**1. Introduction**

Performing experiments on non-Newtonian flows, including grease flows, is considerably time-consuming and costly. Therefore, it is important to numerically analyze the phenomena corresponding to non-Newtonian flows. Numerical approaches can help obtain a variety of data that cannot be determined experimentally. Grease flows can be well defined using Bauer's model; however, owing to the extreme complexity of this model, it is difficult to determine the exact solution as well as approximate solutions for point contact, isothermal, non-Newtonian elastohydrodynamic lubrication (EHL) analyses. Therefore, it is convenient that the non-Newtonian EHL calculation can be executed within a reasonable calculation time and without large modification to the usual Newtonian EHL calculation procedure. Kochi et al. [1] performed experiments on grease under soft EHL conditions and measured the film thickness and traction forces. The method proposed in the present study can be applied to the grease considered in Kochi et al. [1] to validate this theoretical approach.

#### *1.1. Classification of Calculation Methods*

As shown in Figure 1, the Z-direction is considered to be the film thickness direction. The flow velocities along the X- and Y-directions are denoted by *u* and *v*, respectively, which are functions of *x*, *y*, and *z*; however, when considering only *z* dependency, the velocities can be expressed as *u*(*z*) and *v*(*z*), respectively. The numerical methods for isothermal,

**Citation:** Kakoi, K. Formulation to Calculate Isothermal, Non-Newtonian Elastohydrodynamic Lubrication Problems Using a Pressure Gradient Coordinate System and Its Verification by an Experimental Grease. *Lubricants* **2021**, *9*, 56. https://doi.org/10.3390/ lubricants9050056

Received: 16 February 2021 Accepted: 11 May 2021 Published: 14 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

non-Newtonian EHL analyses can be classified in terms of the accuracy of *u*(*z*) and *v*(*z*), as follows:

Method 1: Exact solution of *u*(*z*) and *v*(*z*) is obtained. Method 2: Approximate solution of *u*(*z*) and *v*(*z*) is obtained.

**Figure 1.** Global coordinate system O, X, Y, Z.

Method 2 can be further classified in terms of the employed coordinate system. Method 2-A: Local X-direction is the sliding direction. Method2-B:LocalX-directionisthedirectionofthepressuregradient.


**1.1 A brief description of sol-gel synthesis process**

The sol-gel technology is a wet-chemical process where the principal chemical aspect is the transformation of compounds, known as precursors, that contain Si-OR and Si-OH to form stable colloidal particle suspensions known as sol [8]. The sol can be applied on the substrates by different deposition techniques and then sintered to obtain a coating. During the aging step, a chemical transformation of the sol occurs leading to a rigid network, resulting in a gel [9]. Generally, inorganic or organicinorganic sols are obtained via hydrolysis and polycondensation reactions between silicon alkoxides (Si(OR)4) such as: tetramethoxysilane (TMOS) or tetraethoxysilane (TEOS) and organoalkoxysilanes R′-Si (OR)n-1; where R′ is the organic functional group linked to Si through a nonhydrolyzable covalent bond. During the hydrolysis stage, alkoxide groups are replaced with hydroxyl groups. Once the hydrolysis reaction has initiated, the condensation reaction occurs simultaneously. In this stage, the hydroxyl group and residual alkoxyl group react to form a three-dimensional Si∙O∙Si network [10]. From the reaction pathway point of view, two different Si∙O∙Si formation mechanisms can take place regarding if the reaction is performed under acidic or basic conditions. Therefore, the morphology and the structure of the resulting network strongly depend on the pH of the reaction.

Under acidic conditions [11], the oxygen atom of Si∙O∙R group is protonated in the first step to form a good leaving group. The central silicon atom turns to be more electrophilic and thus more susceptible to react by water to form Si∙OH group (**Figure 1(1)**). An equilibrium condition is established between silanol groups and H+ ions, resulting in positively charged species Si∙OH2 + that interact with a silanol group to form Si∙O∙Si bonds (**Figure 1(2)**). In this case, the polymerization rate is directly proportional to the H+ concentration. Therefore, a large number of monomers or small oligomers with reactive Si∙OH groups are simultaneously obtained. The hydrolysis step reaction is favored, and the condensation step reaction is the ratedetermining step. It was reported that the positively charged species, Si∙OH2 + , react preferentially with the less acidic silanols (silanols attached to the least condensed (Si∙O∙Si) end groups), giving to chain-like networks [13].

Under basic conditions [14], the hydrolysis reaction occurs directly by nucleophilic attack of OH− to the silicon atom to form Si∙OH bonds. In this case, deprotonated silanol (Si∙O− ) anion is formed and then it gets condensed with a silanol group. The condensation reaction is favored, and the hydrolysis reaction is the rate-determining

*The Role of Silane Sol-Gel Coatings on the Corrosion Protection of Magnesium Alloys DOI: http://dx.doi.org/10.5772/intechopen.102085*

### **Figure 1.**

*Mechanism of acid-catalyzed sol-gel process. (1) Hydrolysis mechanism and (2) Condensation mechanism reactions. Image adapted from reference [12].*

step. The hydrolyzed species are immediately consumed because of the fast condensation. Due to the nucleophilic nature of the deprotonated silanol, the Si∙O− preferentially attacks the more acidic silanol (silanols attached to the highest condensed (Si∙O∙Si) end groups), leading to the formation of branched and highly condensed clusters.

## **1.2 Deposition methods and curing process of silane sol-gel coatings**

A typical route of formation of silane sol-gel coating is described as the following process: synthesis of sol-gel > deposition > heat treatment. A sol-gel coating can be applied to Mg metallic substrates through various techniques, such as dip-coating, spin-coating, spraying, and electrodeposition, among others. However, dipping and spinning techniques are the two most used ones, especially for flat surfaces [10]. In the case of complex shapes, uniform coating can be obtained by electro-phoretic deposition method (EPD) [15].

