Modeling of Water Absorption by Dried Palm Nut Soaked at Room Temperature

Copyright © 2019 by author(s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/ by/4.0) ABSTRACT In cracking palm nuts by application of appropriate impact energy, one of the predominant factors that would enhance the release of either high percentage of whole or split kernels is the percentage level of moisture content in the nuts. The split kernels encourage rancidity of oil since the oily surface of the kernel is exposed to environmental influence. There is therefore need to study the absorption of water in dried palm nuts as a pointer to condition dried nuts to moisture content range that would enhance the production of whole kernels. In this study, dried Dura and Tenera palm nuts varieties were obtained from a palm oil processing mill, classified based on their minor diameter into three size ranges of small, medium and large sizes. These nuts were further dried to bone dry mass followed by immersion of each size range of nuts into different vessels containing water. The rate of water absorption was monitored at 3-hourly intervals. The data generated were analyzed. The result showed that the rate of water absorption per nut unit area had similar curves pattern as the drying curve established for palm nuts. Models for water absorption process involving the dried palm nut was developed based on basic underlying principles and data generated from experimental runs. The models were then validated; and found to be very useful in describing the water absorption process per nut unit area in a given time; and predicting moisture content of bone dry mass of nut soaked in water and kept at room temperature.


INTRODUCTION
When some seeds/nuts are soaked, they aid in the dehulling/ cracking of such seeds (Shaefaei and Masoumi, 2013a). Grains soaked at different conditions were shown to have different water absorption rates and water absorption capacities (Bello et where, = water absorption capacity (db%), = weight of seeds/nuts after immersion (g) and = weight of seeds/nuts before immersion (g).
Various researchers have also carried out works on water absorption of seed during soaking (Turhan et al., 2002;Kashaninejad et al., 2009). The relationship between moisture content of seeds and soaking time has been expressed by different models such as Pilosof-Boquet- Bartholomai (1985), Singh-Kulshrestha (1987) and Kashaninejad et al., (2007) models respectively as: where total moisture uptake at time, t ( g per 100 g solid), A = water absorption capacity ( g per g dry solid), B = half-life (hour), = initial moisture content (g per g dry basis), M = moisture content at time, t (g per g dry solid) and = water absorption rate constant ( per hour), = average moisture content at time, t ( kg H2O per kg dry matter), = equilibrium moisture content ( kg H2O per kg dry matter) , = initial moisture content (kg H2O per kg dry matter), k = rate constant and n = number of time interval in an experiment.
Many theoretical and empirical approaches have been employed and in most occasions the empirical models were preferred because of their relative ease of use (Shafaei and Masoumi, 2014b and c). In the study of water absorption in rice, it has been shown that the proper model for predicting the behaviour of water uptake was 'Peleg' model (Jideani and Mpotokwana, 2009;Montanuci et al., 2013) and can also be given as:
In (5), ''±'' becomes ''+'' if the process is absorption or adsorption and ''_'' if the process is drying or desorption (Corzo et al., 2012). The rate of sorption ( ) can be gotten from the first derivative of the Peleg equation: = = The Peleg rate constant, relates to sorption rate at the beginning ( ), at t = to: The Peleg coefficient constant, k2 relates to maximum (or minimum) possible moisture content. As t = , (5) gives the relationship between equilibrium moisture content (Me) and k2. = = The Peleg model has been used to describe sorption processes in various food materials. Oliveira In evaluating water absorption by dried palm nut, it is necessary to standardize the rate of absorption by determining the rate with respect to unit area of the nut since it has various sizes irrespective of the variety. Hence, the developed model would be useful in describing the rate of water absorption process per unit area of the dried palm nut in a given time during soaking at room temperature, and by extension used to predict moisture content of this soaked nut Where, wb denotes wet basis and db denotes dry basis. For absorption, the moisture content (MC) based on (9) and (10) can be expressed as: % MC (db) = 100 (11) % MC (wb) = 100 (12) Equations (11) and (12) can also be written respectively as: The negative sign of the moisture content indicates absorption while positive sign indicates desorption. The rate of absorption is suggested to depend on among any other possible things the following state of the system: a. The size of the material, b. The material thickness of the shell/skin, c. The nature of the material ( plastic, porous, etc) shell/skin, d. The temperature of the medium (liquid) that is used for absorption.
