my project.pdf

8/14/2019 my project.pdf

1/35

1

CHAPTER ONE

1.0 INTRODUCTION

1.1 BACKGROUND OF STUDYIn industries, water absorption by agricultural products such as grains, nuts, seeds etc. is

an important operation in food processing such as rice parboiling (Engels et al., 1986),

fermentation of soybean paste miso (Minamiyama et al., 2003) and fermented maize products

such as ogi and kenkey (FAO, 1992). The soaking process is basically an imitation of nature

since the natural germination of these crops is as a result of the moisture absorbed by plant roots

when it rains.

The water uptake of maize grains is mainly expressed as a percentage increase in weight

of the dry maize. The soaking times can vary from a couple of hours to 24 h depending on the

hardness and density of the seed.

Water absorption in foods follows the mechanism of diffusion. But, variations occur in

different grains, nuts seeds etc. which are functions of the food compositions such as protein, fat

and oils, carbohydrate contents for example, protein which is hydrophilic expected to absorb

water than lipids which are hydrophobic. Hence foods with higher protein content should have

higher absorption capacity than others with higher lipids content (Gen et al., 1998-2001). Thus,

the water absorption rate and characteristics shown by maize may vary in different maize

varieties and other influential factors such as temperature which also determine the absorption

rate by maize grains.

To predict the water uptake of maize grains during soaking, a tool is needed to replace

the laboratory experiment. A mathematical model is one tool that can serve this purpose. If


2/35

2

adequate and proper information are provided, simulations of models can provide a forecast of

future states of soaking process.

Considerable research was reported in the literature to develop an understanding of the

mechanism of moisture movement in natural products, but findings are not yet conclusive (Bello

et al., 2009). This study sought to access and models the effect of temperature on six varieties of

maize during soaking.

1.2Aim and objectives

1.2.1 AimThe aim of this research is to develop a mathematical model to predict the effect of

temperature on the water uptake of six varieties of maize during soaking.

1.2.2 ObjectivesTo achieve the aim stated above, the following specific objectives were followed:

Development of a mathematical model representing water absorption of maize. Determination of the effect of temperature and variety on water absorption of

maize.

Determination of the applicability of Ficks equation in modeling of waterabsorption of maize.

1.3 Significance of studyAbsorption processes is important in the processing operations undergone in the process

industries where wet milling is usually adopted for industrial products like starch and corn-oil.


3/35

3

Therefore there is need for the understanding of the mechanism involved in this soaking process

as it governs the quality of the final products.

1.4 Scope of studyA mathematical model is to be developed which represents water uptake of six varieties of maize

and the effect of temperature on the absorption rate.


4/35

4

CHAPTER TWO

2.0 LITERATURE REVIEW

2.1 A Brief Overview of Maize

Maize (zea mays L.), a crop known in some English speaking countries as corn (meaning

grain) is a large grain cultivated in different countries such as Nigeria, Pakistan, India,

Mesoamerica etc. the leafy stalk produces ears which contain the grain, which are seeds called

kernels. Technically a grain, maize kernels are important multipurpose cereal crop which are

used in cooking as food, fodder, fuel and in the manufacturing of industrial products (Clark

1977; Lui et al. 2001). The sugar-rich varieties called sweet corn are usually grown for human

consumption, while the field corn varieties are used for animal feed and as chemical feedstock.

In the United States, it is used for producing corn ethanol. As food grain, it plays a significant

role throughout the world most especially in countries like Nigeria, Pakistan, India etc. its flour

is used in the preparation of nutritious and tasty meals such as snacks, cakes, bread, and as a

source of dextrose. Its bran has been found very effective in decreasing faecal transit times

(Bressani and Elias, 1983). In order to make maize suitable for food and industrial product like

starch, corn-oil, and animal feeds, wet milling is desirable (Burge and Dunsing, 1989).

However, to make it fit for human consumption, it must be cooked. During cooking heat

gelatinizes starch making it susceptible to starch dissociating enzymes of digestive system.

Starch is used by paper and textiles industries in sizing, surface coating and adhesive application.

Special starch is used in oil research for drilling mud which cools superheated drills. It is also

used as anti-caking mould release, dusting powder and thickening agent (Fasasi et al. 2005).


