drying kinetics of some vegetable products (Mohammed et al., 2009;Duygu, 2012 Table 2, the correlation coefficient (R 2 ), the Root Means Squared Error (RMSE) and the chi-square (χ 2 ) of the fibres located at the center of base (PL-1/4-R3) of the dry stem of raffia vinifera.We observe that five models have a correlation coefficient (R 2 ) which is higher than 0.995 for the three temperatures.There are two term, Diffusion approach, Verma et al. (1985) modified Henderson and Pabis (1961) and finally Midilli et al. (2002) models.Considering the average of the correlation coefficients of the three temperatures of each of the five models above, only Two term, Diffusion approach and Verma et al. (1985) models gives us an identical value of R 2 better whose value is 0.998033 (Simal et al., 2005).Proceeding the same way on the values of the chisquare and the relative error of these last three models, we obtain the lowest values of the identical averages which are respectively 0.0013926 and 0.01721033 for Diffusion approach and Verma et al. (1985) models.Similar steps were carried out for the drying kinetics of mint (Aghfir et al., 2008) and of the sheets of tea (Panchariya et al., 2002).Taking into consideration such an analysis, we can say that the mathematical model which best describes the drying kinetics of dry raffia Vinifera fibres resulting from the stem of the zone located at PL-1/4-R3 is Diffusion approach or Verma et al. (1985) model.For a better appreciation of the choice carried out, we applied this result to the other zones of sampling of the stem.Thus, Table 3 offers the opportunity to evaluate this choice on the cross-section at the base (PL-1/4) of the stem.
It comes out for the studied sample that the Diffusion approach and Verma et al. (1985) models give the same values of correlation coefficient, chisquare and relative error.
It can be deduced that the model which gives a better description of the behaviour of raffia Vinifera fibres resulting from the dry stem are the Diffusion approach and Verma et al. (1985) models.It is in conformity with the study on the dying of onions (Arslan and Özcan, 2010).
Concerning the raffia Vinifera fibres resulting from the fresh stem, methodology in the choice of a mathematical model to describe the drying kinetics remains the same.Initially, we took periphery fibres from the zone close to sheets of the raphia stem (PL-4/4-R1).So, Page, Modified Page, Two term, Diffusion approach, Verma et al. (1985) modified Henderson and Pabis (1961) and finally Midilli et al. (2002) models gave a correlation coefficient higher than 0.995.Then, the means of the correlation coefficient, root means square error and chi-square of the three temperatures enable to obtain equal We can say that Diffusion approach or Verma et al. (1985) models give better description of the drying kinetics of fibres along the stem of raffia.
Figure 5 and 6 illustrate respectively the kinetics of Diffusion approach and Verma et al. (1985) model presented at various temperatures of the study of fibres of the center coming from base (PL-1/4-R3) of the dry stem.We observe that each curve fit well with the experimental points.The curves of the two suggested models give for different temperatures the same observations as previously for fibres of the fresh stem.

Evaluation of effective diffusion coefficient:
Figure 7 represents the variation of the Moisture Ratio (MR) with time t for peripheric fibres resulting from the base of the fresh stem of raffia vinifera at T = 60°C.
We notice that the experimental points of this curve present a bilinear form.We can also say that for the fresh stem as well as for the dry stem and at various zones of sampling, we observe the same behaviour.
Meanwhile, the equation 12 defines that of a line.It means that the curve obtained can be divided into two lines having a slope each.The first slope which defines the initial phase and the 2 nd slope which describes the final phase of diffusion during drying.Such an approach was applied during the study of the mathematical modelling of the drying of the mushroom (Arumuganathan et al., 2009) and in the same way, during the research of the diffusion coefficient during water absorption of the pasta products (Cunningham et al., 2007).
By the help of the software MATLAB R2009b, the slope (k) of the different straight line, the correlation coefficient (R 2 ) and the effective diffusion coefficient of fibres resulting from the various zones of the dry stem were represented in Table 4.
The analysis of the values contained in Table 4 enables us to note that the slope (k) of regression straight line during the initial phase of drying increases according to the temperature.By deduction, it is the case of the effective diffusion coefficient in each crosssection taken in a zone of sampling along the stem of raffia vinifera during this same phase.Similar results were observed during the studies of drying of the mushroom (Arumuganathan et al., 2009), fresh green beans (Souraki and Mowla, 2008;Souraki et al., 2012), bel pepper (Taheri-Garavand et al., 2011), medicinal plant Gundelia tournefortii (Duygu, 2012) and ripe banana (Rastogi et al., 1997).On the other hand, the slope (k) of the regression straight line during the final stage of dehydration does not obey any particular observation.
However, for the fibres from the fresh stem of raffia vinifera, we notice that the correlation coefficient obtained during the two phases is higher than 0.90.In addition, the effective diffusion coefficient in the initial phase increases according to the temperature at any position of the stem.It varies in the interval [1.76×10 - 10 -4.47×10 -10 ] m 2 /s in the initial stage and included in the interval [1.03×10 -11 -1.91×10 -11 ] m 2 /s during the final stage.
Figure 8 and 9 illustrate the evolution of the effective diffusion coefficients at the initial phase of drying of raffia Vinifera fibres resulting respectively from the cross-sections of the dry (PL-2/4) and fresh (PL-4/4) stems at the different temperatures.In general, we note that the diffusion coefficient in a precise crosssection grows from peripheric towards the center.The same observations have been done for all the other zones along the stem.
Table 5 above illustrates some diffusion coefficients obtained during the study of the drying of certain crop products.We observe that the values of the diffusion coefficient of raffia Vinifera fibres at the beginning of drying are higher than those obtained at the end of the process.Meanwhile, we notice that the raffia Vinifera fibres resulting from the two varieties of stem during the initial phase of drying have values rather close to those of green beans, bamboo, pumpkin and sheets of olives.However, we note that the respective diffusion coefficient of carrot, Okra, ripe banana, flax fibres and Lippia m.M. leaves seems to be slightly higher than that of raffia Vinifera fibres in the two phases.On the contrary, the black tea presents a beach of values comparable to that of raffia Vinifera fibres in their final stage.Finally, we note that the diffusion coefficient of raffia textilis fibres resulting from the sheets is in an interval whose values are rather low compared to those obtained during the two phases within the framework of our study.