By dip-coating, the surface treatment is attained by immersing the substrate into the sol-gel solution. The silanol groups Si∙OH interact spontaneously with the Mg∙OH groups that existed on the alloy surface via Van der Waals interactions. Upon the heat treatment, the Si∙OH and Mg∙OH bonds are attached firmly via a condensation reaction producing metallo-siloxane (Mg∙O∙Si) covalent bonds (**Figure 2**), and the remaining Si∙OH groups of the deposited sol condense and form Si∙O∙Si bonds [16].

By controlling the curing temperature, the control of pore volume and size and mechanical strength can be achieved. High temperatures (more than 200°C) are normally used to cure inorganic sol-gel coatings and lower temperatures (less than 200°C) for drying/curing organic-inorganic sol-gel coatings [10]. Depending on

**Figure 2.** *Schematic representation of metallo-siloxane covalent bond formation.* the sol-gel precursors used, an optimal curing temperature should be defined since an inaccurate temperature could result in a decrement of the corrosion resistance properties of the coating and/or on the mechanical properties of the substrates. For instance, room temperature cured sol-gel coatings exhibit crack-free morphology, but a higher water sensitivity compared to coatings cured at a higher temperature. On the other hand, an increment of the curing temperature can lead to cracked coatings due to the stresses that appear during the sintering process [12]. A relatively new approach to densify sol-gel coatings is to use UV radiation [17]. Sol-gel films treated by UV radiation at room temperature can form denser sol-gel coatings able to improve the corrosion resistance of alloys.

## **1.3 Corrosion behavior of Mg alloys in aqueous environment**

The poor corrosion resistance of Mg alloys can be mainly attributed to its high electronegative potential and the poorly protective properties of the quasi-passive oxide/hydroxide layer formed upon Mg. Generally, when the Mg alloys corrode in aqueous electrolyte, the metal changes its oxidation state, forms ionic species, and releases electrons. To maintain electroneutrality, the generated electrons must be consumed by other species. Therefore, the anodic reaction must be accompanied by a reduction reaction, where a molecule, ion, or atom gains electrons. In aqueous solution, water reduction is the dominant cathodic reaction. **Figure 3(1)** illustrates the anodic and cathodic reactions and the overall reaction that takes place during the corrosion of Mg in aqueous environment. The presence of chloride ions in the aqueous solution typically leads to accelerated corrosion processes (**Figure 3(1)**). Mg(OH)2 can convert to MgCl2, with higher solubility, promoting the dissolution of the Mg alloy [18].

On the other hand, the corrosive environment in the human body has a solution consisting of 0.14 M NaCl and other inorganic species, such as Ca2+, PO4 3−, and HCO3 − . In this case, the presence of phosphates and carbonates promotes the formation of partially protective corrosion product layers [19]. It is clear that corrosion products depend on the type of the electrolyte. These corrosion products not only affect the corrosion rate but can also provide different protection properties to the substrate. **Figure 3(2)** shows a schematic representation of possible interactions between corrosion products of Mg alloy surface on a biological environment.

The deposition of a silane coating could control the corrosion of Mg alloys, although it could dissolve in contact with water due to the hydrolysis of the polysiloxane (Si∙O∙Si) network [20] that results in the release of silicic acid (Si(OH)4), which can be expressed as follows [21]:

$$\text{SiO}\_2\text{(s)} + 2\text{H}\_2\text{O} \xrightarrow{\text{s}} \text{Si(OH)}\_4 \tag{1}$$

It is important to determine the corrosion rate to explain the corrosion behavior and provide models that predict the kinetics of the corrosion in an engineering context. The most widely used technique for exploring the corrosion behavior of a coated Mg alloy involves immersing the samples in a corrosive solution, since the corrosion performance is faster than atmospheric corrosion tests [19]. To study the corrosion performance of coated Mg alloys in aqueous solution, a wide range of tests are used [2]. These tests are divided into two large groups: electrochemical and nonelectrochemical

*The Role of Silane Sol-Gel Coatings on the Corrosion Protection of Magnesium Alloys DOI: http://dx.doi.org/10.5772/intechopen.102085*

### **Figure 3.**

*Schematic representation of reactions that take place between Mg alloy surface and (1) NaCl aqueous solution and (2) biological environment (reprinted from Ref. [19], Elsevier).*

tests [22]. The most common electrochemical and nonelectrochemical methods used are mentioned below.

## *1.3.1 Electrochemical techniques*

These methods are important and rapid tools for assessing the corrosion of coated Mg alloys. Between the electrochemical techniques, the most used are Potentiodynamic polarization (PDP) and electrochemical impedance spectroscopy (EIS).

## *1.3.2 Nonelectrochemical techniques*

The most common nonelectrochemical methods used for Mg corrosion research are weight loss measurements, hydrogen collection, and pH measurements.

The electrochemical techniques for exploring the corrosion behavior of coated Mg alloys can be used independently or simultaneously with the nonelectrochemical techniques. The principles of each technique and an overview of the main advantages and limitations of different techniques were provided by Durán et al. [5]. A recent review by Kirkland et al. [23] considers the methodologies used to study the corrosion of biodegradable Mg implant materials.


*Edited by Pooneh Saidi Bidokhti*

The Monte Carlo method is a numerical technique to model the probability of all possible outcomes in a process that cannot easily be predicted due to the interference of random variables. It is a technique used to understand the impact of risk, uncertainty, and ambiguity in forecasting models. However, this technique is complicated by the amount of computer time required to achieve sufficient precision in the simulations and evaluate their accuracy. This book discusses the general principles of the Monte Carlo method with an emphasis on techniques to decrease simulation time and increase accuracy.

Published in London, UK © 2019 IntechOpen © agsandrew / iStock

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

Theory, Application, and

Implementation of Monte

Carlo Method in Science and

Technology

*Edited by Pooneh Saidi Bidokhti*


Estimating Predictiveness

Given the estimate for prediction loss, we estimate predictiveness I[*Z*, →*M X* ] with the following method. We use the encoder network that computes the code vector *h* (24) to also estimate the marginal probability of the past observation sequence, *Pη*( *M*← *X* ). *Pη* has support over sequences of length *M*. Similar to the decoder *ψ*, we use the vector representations *ft* ∈ R*k* computed by the LSTM encoder after processing *X*−*M*...*t* for *t* = −*M*,..., −1, and then compute predictions using the softmax rule

$$P\_{\mathbb{H}}(X\_{l} = s\_{i} | X\_{1...t-1}, Z) \propto \exp((\mathcal{W}\_{o'} f\_{l})\_{i}),\tag{28}$$

where *Wo* ∈ R|*S*|×*k* is another parameter matrix.

