*2.1. Materials and Sample Preparation*

The primer (coating) was a high-solids formulation based on a polyurethane resin with polyisocynate crosslinker, and formulated to a pigment volume concentration (PVC) of 30%, as described elsewhere [43]. The inorganic pigments included Li2CO3, Mg-(hydr)oxide and BaSO4 fillers and TiO2. Trace element analyses of the various inorganic components of the paint indicated that the BaSO4 contained 0.9%m/m Sr, and small amounts of Si, Ca, Al and Ti. The MgO contained 1500–1900 ppm by weight of Ca, 400–700 ppm by weight K and lesser amounts of other elements (Table 1). The Li2CO3 contained alkali metals (Na, K) in the range 400–800 ppm by weight. Particle size distributions for these additives were determined by dispersing in a solvent, which was methylethylketone for Mg-(hydr)oxide, TiO2 and Li2CO3, where water was used for the BaSO4. The BaSO4 particles had the largest particles (up to 50 μm) and the largest spread in particles size. The TiO2 particles were the smallest (up to 14 μm) and slightly smaller than the Mg-(hydr)oxide. The Li2CO3 had the largest size at the lowest end of the distribution and ranged up to 18 μm.

AA2024-T3 was used as a substrate for coating; typical breakdown for this alloy is reported elsewhere [51]. The AA2024-T3 was prepared by standard anodising according to aerospace requirements (AIPI 02-01-003) at Premium AEROTEC, Bremen Germany. This included the following steps: degrease, alkaline clean, acid desmutting followed by anodising in tartaric-sulphuric acid to produce a 2–3 μm thick oxide layer. Subsequently, the primer was applied by spraying using a high-volume, low-pressure (HVLP) spray gun in a single pass to achieve a dry film thickness of approximately 30 μm. In practice, the coating was typically 30 to 40 μm. Finally, the primer was cured for 16 h at 23 ◦C/55% RH, followed by a 30 min baking cycle at 80 ◦C.

**Table 1.** Chemical composition of inorganic additives used in this study.


*3.1. Antihypertensive E*ff*ects*

Hypertension increases the risk of cardiovascular disease [84]. Antihypertensive compounds in foods have been identified using a stroke-prone spontaneously hypertensive (SHRSP) rat model, which is genetically predisposed to hypertension and cerebral stroke [85]. Sansawa et al. [86] investigated the e ffects of dried *Chlorella* powder (*C. regularis*) on blood pressure, cerebral stroke lesions, and the life span of SHRSP rats. In 12-week-old SHRSP rats fed *Chlorella* (5%, 10%, and 20%) for 13 weeks, elevated blood pressure significantly decreased in the 10% and 20% *Chlorella* groups compared with the untreated controls. Serum total cholesterol levels were significantly lower in all *Chlorella* groups, and their average life span was more than that of the controls. To characterize the antihypertensive compounds in *Chlorella*, *Chlorella* powder was fractionated into hot-water-soluble, lipid-soluble, and residual fractions. Blood pressure was significantly lower in rats fed the lipid or residual fraction but not in those fed the hot-water-soluble fraction. The lipid fraction contained substantial amounts of carotenoids, which are potent antioxidants, and phospholipids, which mediate aorta collagen and elastin metabolism. The residual fraction contained a high level of arginine, which increases the production of endothelium-derived relaxing factor. These beneficial e ffects of *Chlorella* powder on SHRSP rats might result from synergism between its numerous bioactive compounds.

To evaluate whether daily *Chlorella* supplementation can reduce blood pressure in subjects with mild to moderate hypertension, a pilot study was conducted in 24 participants administered *C. pyrenoidosa* (10 g of *Chlorella* tablets and 100 mL *Chlorella* extract) [87]. After two months of *Chlorella* supplementation, the average heart rate and sitting systolic and diastolic blood pressures only slightly changed. On the other hand, for some subjects with mild to moderate hypertension, *Chlorella* supplementation reduced or maintained their sitting diastolic blood pressure.

