**Dedication**

*Mass Production Processes*

**of chemicals**

quality tablet.

output materials

react with materials

flow properties

**4. Conclusion**

**Table 2.**

contamination of products.

lently, on the tablet weight.

main-compression force depends on the amount of powder in the die or, equiva-

**3.2 Risk assessment of quality assurance and control during mass production**

**Table 2** shows potential risk variables associated with quality control during mass production. It ranges from issues associated with acceptance sampling of materials and products at the input/output stage to contamination from tableting

Tian et al. [21] carried out quality risk assessment and mitigation of pharmaceutical continuous manufacturing of a case study using flowsheet modelling approach (an engineering approach that can provide a framework to understand the impact of process dynamics on drug quality and associated risks during production, thereby facilitating the development of robust continuous processes) and identified a potential area for model improvement. Using sensitivity analyses they identified the significance of process parameters and material attributes on the dynamic responses and quality attributes of the tablet. They also conducted risk analysis using residence time distribution models to identify the impact of flowrate disturbances on product quality. Consequently, they were able to develop risk mitigation strategies to enable continuous production of high

This chapter discussed quality control of mass production process in the chemi-

cal industry. It reviewed a typical mass production process, identified current practice in the industry in order to guarantee quality assurance during mass production and finally proposed how this could be implemented in the chemical industry. A combination of acceptance sampling and process analytical techniques were deemed suitable for quality control during both batch and mass production. Quality control during bulk pharmaceutical production was studied where robots and machines were subjected to decontamination quality control procedure. Tableting and encapsulating machines for drug production also needed to be properly calibrated and cleaned to ensure constant tablet weight, and also minimise

**Risk variables Impact from risk negligence**

(4) Change in powder bulk density during compaction (4) Variation in tablet weight

(6) Inaccuracy in the dosing position of the tablet press (6) Variation in tablet weight

(5) Impurities in reactant chemicals (5) Impure product

(2) Inadequate cleaning of manufacturing equipment (2) Contamination of product with impurities

(1) (a) Producer's risk (b) Consumer's risk

(7) Variation in tablet weight

(3) Contamination of product with impurities

machines, impure product and variation in tablet weight.

(1) Use of acceptance sampling to evaluate input and

(3) Chemicals used to decontaminate equipment can

(7) Change in filling efficacy due to changes in powder

*Risk assessment of quality control during mass production.*

**146**

This book chapter is dedicated to my son Kelechi Peter Oduoza who died suddenly during the preparation of this manuscript. May his soul and those of all the faithful departed through the mercy of God rest in perfect peace, Amen.


**1. Introduction**

346 Recent Trends in Processing and Degradation of Aluminium Alloys

Engler-Pinto, C.C. Jr., Meyer-Olbersleben, F. & Rézai-Aria, F. (1995). Thermo-Mechanical

Minichmayr, R. (2005). Modellierung und Simulation des thermomechanischen

Riedler, M. & Eichlseder, W. (2004) Effects of dwell times on thermo-mechanical fatigue, *Zeitschrift Materialprüfung*, Jahrg. 46 11-12, Carl Hanser Verlag, München, S. 577-581. Bauschinger, J. (1886). Mitt. mech.-techn. Lab., pp. 289, TH München 13, 1886, Zivil-Ing. 27,

Manson, S.S., Halford, G.R. & Hirschberg, M.H. (1971). Creep-Fatigue Analysis by Strain-

Shercliff, H. R. & Ashby, M. F. (1990). Process Model for Age Hardening of Aluminium Alloys - I. The Model; *Acta metall. Mate*r. Vol. 38, No. 10, 1789-1802, 1990.

Miner, M.A. (1945) Cumulative damage in fatigue, Trans. *ASME Journal of Applied Mechanics*,

Chaboche, J.L. & Lesne, P.M. (1988). A Non-Linear Continuous Fatigue Damage Model, pp.

Kachanov, L.M. On Creep Rupture Time, Izv. Akad. Nauk. SSR, Otd Tekh. Nauk, No. 8, pp.

Kachanov, L.M. (1986). Introduction to Continuum Damage Mechanics, Martinus Nijhoff

Rabotnov, Y.N. (1969). Creep Problems in Structural Members, North Holland Publishing,

Manson, S.S. (1954). Behaviour of materials under conditions of thermal stress, *NACA Report*

Coffin, L.F. (1954). A study of the effects of cyclic thermal stresses on a ductile metal, *Trans.*

Basquin, O.H. (1910). The exponential Law of Endurance Tests, *Proceedings of the ASTM 10*,

Riedler, M., Minichmayr, R. & Eichlseder, W. (2005). Methods for the thermo-mechanical

Neu, R.W.,6 Sehitoglu, H. (1989). Thermo-mechanical Fatigue, Oxidation and Creep, Part II:

Slavik, D. & Sehitoglu, H. (1987). A Constitutive Model for High Temperature Loading, Part

Sehitoglu, H., Zamrik, S.Y., ASME PVP 123, New York, 1987, pp. 65-82. FEMFAT: Finite Elemente Methode und Betriebsfestigkeit, *Manual zur Software FEMFAT*,

fatigue simulation based on energy criterions, pp. 496-503, *6th International Conference of Assessment of reliability of materials and structures: problems and solutions,*

I and II, in Thermal Stress, *Material Deformation and Thermomechanical Fatigue*, Eds.:

Petten, Eds.: Bressers, J., Rémy, L., Steen, M., Vallés, J.L.

Christ, H.-J. (1991). *Wechselverformung von Metallen*, Springer-Verlag, Berlin

Palmgren, A. (1924) Die Lebensdauer von Kugellagern, pp. 339-341 *VDI-Zeitung 58*

Lemaitre, J. & Chaboche, J.L. (1985). Mecanique des Materieaux Solides, Dunod,

Leoben

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26-31.

Amsterdam

pp. 625-630.

ECS Steyr, 2005.

No. 1170

Zamrik, S.Y., *ASME*, New York

1-17 *, Fat. Fract. Engng. Mater. Struct.*, 11

Ramberg, W. & Osgood, W.R. (1943). In: *NACA Technical Note* 902.

Life Prediction, *Metal Transactions*, pp. 1769-1783, Vol. 20A

12-3, pp. A159-A164.

Publ., Dodrecht, Holland

*ASME 76*, pp. 931-950.

*RELMAS 2005*, St. Petersburg

Fatigue Behaviour of SRR99, Fatigue under Thermal and Mechanical Loading: Mechanisms, pp. 151-157*, Mechanics and Modelling, Kluwer Academic Publishers*,

Ermüdungsverhaltens von Aluminiumbauteilen, Dissertation, Montanuniversität

Range Partitioning, Design for Elevated Temperature Environment, pp. 12-24, Ed.:

Silicon carbide (SiC) particulate-reinforced aluminium matrix composites (AMC) are attractive engineering materials for a variety of structural applications, due to their superior strength, stiffness, low cycle fatigue and corrosion fatigue behaviour, creep and wear resistance, compared to the aluminium monolithic alloys. An important feature of the microstructure in the Al/SiC composite system is the increased amount of thermal residual stresses, compared to unreinforced alloys, which are developed due to mismatch in thermal expansion coefficients of matrix and reinforcement phases. The introduction of the reinforcement plays a key role in both the mechanical and thermal ageing behaviour of the composite material. Micro-compositional changes which occur during the thermomechanical forming process of these materials can cause substantial changes in mechanical properties, such as ductility, fracture toughness and stress corrosion resistance.

The satisfactory performance of aluminium matrix composites depends critically on their integrity, the heart of which is the quality of the matrix/particle reinforcement interface. The nature of the interface depends in turn on the processing of the AMC component. At the micro-level, the development of local concentration gradients around the reinforcement can be very different to the nominal conditions. The latter is due to the aluminium alloy matrix attempt to deform during processing. This plays a crucial role in the micro-structural events of segregation and precipitation at the matrix-reinforcement interface.