Because we consider stationary processes, we have that the cross-entropy under *Pη* of →*M X* is equal to the cross-entropy of *M*← *X* under the same encoding distribution: E*XM*← *X* →*M X* log *Pη*(→*MX* ) = −E*XM*← *X* →*M X* log *Pη*(*M*←*X* ). Using this observation, we estimate the predictiveness I[*Z*, →*MX* ] = H[→*MX* ] − H[ →*M X* |*Z*] by the difference between the corresponding cross-entropies on the test set [37]:

$$-\mathbb{E}\_{X\_{M\_{\stackrel{M\_{\tau}}}{X}\stackrel{\rightarrow}{\rightarrow}^{M}}}\left[\log P\_{\eta}\left(\stackrel{\rightarrow}{X}{X}\right) - \log P\_{\emptyset}\left(\stackrel{\rightarrow}{X}^{M}|Z\right)\right],\tag{29}$$

which we approximate using Monte Carlo sampling on the test set as in (26) and (27).

In order to optimize parameters for estimation of *Pη*, we add the cross-entropy term −E*XM*← *X* →*M X* log *Pη*(*M*←*X* ) to the PRD objective (19) during optimization, so that the full training objective comes out to:

$$\min\_{\boldsymbol{\Phi}, \boldsymbol{\Phi}, \boldsymbol{\Phi}, \boldsymbol{\eta}} \left[ \mathbb{E}\_{\begin{subarray}{c} M \leftarrow \boldsymbol{\Delta} \\ \boldsymbol{X} \end{subarray}} \left[ -\mathbb{E}\_{\begin{subarray}{c} Z \sim \boldsymbol{\rho} \left( \boldsymbol{X} \right) \end{subarray}} \left[ \log P\_{\boldsymbol{\theta}} \left( \boldsymbol{X} \, \middle| \, \boldsymbol{Z} \right) \right] + \boldsymbol{\lambda} \cdot \text{D}\_{\mathbf{KL}} \left[ \left( P\_{\boldsymbol{\theta}} (\boldsymbol{Z} \, \middle| \, \boldsymbol{X} \, \middle| \, \boldsymbol{\eta} (\boldsymbol{Z}) \right) \right] - \log P\_{\boldsymbol{\eta}} (\boldsymbol{X} \, \middle| \, \boldsymbol{X} \right) \right]. \tag{30}$$

Again, by Gibbs' inequality and Propositions 1 and 2, this is minimized when *Pη* represents the true distribution over length-*M* blocks *P*( *M*← *X* ), *Pφ*(*Z*| *M*← *X* ) describes an optimal code for the given *λ*, *q* is its marginal distribution, and *Pψ*( →*M X* |*Z*) is the Bayes-optimal decoder. For approximate solutions to this augmented objective, the inequalities (22) and (23) will also remain true due to Propositions 1 and 2.


**3. Fish and fisheries of tropical lakes (L. Victoria and L. Tana)**

Fishes and fisheries of Lake Victoria and Lake Tana will be reported here, as natural examples of tropical large water bodies of the Nile basin. The combined surface area of these lakes is

quantity of fish landed in Lake Victoria fisheries reaching a total of 500,000 tons per year. This figure was in decline by the late 1990's and early 2000's when it reached a total of 340,000 ton per year (Fig. 2). This reduction was mainly due to the overexploitation of the fisheries resources, and to the increase in the number of motorized boats, and to the Nile perch processing industries. Reportedly the number of fishing boats in the lake increased from 12,000 boats during 1982 to 22,700 boats during 1990 and more than 52,000 boats in 2002 [6]. In recent years, as fishing pressure on the Nile perch has intensified, there are signs of recovery in at least some of the former haplochromine species that were thought to be extinct from the lake

**Total Fish Landing of Lake Victoria during the period 1977-2002**

1992

**Figure 2.** Variation of the total fish landing of Lake Victoria during the period 1977-2002 [8]

the ratios 3.75, 3.0 and 1.75 for the three fishes, respectively.

2000

**Year**

Extracted data from the results obtained by [6], from the ECOPATH prediction model have revealed that the stock biomass (tons km-2) of the fishes (Nile perch, tilapia and sardine) are different in the waters of Lake Victoria shared by different countries. The same is also true for the ratios of production per biomass except for the sardine species (Fig. 3). The data also shows that the Ugandan lake areas have lowest stock of Nile perch biomass, while the highest stocks are found in the Kenyan lake areas. Interestingly, the Ugandan stock biomass of tilapia is the highest while the Tanzanian stocks are the lowest. The sardine stock biomass is higher in the Kenyan lake areas followed by the Tanzanian, with the lowest recorded in the Ugandan lake areas (Fig. 3). An overall estimate shows that the average stock biomass for the whole of Lake Victoria is 4.59 tons km-2 for the Nile perch, 3.27 tons km-2 for the sardine and 2.36 tons km-2 for the tilapia. The same trend is observed for the estimate of production/biomass year-1, giving

2002

The Nile Fishes and Fisheries http://dx.doi.org/10.5772/57381 353

environment [9], [10], [5].

0

1977

Kenya Uganda Tanzania

50,000

100,000

150,000

**Tons/year**

200,000

250,000

**Table 1.** National areas within the Nile Basin "Source [14]"

75% of the total of the five tropical lakes of the Nile basin. They are also important because they lie at the source of both the White Nile and the Blue Nile, respectively. Their main fishes are representative of the fish species living in the other lakes (Edward, Albert and Kyoga). Details on the other tropical lakes (Edward, Albert, Kyoga, and George) fish fauna and its fisheries are found elsewhere [4], [5].