5/35

5

Maize can be processed into wide varieties of foods and beverages which can be

consumed as breakfast meals. For example in Nigeria, it is used as food such as ogi which is

commonly fed to infants as a weaning food. It is prepared by soaking maize in water for 1 day

(24 h) after which it is washed and milled. Water is then added to the milled dough and left for

another 24 h for fermentation to occur. The fermented dough is then sieved to separate the liquid

and the slurry which is left behind is allowed to settle. The slurry can be used to make ogi by

mixing a portion of it with boiling water and other ingredients to sweeten it such as sugar, milk

etc. before consumption.

2.2 The anatomy of maize

The maize kernel is classified botanically as a caryopsis. In consequences it is a fruit

composed by one seed and the remnants of the seed coat and nucleus and is permanently

enclosed in a pericarp. The kernel is attached to the air by the pedicel which remains attached to

the base of the kernel.


6/35

6

Fig. 2.1 Anatomy of Maize Seed

Source: http://www.masish.uab.cat/masish/


7/35

7

Pericarp

The pericarp consists in the transformed ovary wall that covers the seed and act as a

protection for the embryo and endosperm.

Endosperm

The endosperm forms most of the volume and weight of the kernel. It can be divided into

three part; starchy endosperm, aleurone layer and basal transfer layer.

Embryo

The embryo is located in one face of the basal part of the kernel. Mature embryo is

composed by a central embryo axis and the scutellum.

2.3 Different varieties of corn

Different varieties of maize exist, six of which are:

Dent corn: this has kernels which have an indentation on their tops and contains soft,

starchy corn under their dented tops.

Flint corn: this is also known as Indian corn. They have very hard kernels that when

dried are tough to grind. Different colours dominate the kernels in each cob and these are

usually dark brown, orange, and yellow due to open pollination. They are used for

decorative purposes when harvested.

Flour corn: this has soft kernels that are very easy to grind


8/35

8

Pop corn: this kernels burst open when heated. They are harvested for these kernels that

are removed from the cob; they are dried and packaged for popping.

Pod corn: this is not well known and is seldom grown today, they produce tiny husks on

which grow multicoloured kernels. It is only of ornamental significance.

Sweet corn: this is the kind of corn in which most people are familiar with, it differs

from the other types of corn because its kernels lack the ability to convert sugar to starch,

and hence it retains its sweet taste for a short period of time after it is harvested.


9/35

9

Fig. 2.2 maize cob

Source: http://www.masish.uab.cat/masish/


10/35

10

2.4 Health benefits of maize

Maize is a high nutritional food which is rich in dietary fibers. It delivers several

benefits to consumers which include controlling diabetes, prevention of heart ailments, lowering

of hypertension and prevention of neural-tube defects at birth. Corn or maize is one of the most

popular cereals in the world and provides health benefit not only in the amount of calories for

metabolism, but also rich source of vitamins A, B, C and other minerals. Its high fiber content

helps in preventing digestive ailments such as constipation as well as colorectal cancer. It also

consists of anti-oxidants which act as anti-cancer agents and prevent Alzheimers.

The following are some of the benefits of maize:

Rich Source of Calories: corn is a rich source of calories and forms a part of the dietsamong many populations. The calorific content of corn is 342 calories per 100grams,

among the highest in cereals (Tripurasundari et al., 1999).

Prevention of Hemorrhoids and Colorectal cancer: the fiber content of corn is 18.4% ofthe daily recommended amount. This aids in alleviating digestive problems such as

constipation and hemorrhoids, as well as lowering the risk of colon cancer

(Tripurasundari et al., 1999).

Rich Source of Vitamins: corn is a rich source of vitamin B constituents, especiallyThiamin and Niacin. Thiamin is essential for maintaining nerve health and cognitive

function. Niacin deficiency leads to pellagra (a disease characterized by diarrhea,

dementia and dermatitis) and is commonly observed in malnourished individuals. Corn is

also a good source of pantothenic acid which is a vitamin necessary for carbohydrate as

well as protein and lipid metabolism in the body. Other vitamins are vitamin A which is


11/35

11

essential for maintenance of vision and skin, vitamin E, a natural antioxidant essential for

growth (Tripurasundari et al., 1999).