The strength of particulate-reinforced composites also depends on the size of the particles, interparticle spacing, and the volume fraction of the reinforcement [1]. The microstructure and mechanical properties of these materials can be altered by thermo-mechanical treatment as well as by varying the reinforcement volume fraction. The strengthening of monolithic metallic material is carried out by alloying and supersaturating, to an extent, that on suitable heat treatment the excess alloying additions precipitates out (ageing). To study the deformation behaviour of precipitate hardened alloy or particulate reinforced metal matrix composites the interaction of dislocation with the reinforcing particles is much more dependent on the particle size, spacing and density than on the composition [2]. Furthermore, when a particle is introduced in a matrix, an additional barrier to the movement of dislocation is created and the dislocation must behave either by cutting through the particles or by taking a path around the obstacles [3].

Deformation Characteristics of Aluminium Composites for Structural Applications 349

This chapter discusses first the relationship between the interfacial strength with the thermo-mechanical deformation process and the resulting macroscopic mechanical behaviour of particle-reinforced aluminium matrix composites. Micro-compositional changes which occur during the thermo-mechanical processing of these materials can cause substantial changes in mechanical properties such as ductility, fracture toughness, or stress corrosion resistance. A mico-mechanistic model will be presented for predicting the interfacial fracture strength in AMCs in the presence of magnesium segregation. Finally, the use of powerful nondestructive evaluation tools, such as infrared thermography, will be discussed to evaluate the state of stresses at the crack tip and to monitor fatigue crack

In the second part of the chapter the structural integrity of Aluminium Honeycomb (HC) sandwich panels is compared with the new core material concept of aluminium foams. Aluminium Honeycomb sandwich panels are used to reduce weight whilst improving the compressive strength of the structure with the aerospace industry being one of the prime users of HC sandwich panels for structural applications. The cost of producing all welded HC structures has been the key factor for not using this technology on a mass production basis. An alternative to the aluminium honeycomb (HC) sandwich panels is the metallic foam sandwich panel, which has been gaining interest in the same field. These foams are anisotropic, exhibit non-linear mechanical behaviour, and they have the potential for use at temperatures up to 200oC. They have superior impact energy absorption, and improved strength and weight savings. The lower weight as compared to conventional solid wrought aluminium alloys will mean a reduction in fuel consumption thus providing economical

This chapter attempts to investigate whether aluminium honeycomb sandwich panels, with their homogenous hexagonal core can be successfully replaced by metallic foam sandwich panels, which have an inhomogeneous core. A successful replacement would improve the confidence of manufacturers in the exploitation of this new material in replacing traditional materials. Current levels of understanding of cyclic stressing in metallic foam sandwich panels is limited and models of long term understanding of this aspect of failure are very important for both aerospace and automotive sectors. Burman et al [16] suggests that fundamental fatigue models and concepts proven to work for metals can be applied to metallic foam sandwich panels. A study by Shipsha et al [17] investigated experimentally both metallic foam and other cellular foams, using compact tension specimens. Shipsha's et al research is extremely interesting and implies that a sandwich panel should be considered whole and not two separate entities. Banhart and Brinkers has shown that it is very difficult to detect the features leading to fatigue failure in metallic foams due to the metallic foam being already full of micro cracks [18]. However, Olurin [19] investigation suggest that the fatigue crack growth mechanism of Alulight and Alporas foam is of sequential failure of cell faces ahead of crack tip. The main conclusion is that for a given ΔK, the fatigue crack propagation rate, da/dN decreases with increasing density and for a given stress intensity,

the fatigue crack propagation rate increases when the mean stress is increased.

Current levels of understanding of cyclic stressing in aluminium foams is limited and models of long term understanding of this aspect of failure are important for both aerospace and automotive sectors. This is particularly important for low-density foam and honeycomb materials which despite thin ligament thickness, have good properties in compression. A method of analysis is proposed to predict life expectancy of aluminium honeycomb and

growth in particle-reinforced aluminium alloy matrix composites.

savings.

metallic foam sandwich panels.

At present, the relationship between the strength properties of metal matrix composites and the details of the thermo-mechanical forming processes is not well understood. The kinetics of precipitation in the solid state has been the subject of much attention. Early work on growth kinetics has been developed for the grain boundary case [4] and for intragranular precipitation [5]. These approaches have been integrated to produce a unified description of the inter- and intra-granular nucleation and growth mechanisms [6, 7]. More recently, successful attempts have been made to combine models of precipitate growth at interfaces with concurrently occurring segregation in aluminium alloys [8]. Studies of the relation between interfacial cohesive strength and structure have only recently become possible. This is due to of remarkable advances in physical examination techniques allowing direct viewing of interface structure and improved theoretical treatments of grain boundary structure.

The ability of the strengthening precipitates to support the matrix relies on the properties of the major alloying additions involved in the formation of these precipitates. The development of precipitates in Al-based alloys can be well characterised through heat treatment processing. Heat treatment affects the matrix properties and consequently the strain hardening of the composite. Furthermore, the distribution and concentration of these precipitates greatly affect the properties of the material where homogenous distribution of small precipitates provides the optimum results.

The role of the reinforcement is crucial in the microdeformation behaviour. The addition of SiC to aluminium alloy increases the strength and results in high internal stresses, in addition to the ones caused by the strengthening precipitates. Furthermore, the SiC reinforced particles are not affected by the heat treatment process. A great deal of attention has been recently devoted to understanding the strengthening mechanisms in metal matrix composites, which are distinguished by a large particulate volume fraction and relatively large diameter. Another important matter in understanding and modelling the strength of particulate MMCs is to consider the effect of particle shape, size and clustering [9-11], as well as the effects of clustering of reinforcement on the macroscopic behaviour and the effects of segregation to the SiC/Al interfaces [12]. Important role also play the effects of casting condition and subsequent swaging on the microstructure, clustering, and properties of Al/SiC composites [13].

Aluminium honeycomb sandwich panel constructions have been successfully applied as strength members of satellites and aircraft structures and also in passenger coaches of highspeed trains such as the TGV in France and the Shinkansen in Japan [14]. However, the cost of producing the all welded honeycomb structure has been a key factor for not using this technology on mass production rate. Recent developments in manufacturing methods have given rise to a range of commercially viable metallic foams, one being Alulight. In comparison to aluminium honeycomb core construction, metallic foams show isotropic properties and exhibit non linear mechanical deformation behaviour. The metallic foams have the potential to be used at elevated temperatures up to 200oC [15]. They also have superior impact energy absorption and improved strength and weight savings. However, the successful implementation of both aluminium honeycomb and metallic foam sandwich panels for aerospace and transportation applications is dependent upon an understanding of their mechanical properties including their resistance to fatigue crack growth and the resistance of aluminium alloys to environmentally induced cracking or stress corrosion cracking.