#### **3.1. Lake Victoria (Kenya, Tanzania and Uganda)**

Lake Victoria is the largest natural lake in Africa (Fig. 1) and the second largest lake in the world after Lake Superior (USA-Canada). It has a surface area of 68,800 km2 and a very large catchment area of 193,000 km2 . The shoreline measures 3450 km in length and the lake has a mean depth of 40 m and a maximum depth of 80 m. The lake is shared by Kenya (6%), Uganda (43%), and Tanzania (51%). The lake basin is estimated to have a population of 30 million individuals which is growing at a rate of >3% per annum. Three major cities (Kampala, Kisumu and Mwanza) with a combined population of about six million inhabitants depend on the lake for domestic and municipal water supply and waste disposal. Recent data has shown it is becoming eutrophic [6].

Two introduced species, Nile perch (*Lates niloticus*) and Nile tilapia (*Oreochromus niloticus*), and one native cyprinid (*Rastrineobola argentea*) dominate the lake's fisheries. The introduction of the Nile perch (*L. niloticus*), in the early 1960's had major ecological consequences. It is believed that some 200 endemic halochromine species (previously comprising 90% of the lake fish biomass) have become extinct in the lake due to predation by the Nile perch [7]. Most of these species had no commercial value, but are now considered relevant to the sustainability of the Lake Victoria ecosystem [8]. Lake Victoria fisheries production has increased markedly since the introduction of the Nile perch. Despite the general unreliability of published data, there is agreement that between the late 1980's and early 1990's there was an increase in the quantity of fish landed in Lake Victoria fisheries reaching a total of 500,000 tons per year. This figure was in decline by the late 1990's and early 2000's when it reached a total of 340,000 ton per year (Fig. 2). This reduction was mainly due to the overexploitation of the fisheries resources, and to the increase in the number of motorized boats, and to the Nile perch processing industries. Reportedly the number of fishing boats in the lake increased from 12,000 boats during 1982 to 22,700 boats during 1990 and more than 52,000 boats in 2002 [6]. In recent years, as fishing pressure on the Nile perch has intensified, there are signs of recovery in at least some of the former haplochromine species that were thought to be extinct from the lake environment [9], [10], [5].

**Figure 2.** Variation of the total fish landing of Lake Victoria during the period 1977-2002 [8]

75% of the total of the five tropical lakes of the Nile basin. They are also important because they lie at the source of both the White Nile and the Blue Nile, respectively. Their main fishes are representative of the fish species living in the other lakes (Edward, Albert and Kyoga). Details on the other tropical lakes (Edward, Albert, Kyoga, and George) fish fauna and its

**Country Area in basin (km3) Percentage of total country area in**

Burundi 13 000 46% D R Congo 22 300 1% Eritrea 25 700 21% Ethiopia 366 000 32% Egypt 307 900 33% Kenya 52 100 9% Rwanda 20 400 83% Sudan 1943 100 78% Tanzania 118 400 13% Uganda 238 700 98%

Lake Victoria is the largest natural lake in Africa (Fig. 1) and the second largest lake in the

mean depth of 40 m and a maximum depth of 80 m. The lake is shared by Kenya (6%), Uganda (43%), and Tanzania (51%). The lake basin is estimated to have a population of 30 million individuals which is growing at a rate of >3% per annum. Three major cities (Kampala, Kisumu and Mwanza) with a combined population of about six million inhabitants depend on the lake for domestic and municipal water supply and waste disposal. Recent data has shown it is

Two introduced species, Nile perch (*Lates niloticus*) and Nile tilapia (*Oreochromus niloticus*), and one native cyprinid (*Rastrineobola argentea*) dominate the lake's fisheries. The introduction of the Nile perch (*L. niloticus*), in the early 1960's had major ecological consequences. It is believed that some 200 endemic halochromine species (previously comprising 90% of the lake fish biomass) have become extinct in the lake due to predation by the Nile perch [7]. Most of these species had no commercial value, but are now considered relevant to the sustainability of the Lake Victoria ecosystem [8]. Lake Victoria fisheries production has increased markedly since the introduction of the Nile perch. Despite the general unreliability of published data, there is agreement that between the late 1980's and early 1990's there was an increase in the

. The shoreline measures 3450 km in length and the lake has a

and a very large

**Nile Basin**

world after Lake Superior (USA-Canada). It has a surface area of 68,800 km2

fisheries are found elsewhere [4], [5].

352 Biodiversity - The Dynamic Balance of the Planet

catchment area of 193,000 km2

becoming eutrophic [6].

**3.1. Lake Victoria (Kenya, Tanzania and Uganda)**

**Table 1.** National areas within the Nile Basin "Source [14]"

Extracted data from the results obtained by [6], from the ECOPATH prediction model have revealed that the stock biomass (tons km-2) of the fishes (Nile perch, tilapia and sardine) are different in the waters of Lake Victoria shared by different countries. The same is also true for the ratios of production per biomass except for the sardine species (Fig. 3). The data also shows that the Ugandan lake areas have lowest stock of Nile perch biomass, while the highest stocks are found in the Kenyan lake areas. Interestingly, the Ugandan stock biomass of tilapia is the highest while the Tanzanian stocks are the lowest. The sardine stock biomass is higher in the Kenyan lake areas followed by the Tanzanian, with the lowest recorded in the Ugandan lake areas (Fig. 3). An overall estimate shows that the average stock biomass for the whole of Lake Victoria is 4.59 tons km-2 for the Nile perch, 3.27 tons km-2 for the sardine and 2.36 tons km-2 for the tilapia. The same trend is observed for the estimate of production/biomass year-1, giving the ratios 3.75, 3.0 and 1.75 for the three fishes, respectively.