Arterial sti ffness is a well-established risk factor of cardiovascular disease [88]. Previous studies have reported that antioxidants [89], potassium [90], and *n*-3 unsaturated fatty acids [91] decrease arterial sti ffness. Nitric oxide (NO), derived from arginine in the vascular endothelium, is an important modulator of arterial sti ffness [92]. *Chlorella* products contain antioxidants, vitamins, potassium, arginine, and *n*-3 unsaturated fatty acids. To evaluate the e ffects of *Chlorella* supplementation on arterial sti ffness, a single-blinded, placebo-controlled crossover study was conducted in 14 young participants who were administered *C. pyrenoidosa* (6 g/day) or placebo for four weeks, with a 12-week washout period between trials, in a randomized order [93]. No di fferences were observed in blood pressure or heart rate before and after supplementation in both the placebo and *Chlorella* groups. Brachial-ankle pulse wave velocity, a measure of arterial sti ffness, decreased in the *Chlorella* group but not in the placebo group [93]. A similar trial in 32 middle-aged and older subjects reports that the brachial-ankle pulse wave velocity decreased after *Chlorella* supplementation but not after placebo supplementation [94]. These changes in brachial-ankle pulse wave velocity with *Chlorella* supplementation correlated with the plasma NOx level. These results suggest that *Chlorella* supplementation decreases arterial sti ffness in both younger and older subjects.

The e fficacy of *Chlorella* supplementation in reducing cardiovascular risk factors was assessed in a meta-analysis of 19 randomized controlled trials including 797 subjects [95].  Antihypercholesterolemic and Antihyperlipemic E*ff*ects*

Elevated total cholesterol and triglycerides and abnormal metabolism of lipoproteins and apolipoproteins are responsible for an increased risk of cardiovascular disease [96–98]. The indigestible components of foods, such as dietary fiber, decrease serum cholesterol by inhibiting the intestinal absorption of neutral steroids [99]. *Chlorella* supplementation reportedly decreases serum cholesterol levels in model animals [100]. To identify the bioactive compounds responsible for this e ffect, the indigestible fraction of *C. regularis* powder was isolated and characterized, revealing a content of 43% crude protein, 37.3% dietary fiber, 6.9% carbohydrate, 5.4% moisture, 4.3% crude fat, and 2.7% ash [101]. Rats fed a diet with 5.3% of this indigestible fraction demonstrated lower serum and liver cholesterol levels and higher fecal neutral steroid levels as compared with those fed a diet of 12.7% *Chlorella* powder. Both *Chlorella* powder and the indigestible fraction exhibited a high bile-acid binding capacity in vitro. Furthermore, the indigestible fraction increased the hepatic mRNA levels of cholesterol 7α-hydroxylase, which is the rate limiting enzyme for cholesterol catabolism and bile-acid synthesis [102]. These results indicate that the indigestible fraction of *Chlorella* possesses hypercholesteromic activity, which improves cholesterol catabolism via the upregulation of hepatic cholesterol 7α-hydroxylase expression.

*Chlorella* supplementation is also reported to decrease serum cholesterol levels in hyperlipemia and mild hypercholesterolemic patients in a small, open-label trial [103]. To evaluate the preventive role of *Chlorella* in maintaining serum cholesterol levels against excess dietary cholesterol intake, a double-blind, randomized, placebo-control study was conducted in 63 mildly hypercholesterolemic subjects treated with either *C. vulgaris* (5 g/day) or placebo for four weeks [104]. A similar trial investigated cholesterol levels in 34 participants administered 510 mg of dietary cholesterol from three eggs concomitantly with either *Chlorella* (*C. vulgaris*) (5 g/day) or a matched placebo for 4 weeks [105]. Participants on the three-egg diet alone exhibited significant elevation in serum total cholesterol, low-density lipoprotein cholesterol, and high-density lipoprotein cholesterol levels. The administration of *Chlorella* in addition to the three-egg diet significantly suppressed these increases in total cholesterol and low-density lipoprotein cholesterol levels and significantly increased serum lutein and α-carotene levels [105]. In mildly hypercholesterolemic subjects, *Chlorella* administration resulted in marked changes in total cholesterol, triglycerides, lutein/zeaxanthin, and α-carotene levels as well as a significant decrease in very low-density lipoprotein cholesterol, apolipoprotein B, non-high-density lipoprotein, and high-density lipoprotein/triglyceride levels [104]. These results suggest that *Chlorella* might inhibit the intestinal absorption of dietary and endogenous lipids. In addition, the observed changes in serum lipids may be associated with changes in serum carotenoids. These results suggest that daily consumption of *Chlorella* provides potential health benefits by reducing the levels of serum lipid risk factors, such as triglycerides and total cholesterol, in mild hypercholesterolemic subjects.