At present, the relationship between the strength properties of metal matrix composites and the details of the thermo-mechanical forming processes is not well understood. The kinetics of precipitation in the solid state has been the subject of much attention. Early work on growth kinetics has been developed for the grain boundary case [4] and for intragranular precipitation [5]. These approaches have been integrated to produce a unified description of the inter- and intra-granular nucleation and growth mechanisms [6, 7]. More recently, successful attempts have been made to combine models of precipitate growth at interfaces with concurrently occurring segregation in aluminium alloys [8]. Studies of the relation between interfacial cohesive strength and structure have only recently become possible. This is due to of remarkable advances in physical examination techniques allowing direct viewing of interface structure and improved theoretical treatments of grain boundary

The ability of the strengthening precipitates to support the matrix relies on the properties of the major alloying additions involved in the formation of these precipitates. The development of precipitates in Al-based alloys can be well characterised through heat treatment processing. Heat treatment affects the matrix properties and consequently the strain hardening of the composite. Furthermore, the distribution and concentration of these precipitates greatly affect the properties of the material where homogenous distribution of

The role of the reinforcement is crucial in the microdeformation behaviour. The addition of SiC to aluminium alloy increases the strength and results in high internal stresses, in addition to the ones caused by the strengthening precipitates. Furthermore, the SiC reinforced particles are not affected by the heat treatment process. A great deal of attention has been recently devoted to understanding the strengthening mechanisms in metal matrix composites, which are distinguished by a large particulate volume fraction and relatively large diameter. Another important matter in understanding and modelling the strength of particulate MMCs is to consider the effect of particle shape, size and clustering [9-11], as well as the effects of clustering of reinforcement on the macroscopic behaviour and the effects of segregation to the SiC/Al interfaces [12]. Important role also play the effects of casting condition and subsequent swaging on the microstructure, clustering, and properties

Aluminium honeycomb sandwich panel constructions have been successfully applied as strength members of satellites and aircraft structures and also in passenger coaches of highspeed trains such as the TGV in France and the Shinkansen in Japan [14]. However, the cost of producing the all welded honeycomb structure has been a key factor for not using this technology on mass production rate. Recent developments in manufacturing methods have given rise to a range of commercially viable metallic foams, one being Alulight. In comparison to aluminium honeycomb core construction, metallic foams show isotropic properties and exhibit non linear mechanical deformation behaviour. The metallic foams have the potential to be used at elevated temperatures up to 200oC [15]. They also have superior impact energy absorption and improved strength and weight savings. However, the successful implementation of both aluminium honeycomb and metallic foam sandwich panels for aerospace and transportation applications is dependent upon an understanding of their mechanical properties including their resistance to fatigue crack growth and the resistance of aluminium alloys to environmentally induced cracking or stress corrosion

structure.

small precipitates provides the optimum results.

of Al/SiC composites [13].

cracking.

This chapter discusses first the relationship between the interfacial strength with the thermo-mechanical deformation process and the resulting macroscopic mechanical behaviour of particle-reinforced aluminium matrix composites. Micro-compositional changes which occur during the thermo-mechanical processing of these materials can cause substantial changes in mechanical properties such as ductility, fracture toughness, or stress corrosion resistance. A mico-mechanistic model will be presented for predicting the interfacial fracture strength in AMCs in the presence of magnesium segregation. Finally, the use of powerful nondestructive evaluation tools, such as infrared thermography, will be discussed to evaluate the state of stresses at the crack tip and to monitor fatigue crack growth in particle-reinforced aluminium alloy matrix composites.

In the second part of the chapter the structural integrity of Aluminium Honeycomb (HC) sandwich panels is compared with the new core material concept of aluminium foams. Aluminium Honeycomb sandwich panels are used to reduce weight whilst improving the compressive strength of the structure with the aerospace industry being one of the prime users of HC sandwich panels for structural applications. The cost of producing all welded HC structures has been the key factor for not using this technology on a mass production basis. An alternative to the aluminium honeycomb (HC) sandwich panels is the metallic foam sandwich panel, which has been gaining interest in the same field. These foams are anisotropic, exhibit non-linear mechanical behaviour, and they have the potential for use at temperatures up to 200oC. They have superior impact energy absorption, and improved strength and weight savings. The lower weight as compared to conventional solid wrought aluminium alloys will mean a reduction in fuel consumption thus providing economical savings.

This chapter attempts to investigate whether aluminium honeycomb sandwich panels, with their homogenous hexagonal core can be successfully replaced by metallic foam sandwich panels, which have an inhomogeneous core. A successful replacement would improve the confidence of manufacturers in the exploitation of this new material in replacing traditional materials. Current levels of understanding of cyclic stressing in metallic foam sandwich panels is limited and models of long term understanding of this aspect of failure are very important for both aerospace and automotive sectors. Burman et al [16] suggests that fundamental fatigue models and concepts proven to work for metals can be applied to metallic foam sandwich panels. A study by Shipsha et al [17] investigated experimentally both metallic foam and other cellular foams, using compact tension specimens. Shipsha's et al research is extremely interesting and implies that a sandwich panel should be considered whole and not two separate entities. Banhart and Brinkers has shown that it is very difficult to detect the features leading to fatigue failure in metallic foams due to the metallic foam being already full of micro cracks [18]. However, Olurin [19] investigation suggest that the fatigue crack growth mechanism of Alulight and Alporas foam is of sequential failure of cell faces ahead of crack tip. The main conclusion is that for a given ΔK, the fatigue crack propagation rate, da/dN decreases with increasing density and for a given stress intensity, the fatigue crack propagation rate increases when the mean stress is increased.

Current levels of understanding of cyclic stressing in aluminium foams is limited and models of long term understanding of this aspect of failure are important for both aerospace and automotive sectors. This is particularly important for low-density foam and honeycomb materials which despite thin ligament thickness, have good properties in compression. A method of analysis is proposed to predict life expectancy of aluminium honeycomb and metallic foam sandwich panels.

Deformation Characteristics of Aluminium Composites for Structural Applications 351

favourable precipitate size and distribution pattern. However, the cycle used for optimising one property, e.g. tensile strength, is usually different from the one required to optimise a

Heat treatment of composites though has an additional aspect to consider, the particles introduced in the matrix. These particles may alter the alloy's surface characteristics and

The heat treatments were performed in Carbolite RHF 1200 furnaces with thermocouples attached, ensuring constant temperature inside the furnace. There were two different heat

The T6 heat treatment consists of the following steps: solution heat treatment, quench and

**2 7**

**Hours**

different property, e.g. yield strength, corrosion resistance.

treatments used in the experiments, T6 and modified-T6 (HT-1) [21, 22].

*Quench*

**Solution Treatment Age Hardening**

results in higher mechanical deformation response of the composite.

Fig. 1. T6 Heat treatment diagram showing the stages of the solution treatment for 2 hours

In the solution heat treatment, the alloys have been heated to a temperature just below the initial melting point of the alloy for 2 hours at 530±5ºC where all the solute atoms are allowed to dissolve to form a single phase solid solution. Magnesium is highly reactive with Silicon at this temperature and precipitation of Mg2Si is expected to be formed. The alloys were then quenched to room temperature. In age hardening, the alloys were heated to an intermediate temperature of 155ºC for 5 hours where nucleation and growth of the β' phase. The desired β phase Mg2Si precipitated at that temperature and then cooled at room temperature conditions. The precipitate phase nucleates within the grains at grain boundaries and in areas close to the matrix-reinforcement interface, as uniformly dispersed particles. The holding time plays a key role in promoting precipitation and growth which

The second heat treatment process was the modified-T6 (HT-1) heat treatment, where in the solution treatment the alloys have been heated to a temperature lower than the T6 heat treatment, at 450±5ºC for 1 hour, and then quenched in water. Subsequently the alloys were heated to an intermediate temperature of 170±5ºC for 24 hours in the age hardened stage

increase the surface energies [21].

age hardening (Fig. 1).

530

**Tem**

**perature ºC**

20

155

0

and artificial ageing for 5h

and then cooled in air (Fig. 2).


**6. Conclusions**

In this paper, the multi-objective optimization algorithm is applied to solve the different models by GA and optimized NSGA-II. The results of the single-objective and multi-objective calculation are compared and analyzed, and the following conclusions are obtained.

(1) Compared with the GA, MOPSO, and NSGA-II algorithms, the feasibility and effectiveness of the optimized NSGA-II are verified.