In 1992-1993 about 113 reed boats were counted on the lake and about 374 gill nets were in use, with an overall daily haul averaging 12.3 kg (7.8 kg Nile tilapia, 4.3 kg *Labeobarbus* spp. and 0.2 kg African catfish). Here it is important to indicate that *Labeobarbus* spp. in this lake is represented by nearly 15 species. It was also reported at that time that the fishermen in the lake numbered about 400 individuals. This meant that each reed boat had only one fisherman [12]. The introduction of motorboats to Lake Tana fisheries was a consequence of the increasing demand for fish from the capital Addis Ababa. This introduced an additional 130 professional fishermen, which markedly negatively influenced the fish stock in the lake. In fact, the annual total catch fell to 255 metric tons in 2001 from a value of 360 metric tons in 1997. Not only was there a reduction in total catch but also the percentage composition of the individual fish species yield varied between 1993 and 2001, so that the catch of *Labeobarbus* spp. declined by almost third in 2001 compared to 1993. Notably, the catch of Nile tilapia increased 50% in 2001 compared to 1993 (Fig. 4). This may reflect the intensive exploitation of *Labeobarbus* spp. and

by nearly 15 species. It was also reported at that time that the fishermen in the lake numbered about 400 individuals. This meant that each reed boat had only one fisherman [12]. The introduction of motorboats to Lake Tana fisheries was a consequence of the increasing demand for fish from the capital Addis Ababa. This introduced an additional 130 professional fishermen, which markedly negatively influenced the fish stock in the lake. In fact, the annual total catch fell to 255 metric tons in 2001 from a value of 360 metric tons in 1997. Not only was there a reduction in total catch but also the percentage composition of the individual fish species yield varied between 1993 and 2001, so that the catch of Labeobarbus spp. declined by almost third in 2001 compared to 1993. Notably, the catch of Nile tilapia increased 50% in 2001 compared to 1993 (Fig. 4). This may reflect the intensive exploitation of Labeobarbus spp. and the superior ability of the Nile tilapia to multiply in the lake.

50

during periods of high water level. The inland fisheries of Sudan are

during periods of high water level. The inland fisheries of

70

Labeobarbus spp O. niloticus C.garipinus

The Nile Fishes and Fisheries http://dx.doi.org/10.5772/57381 355

), its inland water

), its inland water

145 140

1993 2001 Year

Figure 4. Total catch of the three main species from Lake Tana during the years 1993 and 2001 [13]

Although Sudan is a country with a very large surface area (2,505,825 km2

Although Sudan is a country with a very large surface area (2,505,825 km2

**Figure 4.** Total catch of the three main species from Lake Tana during the years 1993 and 2001 [13]

based on the Nile river tributaries, contributing over 90% of the estimated production potential of the country. The Sudd swamps in the south (Fig. 1), and the man-made lakes on the White Nile, the Blue Nile, Atbara river and the main Nile river (Lake Nasser portion in Sudan "Nubia") count as the major fishing localities with respect to fish resource magnitude and exploitation thrust [13]. The total fish production of the various inland water bodies and wetlands are estimated at 50,000 tons year -1. This figure is not representative of the full potential of the various fisheries (Table 2), as in some areas civil war disturbances and dense cover of aquatic macrophytes, and inadequate fishing gear have had a

**4. Fish and fisheries of Mid Nile (Sudan freshwater fish and fisheries)**

Sudan are based on the Nile river tributaries, contributing over 90% of the estimated produc‐ tion potential of the country. The Sudd swamps in the south (Fig. 1), and the man-made lakes on the White Nile, the Blue Nile, Atbara river and the main Nile river (Lake Nasser portion in Sudan "Nubia") count as the major fishing localities with respect to fish resource magnitude and exploitation thrust [13]. The total fish production of the various inland water bodies and wetlands are estimated at 50,000 tons year -1. This figure is not representative of the full

the superior ability of the Nile tilapia to multiply in the lake.

130

Tons/year

bodies occupy only 114,000 km2

bodies occupy only 114,000 km2

negative effect on local fish production.

90

4. Fish and fisheries of Mid Nile (Sudan freshwater fish and fisheries)

7

Figure 3, Biomass potentials of different water sectors of Lake Victoria for the main three fish species (tons km-2) [8] **Figure 3.** Biomass potentials of different water sectors of Lake Victoria for the main three fish species (tons km-2) [8]

 The artisanal fishing gear was in use on traditional fishing boats in Lake Victoria fisheries until the industrial exploitation of the Nile perch for international commercialization. At that time, motorized boats and improved fish gear "even illegal" was used. The most common gear used in Lake Victoria fisheries are gill nets and long-line hooks. During the period of 2000 and 2004, the numbers of gill nets in use increased by 50% reaching 980,000 gill nets, while the numbers of long-line hooks is estimated at 8 million in 2001. This number was adjusted to only 6 million during [6]. The current haul is estimated at 45 kg boat -1 day -1 compared with the 80 kg boat -1 day -1 figure during 1990's. This indicates over-intensive exploitation of the fisheries of Lake Victoria fish resources and argues for sustainable management intervention. 3.2. Lake Tana (Ethiopia) Lake Tana is the largest lake in Ethiopia (surface area 3,050 km2 ). It lies at an altitude of approximately 1800 m ASL in the north-western highlands of Ethiopia, 500 km north of the capital The artisanal fishing gear was in use on traditional fishing boats in Lake Victoria fisheries until the industrial exploitation of the Nile perch for international commercialization. At that time, motorized boats and improved fish gear "even illegal" was used. The most common gear used in Lake Victoria fisheries are gill nets and long-line hooks. During the period of 2000 and 2004, the numbers of gill nets in use increased by 50% reaching 980,000 gill nets, while the numbers of long-line hooks is estimated at 8 million in 2001. This number was adjusted to only 6 million during 2006 [6]. The current haul is estimated at 45 kg boat -1 day -1 compared with the 80 kg boat -1 day -1 figure during 1990's. This indicates over-intensive exploitation of the fisheries of Lake Victoria fish resources and argues for sustainable management intervention.