Provides Necessary Minerals: corn contains abundant phosphorous (which aidsmaintenance of normal growth, bone health and kidney functioning.), magnesium (which

enhance normal heart rate and for bone strength), manganese, zinc, iron and copper.

Trace minerals such as selenium is also present (Tripurasundari et al., 1999).

Antioxidant Property: according to studies carried out at Cornell University, corn is a richsource of antioxidants which fight the cancer causing free radicals. Hence it is effective

in fighting against breast and liver cancer (Rui Hai Lui, 2002)

Cardio Protective Attributes: researchers has made it known that corn oil has proven to beeffective as anti-atherogenic effect on the cholesterol level thereby preventing the risk of

cardiovascular diseases (Tripurasundari et al., 1999).

Prevents Anaemia: The presence of vitamin B12 and folic acid made it effective inpreventing anaemia (Tripurasundari et al., 1999).

Protection against Diabetes and Hypertension: consumption of kernels helps in themanagement of non-insulin dependent diabetes mellitus and also effective against

hypertension due to the presence of phenolic phytochemicals in the whole corn

(Tripurasundari et al., 1999).

Cosmetic Benefits: Corn can be used to soothe skin rashes and irritations; hence it is usedin the manufacture of cosmetics (Tripurasundari et al., 1999).


12/35

12

2.5 Absorption characteristics of agricultural materials

Water absorption may be defined as the amount of water absorbed by a composite

material when immersed in water for a stipulated period of time under specified conditions. All

organic polymeric materials will absorb moisture to some extent resulting in swelling,

dissolving, leaching, plasticizing, and/or hydrolyzing, events which can result in discoloration,

loss of mechanical and electrical properties, lower resistance to heat, and stress cracking.

The amount of water absorbed by seeds during soaking is affected by different factors

such as the initial moisture content, variety of the seeds, soaking duration, and temperature and

acidity level of the water (Hsu et al., 1983; Karapantsios et al., 2002; Laria et al., 2005).

Water absorption is expressed as increase in weight percent.

.2.1

2.6 Water absorption of maize

Water absorption is the most important event for ensuring nutrient supply to the

germinating embryo and to generate energy for the commencement of active germination and

seedling growth (Abebe and Modi, 2009), this is because the water absorbed by the seed

activates enzymes and facilitates metabolism of the stored starch and protein in seed (Kikuchi et

al., 2006). During the process of water uptake the cell wall enlarges and seed coat becomes

softened allowing oxygen diffusion in seed respiration. The amount of water to be absorbed for

seed germination depends on variety or species. The water needed for maize may be around 34%

(McDonald et al., 2006). The rate of absorption increases with increase of temperature in many

crop seeds such as sorghum (Kader and Jutzi, 2002), cowpea (Captso et al., 2008).


13/35

13

The absorption of water in maize occurs based on the mechanism of diffusion mass

transfer. In industries which make use of maize, soaking is a preliminary step in wet milling

processes and this has made soaking to be a center of attention in absorption processes. The

major objective of soaking is usually to soften the grains of the crop, but other beneficial

nutritional effects can be achieved such as the reduction of toxic substances naturally present in

the crop.

However, this same process which has proven to be of benefit also has its own negative

effects such as the loss of nutrients (mostly water soluble ones) through diffusion. The nutrients

which are commonly affected are pigments, sugar, amino acids, water soluble vitamins and

mineral elements (Bressani et al., 1990). Protein which is hydrophilic is the major component

absorbing water in seeds. Therefore, it is expected that seeds with high composition of protein

will possess high absorption capacity and the present of lipids which are hydrophobic in nature

can reduce absorption rate unless the relative humidity of the surrounding is sufficiently high

(Walters and Hill, 1998).

Priming of seed is done by soaking of seed in water for a certain period of time (Harris et

al., 2001b). But the length of soaking time for maize and chickpea seeds under variable

temperatures and soaking conditions have not yet been established. Therefore, it is essential to

know the duration of priming in relation to temperature to devise good priming protocol for

successful establishment of maize and chickpea in the drought-prone areas of Bangladesh. The

present study was therefore, undertaken with a view to determine the soaking duration of maize

seed (BARI hybrid maize-5) and chickpea seed (BARI chola-5) under variable soaking

conditions and temperatures.