(2) With the single-objective model of maximum power generation, the total power generation is 8.84 billion kW·h, and the guarantee rate of ecological water demand is 74.43%; the single-objective model considering ecological constraints has a total power generation of 8.759 billion kW·h, and increases the ecological guarantee rate to 93.18%, which basically meets the ecological requirements. The comparison of the results of the two models reveals the degree of impact of ecological goals on dispatching.

(3) The single-objective typical annual optimal value basically falls on the multi-objective Pareto-front curve, which is in good agreement with the Pareto-front curve, further demonstrating the accuracy and reliability of each model and algorithm. With the decrease in incoming water, the ecological security situation in the lower reaches of the Yellow River is poor. The multi-objective model gives a global equilibrium solution set of power generation and ecology, which provides the best coordination scheme for the decision makers of reservoir actual operation and river basin management.

(4) In the multi-objective power generation and ecological sensitivity, the weakest year is in the dry year, and the strongest in the wet year, which is the contradiction between the ecological and the power generation in the dry year. To improve the same ecological benefits, it is bound to sacrifice greater power generation benefits. As the situation of ecological security in the dry years is more severe, stage-by-stage measures should be taken to ease the deterioration of the ecological environment.

In this paper, the different ecological water demand processes of each typical year is regarded as the ecological target. The influence of water quality factors such as water and sediment from alluvial water and algae on the ecological flow in Xiaolangdi is neglected. The next step is to establish an ecological and discharge flow response model to determine the process of integrated ecological water demand for the lower reaches of the Yellow River, and then improve the multi-objective optimization scheduling model.

**Author Contributions:** T.B, J.-x.C. and J.L. provided the writing ideas and supervised the study; Y.-p.H. conceived and designed the methods; T.B. and X.L. wrote the paper, and all the authors were responsible for data processing and data analysis. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This study is supported by the National Key R&D Program of China (2017YFC0405900), the China Postdoctoral Science Foundation (2017M623332XB), the Postdoctoral Research Funding Project of Shaanxi Province (2017BSHYDZZ53), the Basic Research Plan of Natural Science in Shaanxi Province (2018JQ5145), the Natural Science Foundation of China (51879213), Guangdong Province Water Conservancy Science and Technology Innovation Project (2017-09).The authors would like to thank the Editors and anonymous Reviewers for their valuable and constructive comments on this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

© 2020 by the authors. 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 (http://creativecommons.org/licenses/by/4.0/).


*3.1.2 ZnS material global properties*

### *<IP_ADDRESS> ZnS crystallographic properties*

The crystallography of compounds II-VI6 to which Zinc Sulfide belongs poses some problems because of the polymorphism of these compounds. They can have crystallographic structures of two main types: the cubic structure of the sphalerite type (Zinc Blende), and the hexagonal structure of the Wurtzite type. The cubic structure (Zinc Blende) is stable at room temperature (27°C), while the hexagonal structure is more stable at very high-top temperatures of around 1020°C [10]. Indeed, with a lattice parameter *aCIGS* ¼ 0*:*58 *nm* for the CIGSe chalcopyrite structure and *a*0\_*ZnS* ¼ 0*:*541 *nm* respectively*a*0\_*ZnS* ¼ *b*0\_*ZnS* ¼ 0*:*3811*nm* for ZnS in its cubic and hexagonal structure respectively, CIGSe forms a better lattice agreement with ZnS in its sphalerite structure which is furthermore its stable structure [11].

A deposition technique by ALD [12] or by laser sputtering [11] would make it possible to obtain a layer of ZnS having a crystallographic orientation preferentially sphalerite.

**Table 1.** *Chemical elements of the Mendeleev table of columns II and VI [13].*

#### *<IP_ADDRESS> ZnS Opto-electrical properties*

The spectrum of white light extends from the ultraviolet characterized by short wavelengths (λ < 380 nm) to the infrared characterized by long wavelengths (λ > 780 nm) through the visible spectrum whose wavelengths are between 380 nm < λ < 780 nm. The absorption spectrum of ZnS is an important element that characterizes its absorption power when subjected to illumination. It is all the more significant as it extends over a frequency band that is difficult to absorb by other materials. The important element to characterize it is the value of the band gap of the material. The energy value of the band gap, *Eg* of ZnS can be determined by an optical approach through its absorption spectrum. The formula that describes light absorption ability of a material given his band gap is well highlighted by Rayan, Elseman and co-workers [14–16] and is given by:

$$\left(ab\nu\right)^{2} = A\left(h\nu - E\_{\text{g}}\right) \tag{1}$$

• **Second window layer: i-ZnO**

*DOI: http://dx.doi.org/10.5772/intechopen.93817*

*One-dimensional structure of the cell.*

• **First window layer: ZnO: B**

• **The buffer layer: ZnS**

attributed to it:

interface;

**91**

ambient conditions [20].

**Figure 1.**

Zinc oxide is a semiconductor belonging to group II-VI with a number of properties that make it a material widely used in several fields, these are its piezoelectricity, its wide band gap and its intrinsic doping type N. It can exhibit an N-type doping process, for example by adding the atoms of Al, Ga and B and it also exhibits an N-type conductivity due to structural defects. Its forbidden band is 3.3 eV and can vary by adding Mg, Cd or S atoms. It can crystallize according to the Zinc Blende, wurtzite or diamond structures. Only the wurtzite structure is stable under

*Thin-Film Solar Cells Performances Optimization: Case of Cu (In, Ga) Se2-ZnS*

Most CIGSe-based solar cells use Aluminum-doped Zinc oxide (ZnO: Al) as the Transparent Conductive Oxide (TCO). Within the framework of this work we opt for ZnO doped with boron (ZnO: B) as OCT. Boron doping would be more beneficial for solar cells. Its standard thickness varies between 450 and 1400 nm [18].

Its standard thickness varies between 40 and 60 nm. It has an N-type conductivity and its gap is greater than that of the absorber layer. Three roles are mainly

• **An electrical role**: it adapts the width of the forbidden band between the absorber and the window layer and limits the recombination of carriers at the

• **An optical role**: due to its wide forbidden band (*Eg* = 3.68 eV), it makes it possible to absorb the maximum of the light spectrum in the region not

absorbed by the active layer and thus minimizes optical losses;

This formula is only valid for authorized direct transitions. *α* is the absorption coefficient, *A* is a constant to be determined, ɦ is Planck's constant and *ν* is the frequency of the incident photon.

Literature tells us that ZnS is a semiconductor with a wide band gap (> 3.5 eV). This wide band gap gives it high optical transparency in the visible and infrared regions of the solar spectrum and a high absorption coefficient in the ultraviolet region. Its transmission spectrum is recorded between 400 and 850 nm [17], which allows the transmission of photons of higher energy, thus increasing the absorption of the light spectrum in the absorber layer.

It is also a direct gap semiconductor. Indeed, the maximum of the valence band and the minimum of the conduction band are found at the centre of the Brillouin zone (where *K* ! ¼ 0). The transitions are made from band to band without the

intervention of phonons, therefore without loss or dissipation of energy in thermal form [18].

The refractive index of ZnS is 2.41 to 0.5 μm and 2.29 to 1.1 μm in depth [19]. Remember that the electronic structures of Sulfur and Zinc are:

$$Zn: [Ar] \text{4d}^{10} \text{Sr}^2 \text{ S}: [Ne] \text{3d}^2 \text{\textdegree} p^4$$

The 3*p* states of Sulfur form the valence band, the 5 *s* states of Zinc constitute the conduction band. This gives ZnS a wide forbidden band. This wide band gap makes it a very promising material for optoelectronic and solar applications. Its forbidden band is between 3.68 eV and 3.9 eV depending on whether we are in a cubic or hexagonal structure. This band gap value may vary depending on the preparation method and the doping rate [19]. We can also find from the literature that it has a relatively high exciton binding energy (34 *meV*); its structure exhibits a better lattice matching with absorbers having energy bands in the range (1,2–1,5 *eV*) [13] and finally it has a high electrons mobility (165 *cm*2/*V. s*).