**1. Introduction**

With economic development and the continuous expansion of the scale of cities, the number of vehicles increases sharply, inducing a frequent occurrence of road traffic offenses.  Intelligence analysis about these abnormal vehicles makes broader sense for assisting effective vehicle monitoring and management. The intelligence information includes all the holographic states of a vehicle, for example, the basic data of the vehicle and driver, the trajectory, the origin destination (OD) characteristics, aggregation with other vehicles, and others. It is really an important research topic on the real-time intelligence information analysis method by current devices deployed onboard or roadside.

In many intelligence information types mentioned above, the trajectory of the vehicle contains abundant spatial and temporal distribution features. Using a geographic information system (GIS), the trajectory can be accurately projected on an electronic map to give an intuitive presentation of the vehicle's movement. Moreover, through the analysis of massive trajectory data, the trip rules of vehicles, such as the OD, and the travel preferences of the driver can also be obtained. These are very valuable for intelligent macro traffic management. In some microscopic traffic control applications, the vehicle trajectory is also meaningful. For example, the single trajectory prediction can be used to provide support for capturing illegal vehicles [1,2], while multiple trajectories prediction can be used to evaluate the short-time traffic volume for designing a proper traffic signal plan [3–8].

Using the electronic surveillance cameras deployed on roads, the driving status of a vehicle such as the time, license plate number, speed, lane and direction can all be acquired. On the basis of the road network topology, a vehicle passes through a series of intersections and the trajectory of the vehicle can be obtained easily from the driving status data collected by a video-imaging detector at the intersections. Compared with the methods based on location-based-services (LBS) [9–12], wireless fidelity (WiFi) probes [13–15] and cellular signaling [16–19], vehicle trajectory extracted form vehicle license plate data has certain advantages in terms of wide adaptability, accuracy and visualization effects. Fully using the driving status acquired by the video-imaging detectors, this paper studies the vehicle trajectory prediction scheme based on the latent travelling rules extracted from massive vehicle license plate data. For a certain vehicle, the turning characteristic at an intersection is described by a turning probability transition matrix in which the probability is calculated according to statistics of historical trip chains from the vehicle license plate. The experimental study shows that the proposed method presents a better performance in a short-term trajectory prediction.

The rest of the paper is organized as follows. Section 2 presents related work. In Section 3, trip chain building and compensating methods based on vehicle license plates are presented. In Section 4, the turning state transition matrix based on historical trip chains is proposed for trajectory prediction and the one/*k*-step trajectory prediction models are described. The experimental study and the evaluation results are presented in Section 5. In Section 5, we conclude the paper and provide directions for future work.

## **2. Related Work**

Vehicle trajectory is important intelligence information for both urban macroscopic traffic management and microscopic traffic control. Generally, vehicle trajectory uses a vehicle's or driver's location and identity as major data foundations. According to different vehicle or driver locations and identity acquisition types in an urban traffic environment, the current trajectory-building methods can be classified into the following categories: LBS-based methods, WiFi probe-based methods, cellular signaling-based methods and video-imaging-based methods.