14/35

14

Extensive research work has been done on the absorption rate of water by different

grains. As studied by Muthukumarappan and Ganesekaran (1990); Steffe and Singh (1980);

Walton et al.,(1988), diffusion of moisture is generally a function of temperature of the medium.

According to Md. Moshiur et al., (2011). Water absorption rate of maize and chickpea seeds

were influenced significantly by soaking condition. The amount of water absorption was

significantly higher in anaerobic condition than the aerobic condition at each time of

measurement for both in maize and chickpea. This might be related to the fact that the seed under

this condition was kept under water which allowed the water to come in contact with the embryo

and seed surface and thus facilitated the rapid water entry into the seed. On the other hand, in the

present study under aerobic condition seed was placed on the kitchen towel saturated with water.

This system allowed moisture entry into the seed through the portion of seed that was in touch

with the kitchen towel. Also, different temperature level showed significant effect on water

absorption in maize at every hour interval. The present study showed that water absorption

increased with increase in soaking temperature. Similar increase of water absorption with

increase of temperature was reported in different legumes by Seyhan-Gurtas et al., (2001).

2.6.1 Effect of grain composition

Any food grain that is rich in carbohydrate and protein will retain more water than those

rich in fats. This is due to the hydrophobic nature of fats which are repulsive to water while the

carbohydrates proteins absorbed more water as they are hydrophilic (Gen et al., 1998-2001).

2.6.2 Effect of temperature

Not only will temperature affects energy required for absorption of water, it also has

effect on the partial pressure of water vapour of pure water. Hence variation in temperature will

have a significant effect on the absorption rate of water (Oyelade, 1997).


15/35

15

2.7 Importance of soaking

Either for the purpose of feeding or extraction of the oil, most cereals are initially soaked

in water. This hydration of cereals is an important step in the production of traditional food

Nelson et al., (1976). The saturation process makes the extraction of protein easy. The texture

change known to be resulting from the absorption of water during hydration which also affects

softening of the hard pit to facilitate grinding (Lui, 1995). Also, soaking reduces cooking time

and improves product quality (Wang et al., 1979). This is because it is good to reduce cooking

time in order to obtain better quality protein.

However, soaking of agricultural products is time consuming process. For instance, corn

kernels are soaked for about 72 h before milling (Ji et al., 2004.). Soaking grains is very

beneficial to our health, primary because it helps the digestion process. This is because they

consist of enzymes inhibitors which makes it difficult to digest and less nutritious. Grains also

contains phytic acid, which prevents the body from fully absorbing the nutrients like calcium,

magnesium, iron and zinc etc. However, soaking grains will mitigate the effects of these so-

called anti-nutrients. Grains cook faster after they are soaked and will taste fresher and lighter.

Several studies have also demonstrated that legumes require hydration to thoroughly eliminate

anti-nutritional factors, to improve protein digestibility, and to reduce cooking time (Eiienrieder

et al., 1981; Siiva et al., 1981; Kochhar, 1986).

2.8 Modeling of water absorption in maize

Scientific modeling is the process of generating abstract, conceptual, graphical or

mathematical models. Science offers a growing collection of methods, techniques and theory


16/35

16

about all kinds of specialized scientific modeling. Modeling is an essential and inseparable part

of all scientific activity, and many scientific disciplines have their own idea about specific type

of modeling. Modeling involves abstraction, simplification and formalization, in light of

particular method and assumptions, in other to better understanding a particular part or feature of

the word, and to potentially intervene.

A model is a set of mathematical equation describing a bio-chemical system (in this case

plant-atmosphere). Grain model predict the response of grain to temperature and management by

simulating the effect of temperature on soaking. A scientific model seeks to represent empirical

objects, phenomena and physical processes in a logical and objective way. All models are in a

simplified reflection of reality, but despite their inherent falsity, they are nevertheless extremely

useful. Models are typically used when it is either impossible or impractical to create

experimental conditions in which scientist can directly measure outcomes. Direct measurement

of out comes under controlled condition will always be more reliable than modeled estimate of

outcomes.

Mathematical modeling of hydration process is known to be important for the design and

optimization of food process operation. These models can be classified to empirical and

analytical model.