Addis Ababa (Fig. 1). The lake is shallow (average depth 8 m, maximum depth 14 m), and its trophic

#### status is described as oligo-mesotrophic [11]. The lake's fishery is 30 km downstream from the Blue Nile outflows, and is isolated from the lower Nile basin by 40m high waterfalls. Physical and **3.2. Lake Tana** *(Ethiopia)*

hydrological features of the lake water follow a seasonal pattern. Rainfall peaks in July-August are followed by a rise in the lake water level by 1.5 m, reaching highest levels in September- October [12]. In their study, [12] identified the three endemic fish species groups Labeobarbus spp., Clarias gariepinus (African catfish), and Oriochromus niloticus (Nile tilapia), as the main representatives of Lake Tana fisheries. They noted that before 1986 Lake Tana was a subsistence fishery exploited predominantly by reed boat fishing vessels. This type of fishery was limited to the shore areas and targeted the native Nile tilapia using locally made fish traps and small gill nets. In 1992-1993 about 113 reed boats were counted on the lake and about 374 gill nets were in use, with an overall daily haul averaging 12.3 kg (7.8 kg Nile tilapia, 4.3 kg Labeobarbus spp. and 0.2 kg African catfish). Here it is important to indicate that Labeobarbus spp. in this lake is represented Lake Tana is the largest lake in Ethiopia (surface area 3,050 km2 ). It lies at an altitude of approximately 1800 m a.s.l. in the north-western highlands of Ethiopia, 500 km north of the capital Addis Ababa (Fig. 1). The lake is shallow (average depth 8 m, maximum depth 14 m), and its trophic status is described as oligo-mesotrophic [11]. The lake's fishery is 30 km downstream from the Blue Nile outflows, and is isolated from the lower Nile basin by 40m high waterfalls. Physical and hydrological features of the lake water follow a seasonal pattern. Rainfall peaks in July-August are followed by a rise in the lake water level by 1.5 m, reaching highest levels in September-October [12].

6 In their study, DeGraaf et al. [12] identified the three endemic fish species groups Barbs or yellow fish (*Labeobarbus* spp.*)*, African catfish (*Clarias gariepinus)*, and Nile tilapia *(Oriochromus niloticus)*, as the main representatives of Lake Tana fisheries. They noted that before 1986 Lake Tana was a subsistence fishery exploited predominantly by reed boat fishing vessels. This type of fishery was limited to the shore areas and targeted the native Nile tilapia using locally made fish traps and small gill nets.

In 1992-1993 about 113 reed boats were counted on the lake and about 374 gill nets were in use, with an overall daily haul averaging 12.3 kg (7.8 kg Nile tilapia, 4.3 kg *Labeobarbus* spp. and 0.2 kg African catfish). Here it is important to indicate that *Labeobarbus* spp. in this lake is represented by nearly 15 species. It was also reported at that time that the fishermen in the lake numbered about 400 individuals. This meant that each reed boat had only one fisherman [12]. The introduction of motorboats to Lake Tana fisheries was a consequence of the increasing demand for fish from the capital Addis Ababa. This introduced an additional 130 professional fishermen, which markedly negatively influenced the fish stock in the lake. In fact, the annual total catch fell to 255 metric tons in 2001 from a value of 360 metric tons in 1997. Not only was there a reduction in total catch but also the percentage composition of the individual fish species yield varied between 1993 and 2001, so that the catch of *Labeobarbus* spp. declined by almost third in 2001 compared to 1993. Notably, the catch of Nile tilapia increased 50% in 2001 compared to 1993 (Fig. 4). This may reflect the intensive exploitation of *Labeobarbus* spp. and the superior ability of the Nile tilapia to multiply in the lake. by nearly 15 species. It was also reported at that time that the fishermen in the lake numbered about 400 individuals. This meant that each reed boat had only one fisherman [12]. The introduction of motorboats to Lake Tana fisheries was a consequence of the increasing demand for fish from the capital Addis Ababa. This introduced an additional 130 professional fishermen, which markedly negatively influenced the fish stock in the lake. In fact, the annual total catch fell to 255 metric tons in 2001 from a value of 360 metric tons in 1997. Not only was there a reduction in total catch but also the percentage composition of the individual fish species yield varied between 1993 and 2001, so that the catch of Labeobarbus spp. declined by almost third in 2001 compared to 1993. Notably, the catch

of Nile tilapia increased 50% in 2001 compared to 1993 (Fig. 4). This may reflect the intensive exploitation of Labeobarbus spp. and the superior ability of the Nile tilapia to multiply in the lake.

Figure 4. Total catch of the three main species from Lake Tana during the years 1993 and 2001 [13] **Figure 4.** Total catch of the three main species from Lake Tana during the years 1993 and 2001 [13]

4. Fish and fisheries of Mid Nile (Sudan freshwater fish and fisheries)

7

6

fish traps and small gill nets.

[12].

**3.2. Lake Tana** *(Ethiopia)*

Lake Victoria

0.502

Lake Tana is the largest lake in Ethiopia (surface area 3,050 km2

Lake Tana is the largest lake in Ethiopia (surface area 3,050 km2

Lake Victoria fish resources and argues for sustainable management intervention.

approximately 1800 m ASL in the north-western highlands of Ethiopia, 500 km north of the capital Addis Ababa (Fig. 1). The lake is shallow (average depth 8 m, maximum depth 14 m), and its trophic status is described as oligo-mesotrophic [11]. The lake's fishery is 30 km downstream from the Blue Nile outflows, and is isolated from the lower Nile basin by 40m high waterfalls. Physical and hydrological features of the lake water follow a seasonal pattern. Rainfall peaks in July-August are followed by a rise in the lake water level by 1.5 m, reaching highest levels in September- October

In their study, [12] identified the three endemic fish species groups Labeobarbus spp., Clarias gariepinus (African catfish), and Oriochromus niloticus (Nile tilapia), as the main representatives of Lake Tana fisheries. They noted that before 1986 Lake Tana was a subsistence fishery exploited predominantly by reed boat fishing vessels. This type of fishery was limited to the shore areas and targeted the native Nile tilapia using locally made fish traps and small gill nets.