The rate of absorption ( ) of water can therefore be defined as: = K ƒ ( state of the system) Where, K is absorption rate constant. Based on general material balance: Accumulation = input -output + generation (16) For absorption of water, the generation is zero, while there is accumulation of water as a result of soaking of the dried nuts in water.
Let's denote input as (mass of nut at bone dry); and output as (mass of nut at any time t during absorption). + (17) Where, = mass of water absorbed From (17) = (18) = input -output (19) Since palm nuts have various sizes irrespective of its variety, it is necessary to standardize the water absorption with respect to unit area of the material (nut). Hence, (18) and (19) Where, = the area of the nut (mm2) It is assumed that the water absorption per unit area per unit time of absorption is proportional to the change in mass of the nut per unit area per unit time; and can now be written based on (20) as: The area ( ) of nut is obtained as: Where, = Volume of nut (mm3) and Let's denote the initial mass of nut per unit area (dry bone mass per unit area) as: = (25) Let's denote the final mass of nut per unit area at a given time during soaking as: = (26) Note that for absorption, the initial mass is the dry bone mass per unit area; as against for drying, the initial mass in this context is the mass per unit area at a given time.
Equations (21), (24), (25) and (26) can also be written as: Where, = water absorption proportionality constant Where, K = water absorption rate constant. Equation But, from (18) The power to which the water absorption is raised is not known, hence denoted as n and can be expressed based on (35) as: = From (15) and (35), rate of water absorption ( ) is given as: Thus, (36) and (37) can be re-written as: The order of absorption is necessary to be known; hence (38) can be re-written as: = log (-K) n log (39) A plot of log against log gives the slope as n and intercept as log (-K) From (36) and (38) = K dt (40) Subscript i= initial and f= final.
is the mass of water absorbed per unit area of the nut in a given time; and ranges from minimum to maximum possible moisture content of the nut.
But, from (34), the water absorbed per unit area of the nut is proportional to the difference between the nut mass per unit area at dry bone and mass per unit area at any time, t during absorption. This is expressed mathematically as: α Hence, from (44) = Q Where, Q is the proportionality constant that relates to the moisture content that is possible in the nut at a given time during absorption. A plot of against would give a slope equal Q Based on (13)

METHOD
The Dura and the Tenera varieties of palm nut were obtained from an oil processing mill and moisture content determined. For each variety, grizzly screen was used to classify the nuts, based on nut minor axis ), into three size ranges namely: small size range , medium size range ) and large size range 17 mm). Exactly three hundred nuts per size range per variety were randomly selected; and re-dried in a hot air convection oven at 105 0 C to dry bone mass (ASAE, 2000; Aviara et al., 2005). The nuts were removed, kept in desiccators for five minutes and thereafter packaged per size range per variety into six polyethene bags. For a particular size range, 10 nuts were randomly picked from the polyethene bags, weighed using electronic weighing balance as , axial dimensions taken using vernier calipers, numbered with permanent marker and then mixed together to have 20 nuts as a fair representation of mixed nut variety for that size range to be used for each experimental run. Each experiment was carried out in three replicates, and total number of nuts used was 1800. To study the water absorption per unit area of the dried palm nuts, each size range of the mixed nut variety was immersed respectively into three different vessels containing water at room temperature. At 3 hourly interval, twenty nuts were removed, weighed and readings recorded as . The moisture content of the nuts at the 3-hourly intervals was computed. Models for the rate of absorption per unit area and percentage moisture content were developed. The goodness of fit for the models carried out using statistical computation and analysis ( ). The models were tested using different sets of nuts.