2.8.1 Empirical models

Despite the widespread application of computers and their associated software, empirical

equations are still extensively used in view of their simplicity and ease of computation (Turhan

et al., 2002; Sopade et al., 2007). One of the popular empirical non exponential models used is


17/35

17

the Pelegs equation and some of its parameters are of immense practical significance in

hydration kinetics that applied to weight gain during rehydration (Peleg, 1988; Singh and

Kulshrestha, 1987; Turhan et al., 2002; Sopade et al., 2007; Cunningham et al., 2007). However,

other empirical models such as the Arrhenius model, Singh-Kulshresthas model and Pilosofs

model have also been used.

According to the experiment performed by Kashiri et al., (2010) on sorghum kernel, it

was shown and concluded that Pelegs equation successfully represented the water absorption

behavior of sorghum kernels during the soaking process at different temperatures and could be

used to estimate the moisture content at given soaking time and temperature within the

experimental condition considered. The Peleg constants K1 and K2 were a function of

temperature for sorghum and decreased with increase in soaking temperature.

Also, previous studies by Shittu et al., (2007) on the study of water absorption process

during soaking of African breadfruit seeds at five different temperatures followed on exponential

increase with increase in temperature. The experimental data were fitted to three empirical

equations (Singh-Kulshresthas model, Pilosofs model and Arrhenius model) and all these

equations were able to explain most of the experimental data. The predicted water absorption

capacity (Me) was not significantly affected by temperature changes. In terms of residual

moisture plots, Singh-Kulshresthas model gave a more random distribution at all soaking

temperatures, making it a better fitting equation.

Abbay et al.,(2005) in their research on water absorption of paddy, brown rice and husk

during soaking concluded that rate of moisture gain increased with increase in soaking

temperatures and it was in the second falling rate period. The diffusion coefficients for paddy,


18/35

18

brown rice and husk at different temperatures followed Arrhenius-type relation and the activation

energy was estimated using parameter Ea/R of the Arrhenius equation.

Medeni (2001) in his research on the effect of processing on hydration kinetics of three

wheat products of the same variety compared experimental data obtained with Peleg and

Arrhenius model. He concluded that the application of Pelegs model to analyze wheat soaking

was demonstrated. This study has shown that Pelegs model adequately described the rate of

water absorption of the cereals studied in the soaking temperature range of 20-70oC. the

proposed water absorption model could also be used in engineering calculations.

In the study done by Bello et al.,(2009) on water uptake in a cereal grain during soaking,

the diffusion equation for sphere that swells uniformly during hydration process was derived by

means of landau transformation that transform the problem of diffusion with moving boundary,

into one with fixed domain of integration. The resulting equation, that includes an explicit term

for the rate of swelling of solid boundary, was numerically solved to simulate hydration of maize

assume volume additive for water and solid are taken into consideration the variation of the

diffusion coefficient with moisture concentration.

Although different empirical models of absorption have been developed, ranging from

Pelegs model, Pilosofs model, down to the Arrhenius model. The equivalence of these models

has also been demonstrated by experiments. However, Pelegs model is more used (Quicazan et

al.,2012).

2.8.1.1 Pelegs model

Peleg (1988) proposed a two-parameter sorption equation tested its prediction accuracy

during water adsorption of food products. The original form of Peleg model is as shown below


19/35

19

It follows that the absorption rate at the beginning of soaking process is expressed

subsequently as showing that K1is linked to water absorption rate, R0 (Peleg 1988).

The Peleg capacity constant, K2 relates to maximum attainable moisture content. As

t , the equation below gives the relation between equilibrium

Moisture contents (Me) and K2

Where:

M: % grain moisture content, dry basis

t: soaking time

k1: Pelegs constant (time-1

%-1

w.b)

k2: Pelegs constant (%-1

w.b)

A plot of t/(M-Mo) against time (t) gives a straight line, where k1is the intercept on the

ordinate and k2 is the slope of the line. The rate of hydration (W) is given by:


20/35

20

2.8.1.2 Arrhenius model

The Arrhenius equation is as given below

Where:

E: the activation energy of diffusion

T: absolute temperature

R: gas constant

K1: Arrhenius constant

` K0: Arrhenius constant

2.8.2 Analytical model

Extensive research have been made on absorption models and these are not limited to

empirical models only but also to the areas of analytical mathematical models such as the Ficks

model equation. Ficks second law for diffusion was used by various investigators to describe

water absorption in grains and legumes, accepting the hypothesis that the resistance to water

flow is distributed throughout the material and that this does not swell during process (Becker,

1960; Fan et al., 1965; Engels et al., 1986; Patil, 1988; Thakur and Gupta, 2006). Others

solutions have been formulated considering variable diffusion coefficient but neglecting

shrinking (Chu and Hustrulid, 1968; Aguerre et al., 1985; Dutta et al., 1988; Tolaba et al., 1997;

Landman and Please, 1999).