#### *3.1.3 Structure of our solar cell*

In its most common structure, a CIGSe-based cell is formed by a stack of several thin film materials deposited successively on a substrate. Let us consider the following structure:

(Ni/Al)/MgF2/ZnO: B/i-ZnO/ZnS/CuInGaSe2/Mo/SLG (**Figure 1**).

*Thin-Film Solar Cells Performances Optimization: Case of Cu (In, Ga) Se2-ZnS DOI: http://dx.doi.org/10.5772/intechopen.93817*

**Figure 1.**

*One-dimensional structure of the cell.*


**Meet the editors**

Dr. Majid Nayeripour was born in Shiraz, Iran. He received his PhD in Electrical Engineering form Tarbiat Modares University, Tehran, Iran and is currently an assistant professor at Shiraz University of Technology, Shiraz, Iran. He has published more than 60 journal and conference papers, as well as three books. His research interests include Renewable Energy, FACTS Devices and

Power Quality and Impacts of DGs in Power System.

BSc. Mostafa Kheshti was born in Noorabad Mamasani, Iran in 1987. He received his BSc in Electrical Engineering from Shiraz University of Technology. Apart from serving as a technical expert for the Fars Regional Electric Company, he has also published several papers and books, as well as managed several projects. Currently, he is a Master Student at Xi'an Jiaotong University, China.

His research interests include Renewable Energy, Distributed Generation, Smart Grids, Power System and Protection.

Contents

**Preface IX**

**Part 1 Sustainable Growth 1**

Chapter 2 **Sustained Renewability:**

Pius Fatona

Tobias A. Knoch

Ali Osman Yılmaz

Chapter 6 **Taxes Incentives to Promote**

**Part 2 Applications 123**

Chapter 5 **Experiences of Community Wind**

Chapter 1 **EU Energy Policies and Sustainable Growth 3**  Carlo Andrea Bollino and Silvia Micheli

Chapter 3 **Renewable Energy Use and Energy Efficiency –**

Chapter 4 **Renewable Energy and Coal Use in Turkey 61**

**Electrification Projects in Bolivia:**

Laia Ferrer-Martí, Bruno Domenech, Walter Canedo, Carlos Reza, Mirtha Tellez,

Rocío Román and Rocío Yñiguez

Chapter 7 **Structural Design of a Dynamic Model of**

**Res Deployment: The Eu-27 Case 107**  José M. Cansino, María del P. Pablo-Romero,

Frédéric Coupan, Ahmed Abbas, Idris Sadli, Isabelle Marie Joseph and Henri Clergeot

**Approached by Systems Theory and Human Ecology 21**

**A Critical Tool for Sustainable Development 49**

**Evaluation and Improvements for Future Projects 85**

Milton Dominguez, Lorenzo Perone and Jaime Salinas

**the Battery for State of Charge Estimation 125**


**2. Methods of water flow analysis**

#### **2.1. Analytical solutions**

#### *2.1.1. Exact solution*

An exact analytical solution is generally only possible to obtain when the geometry of the flux domain and the hydraulic and boundary conditions are simple (isotropic and homogeneous media). However, soil is a heterogeneous, anisotropic, and discontinuous medium that has different characteristics at each point. Thus, exact solutions are difficult and impractical to obtain in the case of the most complex flow problems, such as those in practical geotechnical engineering. In consequence, approximate solutions are usually sought.

#### *2.1.2. Conformal transformation or mapping*

One of the approximate analytical solutions that is used to solve two-dimensional water flow problems involves obtaining a function that can transform the problem from the complex geometric domain into a problem whose solution is known [7]. These functions transform geometric shapes from a complex plane *ω* into shapes in another complex plane *ζ*. Thus, the mapping procedure defines the correspondence of the points of one shape in a plane *ω* to the points of the respective figure in the plane *ζ*. A transformation or mapping function is called conformal (conformal mapping) when it does not change the angles of intersection or the approximate geometric shapes between the two planes of interest [8]. Based on this concept, the Laplace differential equation can be solved for a domain *G* (**Figure 2b**) if the transformation or conformal mapping of this domain with a simpler domain *G*1 (**Figure 2a**) is known [8–10]. The transformation is carried out by means of the analytical function of a complex variable. One of the best known functions that transform a system of uniform flux in the *ω* plane (**Figure 2a**) into a system of flux with confocal parabolas in the *ζ* plane (**Figure 2b**) is as follows (representing the well-known Kozeny's solution for unconfined flow through dams, **Figure 3**):

$$
\zeta = \alpha^2 \tag{6}
$$

**Figure 2.** Conformal mapping [7].

**Figure 3.** Kozeny's solution for water flow through an earth dam with a horizontal filter [7].

#### *2.1.3. Method of fragments*

obtain in the case of the most complex flow problems, such as those in practical geotechnical

One of the approximate analytical solutions that is used to solve two-dimensional water flow problems involves obtaining a function that can transform the problem from the complex geometric domain into a problem whose solution is known [7]. These functions transform geometric shapes from a complex plane *ω* into shapes in another complex plane *ζ*. Thus, the mapping procedure defines the correspondence of the points of one shape in a plane *ω* to the points of the respective figure in the plane *ζ*. A transformation or mapping function is called conformal (conformal mapping) when it does not change the angles of intersection or the approximate geometric shapes between the two planes of interest [8]. Based on this concept, the Laplace differential equation can be solved for a domain *G* (**Figure 2b**) if the transformation or conformal mapping of this domain with a simpler domain *G*1 (**Figure 2a**) is known [8–10]. The transformation is carried out by means of the analytical function of a complex variable. One of the best known functions that transform a system of uniform flux in the *ω* plane (**Figure 2a**) into a system of flux with confocal parabolas in the *ζ* plane (**Figure 2b**) is as follows (representing the well-known Kozeny's solution for unconfined flow through dams, **Figure 3**):

2

= (6)

z w

engineering. In consequence, approximate solutions are usually sought.

*2.1.2. Conformal transformation or mapping*

94 Groundwater - Contaminant and Resource Management

**Figure 2.** Conformal mapping [7].

The method of fragments is an approximate analytical method of solution for confined flow domains of finite depth. The fundamental assumption is that equipotential lines at different parts of the flow region can be approximated by straight vertical lines that divide the flow region into sections or fragments (**Figure 4**) [8, 11]. This method requires a form factor Φ that is obtained by solving definite integrals set up for each fragment of the flow region. Tables of expressions for different form factors for typical confined flow problems have been developed [8, 11]. The equation for calculating the discharge *q* through all fragments using this method is as follows:

$$q = k \frac{\sum \Delta h\_n}{\sum \Phi\_n} = \frac{k \cdot \Delta h}{\sum\_{n=1}^{n} \Phi\_n} \tag{7}$$

where *k* = hydraulic conductivity of the homogeneous and isotropic medium, Δ*hn* = loss of hydraulic head through fragment *n*, Δ*h* = total loss of hydraulic head, and Φ*n* = dimension‐ less form factor in fragment *n*.

**Figure 4.** Schematic representation of the method of fragments.

The method of fragments was originally proposed to study confined flow in homogeneous and isotropic media, but at present, it has been implemented in anisotropic media [12]. In combination with conformal mapping and the Kozeny's parabola, it has also been applied to solve problems of unconfined flow through homogeneous levees with horizontal filters [13].