RESULTS AND DISCUSSION
The data generated from the study of water absorption per unit area of dried palm nuts at a given time when soaked is presented in Fig. (1).

Fig. 1: A plot of amount of water absorbed per unit area against soaking time.
From Fig. (1), three (3) regimes are observed, namely: rapid intake, gradual intake and fairly constant intake of water regimes. The rapid intake of water by the nuts occurred between 0 and 3 hours. At this period, water diffusion rate per unit area of the nuts was faster and primarily caused by concentration gradient. The gradient tends to move the water molecules to equalize the nut inner concentration. As the soaking time increased, the spores in the shell are to be filled with water. This results in a gradual rate of water intake per unit area between 3 -12 hours. Beyond this period, almost a fairly constant amount of water intake was observed for the nuts. This might be as a result of the shell spores being saturated with water up to 0.0021 g H20 per mm2 per hr at 21 hours. However, the bulk sample data were computed and terminated at 21 hours since there were no data for the small size nut beyond this time due to reaching maximum possible water that can be absorbed by these nuts size.
A plot of the rate of water absorption against time of absorption is presented in Fig.(2). From Fig.(2), three (3) regimes are predominant, namely: rapid rising, rapid falling and fairly constant rate regimes. However, it was observed that the rate of water absorption per unit area increased rapidly between 0 -3 hours.
Between 3 -9 hours, the bulk nut samples showed a rapid falling rate period. This might be due to slow rate of water diffusion from the shell periphery to saturate the interior part of the shell. Between 9 -21 hours, there was a fairly constant rate of water absorption of 0.0001 g H2O per mm2 per hr. At this point, the nuts might have reached moisture saturation point. However, it is suggested that the nut absorption capacity might be influenced among other things by its size, area, and thickness. Generally, it was observed that nuts water absorption rate per unit area curves resemble that of drying rate curves. It may therefore, be suggested that for drying and absorption, (46) can be written as: = (51) Where negative sign is for desorption/drying and positive sign for absorption processes.
More so, a plot of % moisture content (wb) versus time of absorption was carried out as presented in Fig. (3). Where, K= 4.72 × and n = 1.244 Usually, based on Arrhenius Equation, the K values may vary with temperature of the soaking medium. However, a plot of experimental and predicted values of rate of water absorbed per unit area of nut in a given time at room temperature using (52) was carried out on the bulk samples as shown in Fig.(4); and other statistical analysis result are presented in Table 1.   (48) using the obtained values of K, n and Q is given as: The plot of predicted and experimental values of the moisture content for the bulk sample is given in Fig. (5) and statistical analysis for goodness of fit is presented in Table 2.  Generally, from Fig. (4) and (5), the line for the slope equal one is the one for which predicted values is expected to be equal to experimental values. From Tables 1 and 2, the correlation coefficient, r may be approximated to R 2 . The values of R 2 were higher than , MBE and RMSE. These are characteristics of good quality fit. To validate the model for rate of water absorption per unit area of dried palm nut, (52) was used in predicting the rate of water absorption per unit area of the nut in a given time at room temperature using different sets of nuts; while (53) was used for % moisture content estimation. The results are presented in Table 3. (Standard deviation for (52) and (53) are 5.9 × 10 -6 and 0.179 respectively) (Standard error for (52) and (53) are 2.1× 10 -6 and 0.063 respectively)

PRACTICAL APPLICATION
The models developed were tested and found to be useful in predicting the range of moisture content suitable to crack dried nuts to release high percentage of whole kernels when appropriate impact energy is applied.

CONCLUSION
The models (48), (50) and (51) via (52) and (53) could be used to describe the water absorption process per unit area of nut in a given time; and also in predicting moisture content of bone dry bone mass of nut in a given time soaked in water at room temperature.