The LBS-based method mainly uses global positioning system (GPS) floating vehicle data to track the target vehicle. The movement of the vehicle is detected continuously in time and the trajectory can be presented visually combined with the application of an electronic map. In [9], based on the vehicles' historical trips, the relationship between different road segments are built by transforming the road network model into a matrix, and the driving regularity of vehicles is analyzed for the design of the algorithm of vehicle route prediction. In [10], the historical vehicle GPS data is used to match the current trajectories and infer future possible destinations. The method predicts the trajectory by a systematic procedure for describing the features of the similarity of trajectories and destinations. The method also takes the station correlations and the user historical destinations into account. The positive prediction rate of the proposed method can reach 92% under the condition that the test trip has been completed over 70%. In [11], authors propose a vehicle trajectory prediction method based on the hidden Markov model. The relevant parameters are analyzed by historical vehicle GPS data, and the Viterbi algorithm is used to seek the double layers hidden states sequences corresponding to the recent driven trajectory. The future vehicle trajectory is predicted by a novel algorithm based on the hidden Markov model of double-layer hidden states. In [12], using the GPS data, a vehicle trajectory prediction method based on a variable-order Markov model is proposed. Kernel smoothing which combines sequence analysis with the Markov statistic is used for model building. The method presents a higher performance in prediction accuracy. However, these methods are only suitable for some special commercial vehicles

which are equipped with GPS or other onboard positioning devices, and not applicable for most private vehicles.

By installing certain WiFi probe devices [13] at intersections or roads, the WiFi probe-based method generates the trajectory by detecting the passing time and the media access control (MAC) addresses of electronic terminals with WiFi-connecting function, such as the onboard unit and driver's mobile phone. In [14], authors use a WiFi probe as the data collector to scan the mobile devices within a certain range in a certain period of time to obtain the MAC address, reference distance, time stamp and other information of mobile phone. Furthermore, a customer flow prediction model based on seasonal auto regressive integrated moving average (SARIMA) model and BP neural network model is built. In [15], an urban mobility trajectory analysis model based on large-scale WiFi probe request data is built. Unique entries per access point and per hour of WiFi data are aggregated to approximate local population counts by type of user. In the model, spatial network analysis is used to apply the results to the road and pedestrian sidewalk network to identify usage intensity levels and trajectories for individual street segments. The research demonstrates the significant potential in the use of WiFi probe request data for understanding mobility patterns. Similar in [16], authors design a user feature space in which frequent trajectory patterns are used to represent each user as a feature vector based on the anonymized WiFi scan lists. As per the popularity of electronic terminals, the application of WiFi probe is more adaptable than the LBS-based method. However, the identity of the target is denoted by the MAC addresses of the electronic terminal. It is not directly relevant to the vehicle itself. Besides, in order to achieve an urban-wide trajectory analysis, several WiFi probe devices should be built, inducing high expense for construction.

As with the WiFi probe scheme, the cellular signaling-based method also uses the location and identity of electronic terminals to generate the trajectory. By contrast with the former, the location is detected by the mobile station and the identity is generally the mobile user or the MAC of the mobile terminal. For example, in [17], the authors propose a data-driven method for dynamic people-flow prediction based on cellular probe data. The grid-based data transformation and data integration module is proposed to integrate multiple data sources for human daily trajectory generation. Moreover, a dynamic people-flow prediction model based on random forest is also presented. The experimental results show that the proposed method can provide prediction precision of 76.8% and 70% for outbound and inbound people, which is better than the single-feature model. In [18], the authors introduce a mobility modeling method based on real tra ffic data collected from 4G cellular networks, including data collection, trajectory construction, data noise removal, data storage and analysis. The experiments discover the user's mobility features, changing of city hotspots, and mobility patterns. However, locating using a mobile cellular network and mobile base station is inaccurate outdoors without supplementary GPS or WiFi devices. Hence, the precision of these methods is relatively low and they are only suitable for microscopic tra ffic and population evolution analysis.

Fully using the driving status data collected by electronic surveillance cameras on roads, the vehicle trajectory is acquired by time detecting and license plate number series. In [19], an o ffline method for historical OD pattern estimation based on automatic license plate recognition data is proposed. A particle filter is used to estimate the probability of a vehicle trajectory from all possible candidate trajectories combined with the time geography theory. In this method, the path flow estimation process is conducted through dividing the reconstructed complete trajectories of all detected vehicles into multiple trips. The proposed method is verified and the results show that the MAPEs of the OD estimation are lower than 19%. In [20], a vehicle trajectory extraction algorithm based on license plate recognition data is proposed. The license plate and timestamps are used for the establishment of trip chain. Aiming at the data loss problem when detecting a vehicle license plate, the K shortest path algorithm and gray relational analysis are further used for trip chain compensation. The research focuses on extracting the vehicle trajectory and the prediction of future driving state is not studied. In [21], authors propose a vehicle trajectory reconstruction method based on license plate data. In the method, travel time threshold is used to obtain a single travel chain and the similarity of the ideal

solution and depth first search method are used to build a vehicle trajectory reconstruction model. It can effectively solve the problem of incomplete license plate number data. However, the related research mainly focuses on the macroscopic trajectory modeling and OD analysis and is seldom concerned with the microscopic real-time vehicle trajectory prediction.