#### **2.2. Graphical solutions**

#### *2.2.1. Confined flow*

The most popular approximation technique for solving water flow problems is known as the flow net. It is a graphical method that sets up two functions that satisfy the Laplace's equation and that geometrically constitute two families of orthogonal curves: (a) equipotential lines (constant potential *ϕ*) and (b) flow lines or streamlines (constant values of the stream function *ψ*). The graphical representation of these lines is the so-called flow net. A drawing that satisfies the boundary and orthogonality conditions allows water flow problems with homogeneous and isotropic soil to be solved simply and graphically. The expression that calculates the discharge or rate of seepage *q* using a flow net is as follows:

$$q = k \,\Delta h (\frac{n\_f}{n\_e}) = k \,\Delta h \,\text{S} \tag{8}$$

where *k* = hydraulic conductivity of the homogeneous and isotropic medium, Δ*h* = total loss of hydraulic head, *\$* = *nf* /*ne* is the form factor, *nf* = number of flow intervals or flow channels, and *ne* = number of equipotential intervals.

Flow nets are typically drawn on paper. However, nowadays, it is possible to draw flow nets by computer using several numerical techniques based on finite element method (FEM) or finite difference equations [14], such as successive over-relaxation (SOR) [15]. Examples of flow nets that were drawn using these techniques in confined homogeneous and stratified domains are shown in **Figures 5(a and b)**–**7**.

#### *2.2.2. Unconfined flow*

Free surface problems involve boundary value problems in which a portion of the boundary, the free surface, is unknown and must be determined as part of the solution. The presence of the free surface or water table makes the analysis methods more difficult. Dupuit's parabola [16] and Kozeny's parabola [17] are rigorous solutions for drawing the upper flow line and are only applicable for homogenous and isotropic media with specific geometries, such as vertical walls (Dupuit) or with filters (Kozeny). Other approximated methods, such as the *tangent* [18, 19] and *sine* methods [20], allow mainly calculate the discharge point of the upper flow line. Currently, this can be determined using numerical methods such as finite element method (FEM) and finite differences (FD), among others. The Baiocchi's method [21] and the extended pressure technique [22] are two variants of the successive over-relaxation (SOR) method (based on algebraic finite difference equations) that can be used to determine the position of the upper flow line in homogeneous media or media composed of materials with different permeability values, respectively.

The method of fragments was originally proposed to study confined flow in homogeneous and isotropic media, but at present, it has been implemented in anisotropic media [12]. In combination with conformal mapping and the Kozeny's parabola, it has also been applied to solve problems of unconfined flow through homogeneous levees with horizontal filters [13].

The most popular approximation technique for solving water flow problems is known as the flow net. It is a graphical method that sets up two functions that satisfy the Laplace's equation and that geometrically constitute two families of orthogonal curves: (a) equipotential lines (constant potential *ϕ*) and (b) flow lines or streamlines (constant values of the stream function *ψ*). The graphical representation of these lines is the so-called flow net. A drawing that satisfies the boundary and orthogonality conditions allows water flow problems with homogeneous and isotropic soil to be solved simply and graphically. The expression that calculates the

> () \$ *f e*

where *k* = hydraulic conductivity of the homogeneous and isotropic medium, Δ*h* = total loss

Flow nets are typically drawn on paper. However, nowadays, it is possible to draw flow nets by computer using several numerical techniques based on finite element method (FEM) or finite difference equations [14], such as successive over-relaxation (SOR) [15]. Examples of flow nets that were drawn using these techniques in confined homogeneous and stratified domains

Free surface problems involve boundary value problems in which a portion of the boundary, the free surface, is unknown and must be determined as part of the solution. The presence of the free surface or water table makes the analysis methods more difficult. Dupuit's parabola [16] and Kozeny's parabola [17] are rigorous solutions for drawing the upper flow line and are only applicable for homogenous and isotropic media with specific geometries, such as vertical walls (Dupuit) or with filters (Kozeny). Other approximated methods, such as the *tangent* [18, 19] and *sine* methods [20], allow mainly calculate the discharge point of the upper flow line. Currently, this can be determined using numerical methods such as finite element method (FEM) and finite differences (FD), among others. The Baiocchi's method [21] and the extended pressure technique [22] are two variants of the successive over-relaxation (SOR) method (based on algebraic finite difference equations) that can be used to determine the position of the upper

*n q kh kh n* =D =D (8)

/*ne* is the form factor, *nf* = number of flow intervals or flow channels,

discharge or rate of seepage *q* using a flow net is as follows:

**2.2. Graphical solutions**

96 Groundwater - Contaminant and Resource Management

of hydraulic head, *\$* = *nf*

*2.2.2. Unconfined flow*

and *ne* = number of equipotential intervals.

are shown in **Figures 5(a and b)**–**7**.

*2.2.1. Confined flow*

**Figure 5.** Flow nets in homogeneous and isotropic media obtained using the method of successive over-relaxations (SOR) [23].

**Figure 6.** Flow net in a homogeneous and isotropic medium obtained using the finite element method (FEM) [24].

**Figure 7.** Flow net in a stratified soil under an impermeable dam obtained using the method of successive over-relaxa‐ tions (SOR) [23].

A simple graphical procedure to draw the Kozeny's parabola or any parabolic upper flow line in a homogeneous and isotropic medium is as follows (**Figure 8a**): (a) The distance *a0* is calculated with the formula *a0* = *y0/2* = *[(d2* + *h2 ) 1/2-d]/2*; (b)Draw a vertical line through *O* and also a horizontal line through *M*; (c) Divide the *OB* segment in a number of equal parts, and the *MB* segment must also be divided into the same number of equal parts; (d) Draw straight lines joining the point *O* with the divisions made in the *MB* segment; (e) Draw horizontal lines passing through the divisions made in the *OB* segment; (f) The intersections of the previous lines are the points of the parabola sought. **Figures 8(b)** and **9** show upper flow lines obtained using this graphical procedure and other numerical methods. Additionally, **Figures 10** and **11** show flow nets that were numerically calculated in these types of free surface problems.

**Figure 8.** Homogeneous and isotropic embankment: (a) graphical procedure to draw the upper flow line, (b) compari‐ son of the upper flow lines obtained using different methods [14].

**Figure 9.** Comparison of the upper flow lines in a homogeneous and isotropic embankment, obtained using different methods [14].

**Figure 10.** Flow net in a homogeneous and isotropic embankment numerically calculated using the extended pressure technique [14].

**Figure 11.** Flow net in a dam with graded materials obtained using the extended pressure technique [23].

#### **2.3. Numerical solutions (approximate solutions)**

#### *2.3.1. Finite elements*

**Figure 8.** Homogeneous and isotropic embankment: (a) graphical procedure to draw the upper flow line, (b) compari‐

**Figure 9.** Comparison of the upper flow lines in a homogeneous and isotropic embankment, obtained using different

**Figure 10.** Flow net in a homogeneous and isotropic embankment numerically calculated using the extended pressure

son of the upper flow lines obtained using different methods [14].

98 Groundwater - Contaminant and Resource Management

methods [14].

technique [14].

The finite element method (FEM) is a numerical technique that provides approximate solutions to partial differential equations to solve a problem of a particular field. It is more versatile than other methods because it can consider anisotropy, heterogeneity, and multiple boundary conditions. The 2D finite elements that are generally used in water flow problems are triangles [25] or a combination of triangles and squares [26] whose nodes coincide with their vertices; in addition, triangles (2D) and tetrahedra (3D) can be used [27]. The hydraulic head is assumed to vary linearly within each finite element, and the Laplace's equation can be solved using a variational approach. Thus, the solution to this equation in a domain is found by obtaining the minimum of a function that is related to the equation and is defined for this domain. Based on these assumptions and after several mathematical manipulations, the following systems of homogeneous linear equations are set up:

$$\{S\}\{h\_r\} = 0\tag{9}$$

$$\{S\}\{\psi\_r\} = 0\tag{10}$$

The solution to Eq. (9) using a known method, such as Gaussian elimination, helps to determine the hydraulic head *h* at the nodes in the mesh of finite elements where it is unknown. Similarly, the solution to Eq. (10) provides nodal values of the stream function *ψ*. The flow net of the problem can be obtained by drawing the isovalue curves for this pair of families. Likewise, once the hydraulic heads *h* are calculated with Eq. (9), other results for the water flow problem can be obtained, such as the hydraulic gradients, flow velocities, pore pressure, degree of saturation, and flow rate, among others.