However, swelling of biological products during soaking takes place simultaneously with

water diffusion and thus may affect the water absorption rate. Hence, a study of the swelling

phenomena is of importance for better understanding of the soaking process. Consideration of


21/35

21

swelling in soaking process is generally difficult because of the lack of information about

swelling velocity and its relationship with water diffusivity. A mathematical expression of Ficks

second law for drying of an infinite slab that shrinks unidirectionally was formulated by Viollaz

and Suarez (1984) assuming volume additivity for water and dry solid. Gekas and Lamberg

(1991) derived relationships for the diffusion coefficient in systems where volume changes occur

during drying. A mathematical model was developed by Hawlader et al.,(1999) to describe heat

and mass transfer within materials undergoing shrinking during drying.

In the study of maize and other seeds, the application of Ficks law to understand the

phenomenon has been tried (Fan et al., 1965; Turhan et al., 2002). Some models consider that

the diffusion coefficient is independent of temperature and that transfer surface resistance is

negligible (Abu-Ghannam and Mckenna, 1997b).

According to the research done by Tolaba et al., (1997), a diffusion equation for

shrinking and non-shrinking sphere was used to describe the isothermal absorption of water in a

spherical solid and this is represented in the equation below:

The differential expansion of the equation above yield

By substituting , we have


22/35

22

And applying LHopital rule to the resulting equation at the centre since it is undefined at this

centre (at z=0), the obtained equation was

Where:

A= local volumetric concentration of water

D= diffusion coefficient (a function of A)

t=time

r= radius of sphere

R= radius at the surface

2.8.2.1 Ficks model

A widely accepted analytical model or mechanism for the diffusion of agricultural

products is the Ficks second equation (Crank, 1975; Bakshi and Singh, 1980;

Muthukumarappan and Gunasekaran, 1994 a-c), and this is described by the equation below

Where:

t= time (sec)

x,y,z =locations within the object at time (t)


23/35

23

M= mass of moisture (g)

D= diffusion coefficient (m2sec

-1)

Based on the literature, the basic principles of absorption processes are unique but what

happens in one food material is very different from another. Soaking common beans has already

been evaluated (Abu-Ghanam and Mckenna, 1997a), as has wheat (Roman-Gutierrez et al., 2002

and other food materials. The transformations that occur in seeds during soaking as time elapse

have been examined by many studies (Bayram et al., 2004; Nashed et al., 2003). Maize is known

to be composed of food contents such as fats, protein, vitamin, fiber, carbohydrate which makes

it a beneficial nutritious source. The water uptake of maize is affected by many factors such as

temperature, diffusion coefficient e.t.c.


24/35

24

CHAPTER THREE

3.0 METHODOLOGY

3.1 MATERIALS

The six maize varieties selected for this study are dent, pod, flint, flour, pop and sweet

corn. Other materials used are desiccators, tongs, moisture dishes, oven, spatula, weighing

balance, weighing boats, funnels, beaker, filter paper, tissue paper, stop watch, distilled water,

thermostatically controlled water bath.

3.2 Determination of moisture contents

It is important to determine the moisture content before carrying out any analysis because

the result of many analyses is more reliable when reported on a dry basis, using moisture content

to convert results to dry basis figures.

The initial moisture content of each maize sample was determined by first preheating the

oven at a temperature of 1300C. The six samples of the maize varieties were weighed (about 10

grams each) and each was placed in the oven and left for about 16 h after which the final weight

of each sample was obtained.

The moisture content was computed thus:

... 3.1


25/35

25

3.3 Determination of weight of maize grain

Since the grain is small and there is variation in grain size within a variety, one or two

seeds cannot be used. Hence in the establishment of weight of grain, 100 grains of maize were

manually counted and weighed in a dish. The average weight of the 100 grains was used to

represent the weight of each grain.