approximately 1800 m a.s.l. in the north-western highlands of Ethiopia, 500 km north of the capital Addis Ababa (Fig. 1). The lake is shallow (average depth 8 m, maximum depth 14 m), and its trophic status is described as oligo-mesotrophic [11]. The lake's fishery is 30 km downstream from the Blue Nile outflows, and is isolated from the lower Nile basin by 40m high waterfalls. Physical and hydrological features of the lake water follow a seasonal pattern. Rainfall peaks in July-August are followed by a rise in the lake water level by 1.5 m, reaching

In their study, DeGraaf et al. [12] identified the three endemic fish species groups Barbs or yellow fish (*Labeobarbus* spp.*)*, African catfish (*Clarias gariepinus)*, and Nile tilapia *(Oriochromus niloticus)*, as the main representatives of Lake Tana fisheries. They noted that before 1986 Lake Tana was a subsistence fishery exploited predominantly by reed boat fishing vessels. This type of fishery was limited to the shore areas and targeted the native Nile tilapia using locally made

In 1992-1993 about 113 reed boats were counted on the lake and about 374 gill nets were in use, with an overall daily haul averaging 12.3 kg (7.8 kg Nile tilapia, 4.3 kg Labeobarbus spp. and 0.2 kg African catfish). Here it is important to indicate that Labeobarbus spp. in this lake is represented

3.47

2.815

Kenyan Water Tanzanian Water Uganda Water Average L. Victoria

 The artisanal fishing gear was in use on traditional fishing boats in Lake Victoria fisheries until the industrial exploitation of the Nile perch for international commercialization. At that time, motorized boats and improved fish gear "even illegal" was used. The most common gear used in Lake Victoria fisheries are gill nets and long-line hooks. During the period of 2000 and 2004, the numbers of gill nets in use increased by 50% reaching 980,000 gill nets, while the numbers of long-line hooks is estimated at 8 million in 2001. This number was adjusted to only 6 million during [6]. The current haul is estimated at 45 kg boat -1 day -1 compared with the 80 kg boat -1 day -1 figure during 1990's. This indicates over-intensive exploitation of the fisheries of Lake Victoria fish resources and argues

Figure 3, Biomass potentials of different water sectors of Lake Victoria for the main three fish

**Figure 3.** Biomass potentials of different water sectors of Lake Victoria for the main three fish species (tons km-2) [8]

The artisanal fishing gear was in use on traditional fishing boats in Lake Victoria fisheries until the industrial exploitation of the Nile perch for international commercialization. At that time, motorized boats and improved fish gear "even illegal" was used. The most common gear used in Lake Victoria fisheries are gill nets and long-line hooks. During the period of 2000 and 2004, the numbers of gill nets in use increased by 50% reaching 980,000 gill nets, while the numbers of long-line hooks is estimated at 8 million in 2001. This number was adjusted to only 6 million during 2006 [6]. The current haul is estimated at 45 kg boat -1 day -1 compared with the 80 kg boat -1 day -1 figure during 1990's. This indicates over-intensive exploitation of the fisheries of

4.215

2.071

4.59

2.363

3.271

). It lies at an altitude of

). It lies at an altitude of

Nile Perch Nile Tilapia Haplochromins

5.451 5.262

4.271

2.373

for sustainable management intervention. 3.2. Lake Tana (Ethiopia)

highest levels in September-October [12].

species (tons km-2) [8]

Tons/Km2

354 Biodiversity - The Dynamic Balance of the Planet

#### Although Sudan is a country with a very large surface area (2,505,825 km2 ), its inland water bodies occupy only 114,000 km2 during periods of high water level. The inland fisheries of Sudan are **4. Fish and fisheries of Mid Nile (Sudan freshwater fish and fisheries)**

based on the Nile river tributaries, contributing over 90% of the estimated production potential of the

country. The Sudd swamps in the south (Fig. 1), and the man-made lakes on the White Nile, the Blue Nile, Atbara river and the main Nile river (Lake Nasser portion in Sudan "Nubia") count as the major fishing localities with respect to fish resource magnitude and exploitation thrust [13]. The total fish production of the various inland water bodies and wetlands are estimated at 50,000 tons year -1. This figure is not representative of the full potential of the various fisheries (Table 2), as in some areas civil war disturbances and dense cover of aquatic macrophytes, and inadequate fishing gear have had a negative effect on local fish production. Although Sudan is a country with a very large surface area (2,505,825 km2 ), its inland water bodies occupy only 114,000 km2 during periods of high water level. The inland fisheries of Sudan are based on the Nile river tributaries, contributing over 90% of the estimated produc‐ tion potential of the country. The Sudd swamps in the south (Fig. 1), and the man-made lakes on the White Nile, the Blue Nile, Atbara river and the main Nile river (Lake Nasser portion in Sudan "Nubia") count as the major fishing localities with respect to fish resource magnitude and exploitation thrust [13]. The total fish production of the various inland water bodies and wetlands are estimated at 50,000 tons year -1. This figure is not representative of the full potential of the various fisheries (Table 2), as in some areas civil war disturbances and dense cover of aquatic macrophytes, and inadequate fishing gear have had a negative effect on local fish production.

water (55.5 Km3

contribution may be summarized as follows:

motorboats with suitable fishing gear adapted to its bathymetry.

**5.2. Nile branches and irrigation channels fishes and fisheries**

*aureus, Sarotherodon galilaeus* and *Tilapia zilli*) as well as *Clarias* spp.