#### *2.3.2. Finite differences*

The Laplace's equation can be solved using finite difference equations, which are the same as those developed via truncated Taylor series or directly from Darcy's Law [4]. Several methods can be used to evaluate water flow problems that utilize finite differences, including: (a) the classical method of relaxations, (b) the method of successive over-relaxations, and (c) random walks.

#### *<IP_ADDRESS>. Classical method of relaxations*

The classical relaxation method is an iterative process in which solutions for water flow through porous media can be obtained by simply knowing the domain geometry and hy‐ draulic boundary conditions. This method can solve Laplace's equation for a point (node) relative to its surrounding points using an algebraic finite difference equation. For this procedure, a square mesh with dimensions of *δx* = *δy* is drawn in the flow zone if the medium is homogenous and isotropic (similar to those in **Figure 11a** and **b**), and a rectangular mesh with dimensions of *δx* ≠ *δy* is drawn if the medium is anisotropic. The intersections of the squares or rectangles constitute the nodes of the mesh. For these nodes, approximate values of the hydraulic head or potential *h* (points where *h* requires to be calculated) must be assigned while respecting the known values of *h* in the flow boundaries. These values usually correspond to the upper and lower water levels or the upstream water level and downstream water level of the problem at hand. The values assigned in the nodes are arbitrary and can be zero or the result of a reasonable estimation. However, although there are several techniques that can be used to ensure that the value of the potential imposed on the nodes where *h* is not known is as accurate as possible (Young, 1950), it is important to verify the precision of the assigned data manually by calculating the residue in each node [28]. For example, the difference between the hydraulic potential of the four surrounding nodes is calculated with regard to the central or interior node and so on. Therefore, the relaxation procedure involves the systematic refinement of this residue throughout the grid until the residue in all mesh nodes of interest is zero or practically zero. This value indicates that the Laplace's equation in the study domain has been fulfilled, and therefore, the flow problem has been solved for a certain water flow problem. A disadvantage of the method of relaxations is that it is based on assigning arbitrary values to the nodes in the study mesh, which makes it difficult for the residuals to equal zero at an early stage of calculation. As a result, additional steps of reassigning values are generally necessary, which makes the method long and laborious in practice.

#### *<IP_ADDRESS>. Technique of successive over-relaxation*

The technique of successive over-relaxation (SOR) [15] is a modification of the classical method of relaxations in which the process of residual refinement at the nodes is automatic because it utilizes the Gauss-Seidel iterative method (**Figure 12**); this makes it possible to obtain residuals of zero or nearly zero at all the nodes, which allows water flow problems to be solved relatively quickly and easily [29, 30]. An additional significant advantage of the SOR method is that it can solve the so-called free surface problems (or unconfined flow problems), in which the position of the free (or phreatic) surface must be determined to solve the problem. Other improvements to the SOR method have been developed for this type of problem, including (a) the Baiocchi's solution [21] and (b) the extended pressure method [31, 22]. The former method helps to determine the position of the phreatic surface (upper flow line for steady-state flow) in a homogeneous medium (**Figure 10**), and the latter method helps to determine this line in both homogeneous and heterogeneous media (**Figure 11**) [14].

**Figure 12.** Schematic arrangement of nodes in the dam of graded materials in **Figure 11** using the extended pressure method [23].

#### *2.3.3. Random walks*

classical method of relaxations, (b) the method of successive over-relaxations, and (c) random

The classical relaxation method is an iterative process in which solutions for water flow through porous media can be obtained by simply knowing the domain geometry and hy‐ draulic boundary conditions. This method can solve Laplace's equation for a point (node) relative to its surrounding points using an algebraic finite difference equation. For this procedure, a square mesh with dimensions of *δx* = *δy* is drawn in the flow zone if the medium is homogenous and isotropic (similar to those in **Figure 11a** and **b**), and a rectangular mesh with dimensions of *δx* ≠ *δy* is drawn if the medium is anisotropic. The intersections of the squares or rectangles constitute the nodes of the mesh. For these nodes, approximate values of the hydraulic head or potential *h* (points where *h* requires to be calculated) must be assigned while respecting the known values of *h* in the flow boundaries. These values usually correspond to the upper and lower water levels or the upstream water level and downstream water level of the problem at hand. The values assigned in the nodes are arbitrary and can be zero or the result of a reasonable estimation. However, although there are several techniques that can be used to ensure that the value of the potential imposed on the nodes where *h* is not known is as accurate as possible (Young, 1950), it is important to verify the precision of the assigned data manually by calculating the residue in each node [28]. For example, the difference between the hydraulic potential of the four surrounding nodes is calculated with regard to the central or interior node and so on. Therefore, the relaxation procedure involves the systematic refinement of this residue throughout the grid until the residue in all mesh nodes of interest is zero or practically zero. This value indicates that the Laplace's equation in the study domain has been fulfilled, and therefore, the flow problem has been solved for a certain water flow problem. A disadvantage of the method of relaxations is that it is based on assigning arbitrary values to the nodes in the study mesh, which makes it difficult for the residuals to equal zero at an early stage of calculation. As a result, additional steps of reassigning values are generally

necessary, which makes the method long and laborious in practice.

The technique of successive over-relaxation (SOR) [15] is a modification of the classical method of relaxations in which the process of residual refinement at the nodes is automatic because it utilizes the Gauss-Seidel iterative method (**Figure 12**); this makes it possible to obtain residuals of zero or nearly zero at all the nodes, which allows water flow problems to be solved relatively quickly and easily [29, 30]. An additional significant advantage of the SOR method is that it can solve the so-called free surface problems (or unconfined flow problems), in which the position of the free (or phreatic) surface must be determined to solve the problem. Other improvements to the SOR method have been developed for this type of problem, including (a) the Baiocchi's solution [21] and (b) the extended pressure method [31, 22]. The former method helps to determine the position of the phreatic surface (upper flow line for steady-state flow)

*<IP_ADDRESS>. Technique of successive over-relaxation*

walks.

*<IP_ADDRESS>. Classical method of relaxations*

100 Groundwater - Contaminant and Resource Management

The random walk method (RWM) consists of studying the movements of a particle that travels in a random way over the nodes of a mesh of a flow domain (**Figure 13a** and **b**), which allows the hydraulic head to be determined at points of interest by numerical solution of the Laplace's equation in terms of finite differences. This method relies on the so-called Monte Carlo techniques [32, 33], which are an alternative to the usual methods of water flow analysis. Specifically, the method generates a series of random trajectories (via random numbers) that start from node *p*0 in the mesh. Thus, the particle moves randomly through the interior nodes of the mesh and stops when it reaches a boundary node, which is called an absorbent node, because the value of the hydraulic head at that node is known (imposed boundary condition).  The hydraulic head is then determined by counting the number of trajectories that end at different boundaries, multiplying them by the value of the hydraulic head at the respective boundary and dividing the result by the total number of trajectories. This procedure is repeated several times, and the results are an unbiased measure of the hydraulic head at the node of interest:

$$h\_0 = \frac{n\_1 f\_1 + n\_2 f\_2}{n\_1 + n\_2} \tag{11}$$

where *h*0 = hydraulic head calculated at point *p*0 (**Figure 13b**), *f*1 and *f*2 = boundaries with known hydraulic heads, and *n*1 and *n*2 = number of trajectories that reach boundaries 1 and 2, respectively.

**Figure 13.** 2D and 3D meshes with which the homogeneous and isotropic flow regions are modelled by the random walk method [24].