3.4 Determination of water absorption

5 gram samples of each grain variety were weighed into the weighing boats and recorded.

The boats were filled with enough water to cover the grains and the stop watch was started

immediately for 30 mins. The funnel was placed over the beaker and a piece of fluted filter paper

was inserted. After 30 mins, the samples were tipped into the funnel, drained and the spread on a

six layer stack of tissue paper to dry. After 5 mins, each sample were transferred into dry

weighing boats and then re-weighed. This procedure was repeated at different time intervals.

Thus the percentage of water absorbed by the grain over time can be calculated.

3.5 Mathematical Model formulation

Water uptake of maize during soaking was theoretically considered to follow the

principle of diffusion mass transfer and thus was consequently modeled using Ficks law.

3.6 Assumptions

The model development approach for water uptake of maize during soaking depends on

the validation of the following assumptions:

The water flow is considered to be only inward and no reverse or outward flow occurs. The temperature of the system is maintained within 50C of the testing temperature.


26/35

26

Water transport is by molecular transfer only. The process is independent of the structure of maize. The fluid exist in a single phase (liquid only), gas phase is considered negligible.

3.7 Water uptake equation

Fig. 3.1 control volume of maize in x, y plane

From the continuity equation,

{ } . 3.2

Rearranging equation (3.2) gives

X

X

Y

Y


27/35

27

..3.3

Where Considering a two dimensional flow in x, y planes of the control volume

3.4

Where are mass flow rates in x, y directions respectivelyGiven that the volume of the control volume is:

Dividing equation (3.3) by gives:

.3.5

Substituting equation 3.4 in equation 3.5 gives

( )

.. 3.6

Expanding equation (3.6) gives

.3.7

But, by definition of flux , .3.7a

Therefore,

3.7b

3.7c

Where are mass fluxes in x, y directions respectively.Also, by definition of mass concentration ,


28/35

28

..3.7d

Therefore,

.3.7e

Hence, substituting equations 3.7b, 3.7c and 3.7e in 3.7 above yield

.. 3.8

Since water absorbed is by molecular diffusion, it is considered to follow Ficks law equation

given below:

.. 3.9

Combining equations (3.8) and (3.9) gives

..3.10

Hence the water uptake of maize during soaking can be represented as

3.11

. 3.12

Where:

)


29/35

29

3.8 Numerical solution

In simulating the model, implicit finite difference schemes are used to solve the partial

differential equation.

3.8.1 Implicit finite difference formulation

3.8.1.1 Forward difference

Using the forward difference approximation to equation 3.12

.. 3.12a

3.8.1.2 Central difference

. 3.12b

. 3.12c

Substituting equations 3.12a, 3.12b, 3.12c in equation 3.12

. 3.13

Expanding equation 3.13


30/35

30

Let

. 3.15

. 3.16

Substituting equation 3.15 and 3.16 in equation 3.14

( )( ) 3.17

3.8.2 Boundary conditions

In order to investigate the solution of the equation 3.16 above, the boundary conditions in which

Dirchlet condition chosen are stated below:

3.8.2.1 Initial boundary value condition

I.e. for t=0, ,

3.8.2.2 Boundary value condition

I.e. for

And for


31/35

31

Where

L and W are length and width in meters respectively.


32/35

32

REFERENCES

Abhay Kr.; Thakur and A.K. Gupta (2005). Water absorption characteristics of Paddy, Brown

rice and husk during soaking.Journal of Food Engineering75:252-257

Abu-Ghannam, N. and Mckenna, B. (1997). Hydration kinetics of red kidney beans (phaseolus

vulgaris L.).Journal of Food Science62(3):520-523

Aguerre, R.J., Gabitto, J.F., Chirife, J. (1985). Utilization of Fickssecond law for the evaluation

of diffusion coefficient in food process controlled by internal diffusion.Journal of Food

Technology 20:623629.

Becker, H.A, (1960). On the absorption of liquid water by the wheat kernel. Cereal Chemistry

37: 309323.

Bello, M.; Tolaba, M.P.; Auguerre, R.J.; Suarez, C. (2009). Modeling water uptake in cereal

grain during soaking.Journal of Food Engineering97:95-100

Brassani R (1990). Chemistry, technology and nutritive value of maize Tortilla,Food Rev Int. 6:

225-264.