Activation energy:
In this study, we were interested only in the activation energy during the beginning of drying (initial phase).The determination of the    activation energy was carried out according to the extraction zone of fibres for each stem of raffia vinifera.
Figure 10 illustrates the representation of the curve of ln (D eff ) according to 1/T of peripheric fibres resulting from the zone close to sheets (PL-4/4-R1) of fresh stem.
We observe that this curve has the form of a line as initially mentioned in the theoretical study.The different curves done in other zones of sampling of the stem present similar plotting.Looking at the fibres resulting from the dry stem, we notice that the curves of ln D eff according to 1/T have the same graph as the previous one.Similar curves were also obtained for the study of the drying kinetics of the (Panchariya et al., 2002), fruits of chempedak (Chien et al., 2008), pumpkin (Kongdej, 2011) and sweet potato (Ngankham and Pandey, 2012).
The parameters of the relation 14 and the correlation coefficient (R 2 ) are represented in Table 6 for the case of fibres coming from the dry stem.A comparative study of the various values of the activation energy in this table shows that the activation energy vary in the interval [4.72-22.86]KJ/mol/K.In addition, we note that this energy is maximum in the zones close to the sheets on the dry stem of raffia vinifera.
The activation energy of fibres resulting from the fresh stem belongs to the interval [4.65 -12.13]KJ/mol/K.The maximum energy in this case is located once more in the zones close to the sheets.
Finally, we note that the maximum value of the activation energy of fibres of raffia resulting from the dry stem is twice the one coming from the fresh stem.
In general, we can say that the activation energy of raffia fibres during drying is very small compared to the others vegetable products presented in Table 7. Nevertheless the products such as carrot, groundnut shell, potato and certain vegetable wastes give values comparable to those obtained in certain zones of the stem of raffia vinifera.This low activation energy for the raffia fibres is due probably to their microstructure.

CONCLUSION
The water dehydration of raffia Vinifera fibres was explored.The fibres were classified in two varieties.The fibres whose evaluated moisture content vary in the interval [12-16] % called dry fibres and those whose values are included in the interval [19-107] % named fresh fibres.Then, the drying kinetics was approached through the drawing of the different curves according to the type of fibres and the three temperatures 60, 70 and 80°C, respectively.All the curves present two phases.One called initial phase describing the beginning of drying and the other named final stage marking the end of the process characterized by a constant mass.From 14 investigated models, it comes out that only "Diffusion approach" and " Verma et al. (1985)" models give correlation coefficients (R 2 ) identical and higher than 0,999.This permits to conclude that these two models describe the behaviour of dry fibres as well as that of fresh one also during drying.In addition, we continued with the determination of the diffusion coefficient of raffia Vinifera fibres according to their nature.For dry raffia fibres, the diffusion coefficients are included in the intervals [6.32×10 -11 -3.00×10 -10 ] m 2 /s and [1.72×10 -11 -5.92×10 -11 ] m 2 /s respectively for the initial phase and final phase along the stem.For these fibres, we noted a growth of the effective diffusion coefficient from the periphery towards the center in any cross-section located along a stem.As for fresh raffia fibres, the effective diffusion coefficients are located in the intervals [1.76×10 -10 -4.47×10 -10 ] m 2 /s and [1.03×10 -11 -1.91×10 -11 ] m 2 /s respectively during the initial and final phases.The values of these various coefficients are comparable to those of some vegetable fibres.Finally, a reflection was carried out on the determination of the activation energy of raffia fibres.The study was carried out only in the initial phase of drying.Consequently, the activation energy of dry and fresh raffia fibres is included respectively in the intervals [4.72 -22.86]KJ/mol/K and [4.65-12.13]KJ/mol/K.These values are low compared to those of other fibres and vegetable products.

Fig. 1 :
Fig. 1: Localization of the zones of sampling of fibres along the stem of raffia vinifera; (a): longitudinal position, (b): crosssection according to a precise longitudinal position Figure4illustrates the drying kinetics of raffia Vinifera fibres coming from the center located at the bottom (PL-1/4-R3) of the dry stem.

Fig. 2 :
Fig. 2: Evolution of the moisture content of fibres of raffia vinifera along the stem known as dries

Fig. 5 :Fig. 7 :
Fig.5: Representation of Diffusion approach model for raffia fibres vinifera resulting from the dry stem located at PL-1/4-R3 at the temperatures 60°C, 70°C and 80°C Summary of the effective diffusion coefficient Deff according to the slope (k) of the regression straight line and its correlation coefficient (R 2 ) of dry fibres resulting from the stem of raffia Initial stage of diffusion -

Fig. 8 :
Fig. 8: Variation of the effective diffusion coefficient of raffia vinifera fibres resulting from a cross-section at the zone PL-2/4 for the dry stem at initial phase

Table 1 :
Parameters of the mathematical models of fibres located at PL-1/4-R3 of the dry stem of raffia vinifera

Table 3 :
Evaluation of the parameters of the two models chosen for dry fibres coming from PL-1/4 of the raffia vinifera stem

Table 6 :
Summary of the parameters (m) of the straight line, the correlation coefficient (R 2 ), the activation energy Ea and the constant D0 of raffia vinifera fibres of the dry stem