**5.1. Lake Nasser fishes and Fisheries**

year -1) as outlined in an agreement with Sudan in 1959. This quantity satisfies

the freshwater demands of the Egyptian population for use in agricultural irrigation, industry, domestic and navigation purposes. On the way to its Mediterranean destination, the Nile water fills many canals within the irrigation network in the western desert and the Nile delta. It also contributes to the water budget of the Northern Delta lakes [2]. Thus the freshwater inland water fisheries in Egypt include Lake Nasser (the second largest man made reservoir in Africa, after Lake Volta-Ghana), the Nile main river channel, irrigation channels, some water bodies in the Western Desert, the Nile branches (Rosetta and Damietta), and the Northern Delta Lakes (Manzala, Burullus, Idko and Mariut). The excess water is then discharged into the Mediter‐ ranean Sea through the lake connections with the sea via direct and indirect inlet openings [2]

The annual fish yield from freshwater fisheries of the Egyptian Nile basin has increased annually from 157,888 metric tons in 1990 to 224,940 metric tons in 2000 [14]. The catch increased for a number of reasons, such as the nutritive effect of sewage and fertilizer discharge in drainage channels and lakes, the intensified fishing activities and adjustment of incensement statistical techniques. Apart from the intensive aquaculture that has developed during the last twenty years in Egypt, the major contributors to the freshwater fish catch could be listed as Lake Nasser, Nile branches and irrigation channels as well as the northern Delta lakes. Their

Lake Nasser lies behind the AHD and its extension in the northern Sudan is referred to as the Nubia reservoir. This lake has a depth reaching 180m and covers an area of 6216 km2

km2 of which are in Egypt and the rest in Sudan (Fig. 1). The total fish catch from Lake Nasser has been estimated as 28,153 tons year -1 [15]. Tilapia species, mainly the Nile tilapia represent 90% of the total fish catch, while Nile perch and *Barbus* spp. cover the remaining 10%. Despite the large area of the lake, it contributes only about 10% of the total freshwater fish landing in the Egyptian Nile basin. This is probably due to its deep waters and the low number of

There are more than 100 sites recorded along the Nile branches and major irrigation channels at which freshwater fishes are collected for marketing. Most fishermen in these areas are not registered. The fishing fleets at these sites comprise hundreds of small wooden boats (4-6 m in length). The fishing gear used is mostly primitive, though trammel nets are in use in some areas. The common fish species caught from these channels are tilapia species (*O. niloticus, O.*

Although these fishing sites are sparsely distributed and reliable statistics are in short supply, it has been estimated that 34% of the total Egyptian freshwater fish catch is slated to the two

main Nile branches (Rosetta and Damietta) and the major irrigation channels [16].

, 5248

The Nile Fishes and Fisheries http://dx.doi.org/10.5772/57381 357

**Table 2.** Calculated Potential and Effective Fish Catch from Different Inland Water Bodies of Sudan

The predominant fishing gear includes active and passive gill nets, seine nets, trammel nets, long line hooks, cast nets and baskets. The commercially important fish are Nile perch (*Lates niloticus),* Bagrid catfish *(Bagrus bayad),* Silver catfish *(Bagruc docmac),* Nile tilapia *(Oreochromus niloticus),* Carp fish *(Labeo* spp.*),* Barbs fish *(Barbus binny),* Mormyrus fish *(Mormyrus* spp*.),* Nile Distichodus *(Distichodus* spp*.),* Tiger fish *(Hydrocyon* spp.*)* and Nile robber *(Alestes* spp*.).* There are many other species, though they have no commercial value [13].

It is important to state that, apart from the FAO reports, there is almost no scientific literature available on the ecological features and dynamics of fish populations in the inland waters of Sudan. This underlines the importance of organizing a research program on inland fisheries in this area in order to fill the gap of knowledge about the fisheries status in this important part of the Nile basin. This is especially important for the wet lands which are not limited to Sudan but also exist in the ten countries of the Nile basin, and account for an area of almost 200,000 km2 . A characteristic of wetlands fisheries is the variety of traps that are used to catch fish in dominantly submerged or emergent vegetation habitats. Many of these traps have traditional designs adapted to local conditions and most are made from local plant materials - often from wetlands themselves. One type of fish requiring a special fishing technique is the African lungfish(*Protopterusaethiopicus*),whichisnativetoEthiopianwetlandsandinhabitstheseasonal wetlands where it aestivates in the dried soil and is "hunted" during the dry season.


**Ying Zhang, Yuanyuan Li , Xiaomei Chen, Zhixia Meng \* and Shunxing Guo \***

Institute of Medicinal Plant Development, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100193, China<EMAIL_ADDRESS>(Y.Z<EMAIL_ADDRESS>(Y.L<EMAIL_ADDRESS>(X.C.)

**\*** Correspondence<EMAIL_ADDRESS>(Z.M<EMAIL_ADDRESS>(S.G.)

Received: 18 November 2019; Accepted: 9 January 2020; Published: 15 January 2020

**Abstract:** *Anoectochilus roxburghii* is a traditional Chinese herb with high medicinal value, with main bioactive constituents which are flavonoids. It commonly associates with mycorrhizal fungi for its growth and development. Moreover, mycorrhizal fungi can induce changes in the internal metabolism of host plants. However, its role in the flavonoid accumulation in *A. roxburghii* at different growth stages is not well studied. In this study, combined metabolome and transcriptome analyses were performed to investigate the metabolic and transcriptional profiling in mycorrhizal *A. roxburghii* (M) and non-mycorrhizal *A. roxburghii* (NM) growth for six months. An association analysis revealed that flavonoid biosynthetic pathway presented significant differences between the M and NM. Additionally, the structural genes related to flavonoid synthesis and different flavonoid metabolites in both groups over a period of six months were validated using quantitative real-time polymerase chain reaction (qRT-PCR) and high-performance liquid chromatography coupled with tandem mass spectrometry (HPLC-MS/MS). The results showed that *Ceratobasidium* sp. AR2 could increase the accumulation of five flavonol-glycosides (i.e., narcissin, rutin, isorhamnetin-3-O-beta-d-glucoside, quercetin-7-O-glucoside, and kaempferol-3-O-glucoside), two flavonols (i.e., quercetin and isorhamnetin), and two flavones (i.e., nobiletin and tangeretin) to some degrees. The qRT-PCR showed that the flavonoid biosynthetic genes (*PAL*, *4CL*, *CHS*, *GT*, and *RT*) were significantly differentially expressed between the M and NM. Overall, our findings indicate that AR2 induces flavonoid metabolism in *A. roxburghii* during different growth stages, especially in the third month. This shows great potential of *Ceratobasidium* sp. AR2 for the quality improvement of *A. roxburghii*.

**Keywords:** *Anoectochilus roxburghii*; *Ceratobasidium* sp.; metabolome and transcriptome analyses; flavonoid; HPLC-MS/MS; qRT-PCR