Bressani R, Benavides V, Acevedo E, Oritiz MA (1990). Changes in selected nutrient content

and in protein quality of common and quality protein maize during torilla preparation.

Cereal Chemistry. 6: 515-518.

Bressani R, Elias E (1983). Guidelines for the development of processed and packaged weaning

foods. Food Nutrition Bull.5: 32-36.


33/35

33

Burge RM, Dunsing WJ (1989). Processing and dietary fibre ingredient applications of corn

bran, J. Cereal Foods34: 535-538.

Chu, S.T., Hustrulid, A. (1968). Numerical solution of diffusion equations. Transactions of the

ASAE11:705.

Crank, J. (1975). The mathematics of diffusion (2nd

ed.). Oxford University Press.

Engels, C.; Hendrickx, M.; De samblanx, S.; De Gryze, I. and Tobback, P. (1986). Modeling

water diffusion during long grain rice soaking.Journal of Food Engineering5:55-73.

Fan, L.T., Chung, D.S., Shellenberger, J.A., Chung, D.S. (1965). Comparison on the rates of

absorption of water by corn kernels with and without dissolve sulfur dioxide. Cereal

Chemistry 38:540548.

FAO. (1992). Maize in Human Nutrition.Food and Agriculture Organization of the United

Nations, Rome.

Fasasi OS, Adeyemi IA, Fagbenro OA (2005). Proximate composition and multi-enzyme in vitro

protein digestibility of maize-tilapia flour blends.Journal of Food Technology. 3(3): 342-

345.

Gen, Laddic (1998-2001). Moisture isotherms and conversion of indices used to describe

moisture relations in stored grain (SIRO, stored Grain research Laboratory, Australia).

Hsu, K. H. (1983a). A diffusion model with a concentration-dependent diffusion coefficient for

describing water movement in legumes during soaking.Journal of Food Science, 48(2),

618622, 645.


34/35

34

Hsu, K. H. (1983b). Effect of temperature on water diffusion in soybean. Journal of Food

Science, 48(4), 13641365.

Kang, S.; S.R. Delwiche (2000). Moisture diffusion coefficient of single wheat kernels with

assumed simplified geometrics: analytical approach, Trans. ASAE43:1653-1659

Landman, K.A., Please, C. (1999). Modelling moisture uptake in a cereal grain.IMA Journal of

Mathematics Applied in Business and Industry 10:265287.

Liu, D.H.; W.S. Jiang and W.Q. Hou (2001). Uptake and accumulation of copper by roots of

maize (zea mays L.).Journal of Environmental Science13:228-232

Medeni, M. (2001). Effect of processing of hydration kinetics of three wheat products of the

same variety.Journal of Food Engineering 52:337-341

Minamiyama, Y.; Takemura, S.; Yoshikawa, T. and Okada S. (2003). Fermented grain products,

production, properties and benefits to health.Pathophysiology9:221-227

Muthukumarappan, K. and Gunasekaran, S. (1990). Vapor diffusivity and hygroscopic

expansion of corn kernels during adsorption. Transactions of the ASAE33(5):1637-1641

Oyelade, O.J (1997). Moisture Isotherms of Cowpea flour at 30oC and 40

oC. M.S.C thesis,

Faculty of Technology, University of Ibadan.

Peleg, M. (1988). An empirical model for the description of moisture sorption curves. Journal of

Food Science, 53(4), 12161217, 1219.

Singh, B. P. N., & Kulshrestha, S. P. (1987). Kinetics of water sorption by soybean and

pigeonpea grains.Journal of Food Science, 52(6), 5381541, 1544.


35/35

Viollaz, P.E., Suarez, C. (1984). An equation for diffusion in shrinking or swelling bodies.

Journal of Polymer Science. Polymer Physics Edition22:875879.

Walters, C. and Hill, L.M. (1998). Water sorption isotherms of seed from ultradry experiments.

Seed Science Research. 8:69-73

Wang, L.; Swain, C.W.; Hesseltine, H.D (1994). Health, Hydration of whole soybean affects

solids losses and cooking quality. Journal of Food Agriculture64:1-7

my project.pdf

Documents