The RWM has been utilized to solve confined water flow problems [33] and also to calculate the equivalent permeability *k*equivalent in simulated heterogeneous media (**Figure 14**) [24]:

**Figure 14.** Example of a random walk with the PASECA-2003 algorithm [24].

#### **2.4. Stochastic solutions**

The uncertainty due to the spatial variation of permeability is the most important factor that must be taken into account in the analysis of water flow through soils. **Figure 15** summarizes the main techniques that are used to evaluate the propagation of this uncertainty. It is common to utilize probabilistic techniques in combination with numerical methods, such as finite elements (FEM), finite differences (FDM), integral equations (BEM), and random walks (RWM). A stochastic analysis permits a more realistic evaluation of water flow problems and can be useful in defining zones of uncertainty, which can be used to identify the parts of the flow region that are prone to significant variations in properties such as the hydraulic head and hydraulic gradient, as is illustrated in **Figures 16** and **17**, respectively, [24]

**Figure 15.** A summary of the main techniques that are used to evaluate uncertainty in water flow analyses [24].

**Figure 13.** 2D and 3D meshes with which the homogeneous and isotropic flow regions are modelled by the random

The RWM has been utilized to solve confined water flow problems [33] and also to calculate the equivalent permeability *k*equivalent in simulated heterogeneous media (**Figure 14**) [24]:

The uncertainty due to the spatial variation of permeability is the most important factor that must be taken into account in the analysis of water flow through soils. **Figure 15** summarizes the main techniques that are used to evaluate the propagation of this uncertainty. It is common to utilize probabilistic techniques in combination with numerical methods, such as finite elements (FEM), finite differences (FDM), integral equations (BEM), and random walks (RWM). A stochastic analysis permits a more realistic evaluation of water flow problems and can be useful in defining zones of uncertainty, which can be used to identify the parts of the

**–** 1D water flow analysis→ *k*equivalent is the harmonic mean **–** 2D water flow analysis→ *k*equivalent is the geometric mean

102 Groundwater - Contaminant and Resource Management

**–** 3D water flow analysis→ *k*equivalent tends to the arithmetic mean

**Figure 14.** Example of a random walk with the PASECA-2003 algorithm [24].

walk method [24].

**2.4. Stochastic solutions**

**Figure 16.** Standard deviation of the hydraulic head (m) under a sheet pile in a medium of two stratified isotropic ma‐ terials [24].

**Figure 17.** Standard deviation of the (dimensionless) hydraulic gradient under a spillway structure in a medium of two stratified isotropic materials [24].


**7.1 Poly immunoglobulin receptor (pIgR)**

The transfer of IgA from the production site in the mucosal and glandular tissue areas to the secretions takes place in an active process with the involvement of membrane polymer receptors (**Figure 5**).

The pIgR receptor is a membrane glycoprotein consisting of five Ig-like domains (reinforced with disulfide bounds) at the cell surface, an intramembrane fragment, and a 100-amino acid sequence within the cytoplasm.

The human immunoglobulin polymer receptor gene is located on chromosome 1. The genes of these receptors in epithelial cells are affected by cytokines such as IFN-γ in vitro and are expressed on the surface of these cells. Therefore, it can be said that mucosal inflammation has an aggravating role in the transfer of slgA to secretions [1, 66].

#### **Figure 5.**

*Mechanism of IgA dimer production in lamina propria and its transmission by epithelial cells. Lamina propria plasma cells produce IgA dimers (A). These antibodies are transported into the epithelial cells via pIgR at the basal surface (B). Following the release of IgA from the luminal surface of these cells by the mechanism of transcytosis (C), due to proteolytic cleavage, part of the receptor remains attached to the IgA dimer, which is the secretory component or SC (D).*

#### **7.2 Binding of IgA to the immunoglobulin receptor**

IgA binds to the first Immunoglobulin-like domain of the Poly-Ig receptor. Following the separation of pIgR from the epithelial cell, a disulfide bond is established between the cysteine of the fifth SC region and the Fc portion of one of the IgA monomer monomers. Domains 2, 3, and 4 of the secretory component do not participate in the binding but are necessary for the establishment of the two cysteine roots [66].


Customized implants

The clinical unmet need addressed by customized 3D printed titanium acetabular implants was the poor outcome resulting from the use of conventionally manufactured triflange implants, jumbo cup, cages and augments to reconstruct massive acetabular defects [14–18]. These defects most commonly occur following previous failed implants. Conventionally manufactured implants failed due to poor fixation to the bone as a result of the complex shape of the defect and low surface area of host bone with good blood supply. 3D printed implants have overcome both of these problems (Figure 1a).

**Figure 1.** Images showing backside and internal surface of (**a**) custom and (**b**) off-the-shelf 3D printed implants. Post-operative X-ray images are also shown.


*5.5.2 Animal feed*

Collagen peptide due to its organic compounds such as fats, proteins and minerals plays an important role in the preparation of highly valuable animal feed [84]. Fat, protein and mineral products are in especially high demand in the animal feed industry because pure fats are excellent sources of energy and collagen is of importance for the healthy growth of animals [138].

As a collagen peptide, which is recovered from leather solid wastes, gelatin is primarily added to animal feed based on its hydrophilic properties. Its jelly-like consistency holds feed together, making it transportable and extends its shelf life [107, 139]. When animal feed is enriched with vitamins, the gelatin coatings also protect these from light and oxygen. A positive side effect of adding gelatin to feed ensures that the fur of animal remains wonderfully glossy [107, 140].

There are also many fields for collagen peptides and gelatin usage. They can be used for photography and X-ray films and inkjet applications [141], industrial paper production [93], leather board [142], glue manufacture [143], feedstock for biodiesel production [144], leather tanning and retanning agent [145] and many more specific applications, etc.


**5. Conclusions**

Our investigations identify GSTO2 isoforms as functionally active surface-borne enzymes on mouse and boar spermatozoa. We propose that GSTO2 may facilitate the regulation of the oxidative environment of the plasmalemma indirectly, through the replenishment of antioxidant molecules such as ascorbic acid and glutathione. Overall, this study highlights the importance of oxidative-reductive regulation and demonstrates the wide-reaching negative implications its dysregulation can have on overall sperm fitness.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2076-3921/8/12/601/s1, Figure S1: Mouse and boar GSTO sequence comparison, Figure S2: GSTO inhibitor binding specificity in whole mouse and boar spermatozoa, Figure S3: The Assessment of sperm viability between treatment groups, Figure S4: The level of protein tyrosine phosphorylation during in vitro capacitation in boar spermatozoa, Figure S5: The difference in cellular reactive oxygen species (ROS) levels of GSTO Inhibited and Control capacitated spermatozoa.

**Author Contributions:** Conceptualization, L.E.H., P.S., C.O. and R.O.; Data curation, L.E.H., M.Z., J.M. and W.X.; Formal analysis, L.E.H.; Funding acquisition, R.O.; Investigation, L.E.H., M.Z., J.M., W.X. and C.O.; Methodology, L.E.H., M.Z., W.X., C.O. and R.O.; Supervision, P.S. and R.O.; Writing—original draft, L.E.H. and R.O.; Writing—review and editing, M.Z., J.M., P.S., C.O. and R.O.

**Funding:** This research was funded by the Canadian Institute of Health Research (84440) and the Natural Science and Engineering Research Council of Canada (RGPIN/05305) to RO and the Agriculture and Food Research Initiative Competitive Grant no. 2015-67015-23231 from the USDA National Institute of Food and Agriculture and seed funding from the Food for the 21st Century Program of the University of Missouri to PS.

**Acknowledgments:** We would like to express our thanks to the National Swine Research and Resource Center sta ff for their help with semen collection and process.

**Conflicts of Interest:** The authors declare no conflict of interest.