Legumes, Sustainable Alternative Protein Sources for Aquafeeds

*Fateme Hekmatpour and Mansour Torfi Mozanzadeh*

## **Abstract**

Aquaculture produce a great portion of aquatic derived proteins for human in the world. It has the highest and the fastest growth rate among the protein producing industries. Fish meal (FM) is the main and the most expensive ingredient for aquafeeds production. It provides protein, essential amino acids, energy, minerals and vitamins in aquafeeds. Given the current rapid development of aquaculture industry the competition for limited global supplies of FM may reduce its availability and elevate its price. Thus, finding high quality, economic and environmentally friendly alternative protein sources (APS) for aquafeeds production is vital for sustainability of the aquaculture industry. Among various APS, legumes have been proved to be promising APS because they have medium protein content with suitable amino acid profile, high digestible protein and energy levels, and appropriate minerals and vitamins for the most cultured aquatic species. They also are cost-effective and highly accessible. However, they contain various anti-nutritional factors that may reduce feed palatability and may negatively affect growth and health of cultured aquatic animal species. This chapter provide information regarding legumes and their derivatives as APS, their nutritional quality and their potential drawbacks. In addition, strategies for increasing the efficiency of legumes in aquafeeds are reviewed and discussed.

**Keywords:** additives, anti-nutritional factors, aquaculture, nutrients digestibility, essential amino acids

#### **1. Introduction**

The aquafeed market is estimated to account for USD 50.6 billion in 2020 and with compound annual growth rate of 7.2%, it is projected to reach USD 71.6 billion by 2025 [1]. Two main factors amplify such a lucrative revenue in aquafeed market including increase in global seafood consumption (122% from 1990 to 2018) and fast grow rate in aquaculture production (527% from 1990 to 2018) [2]. In fact, the annual growth rate of aquaculture industry was about 10% during the 1990s and about 5.8% annually from 2000 to 2018 indicating aquaculture is the fastest growing food production sector in the world [3]. According to Food and Agriculture Organization of the United Nations [2] the aquaculture accounted for 52% (54.3 million tonnes (MT)) of global fish production that means this industry supplied 17% of total animal proteins for the global population [2]. About 70% of aquaculture production relied on the aquafeeds, which is the main expenditure ( 40%–70% of the total expenses) and the largest input in this industry [4, 5]. Thus, the

development of the aquafeed industry along with the improvement of feed efficiency are prerequisite to achieve the projected aquaculture production. On the other hand, aquafeed production industries mainly depend on marine-derived ingredients namely fish meal (FM) and fish oil (FO), but increasing demands for these marine-derived feedstuffs along with overexploitation and/or static tendency in capture fisheries of small pelagic fish resulted in uncertain supply and the inflation of their prices that adversely affect the profitability margins of aquaculture [6, 7]. It has been reported that about 70% to 80% of all produced FM is used in aquafeed industry [3]. Thus, seeking out environmentally friendly and economic alternative ingredients for substitution of FM and FO in aquafeeds formulation is a fundamental goal for aquaculture sustainability [7].

An alternative feedstuff for FM should possess some properties such as high availability, commercial competitive cost as well as ease of shipping and storage [8]. In addition, by considering nutritional aspects, an alternative protein source (APS) should have low quantities of fiber (< 6%), carbohydrates including starch (< 20%) and non-starch polysaccharides (NSP)(< 8%), anti-nutritional factors (ANF), high digestible protein level (≥ 48%), appropriate essential amino acid (EAA) profile (arginine > 3, lysine > 3.5, methionine > 1.5, threonine > 2.2% of total AA profile) and suitable palatability [6, 8]. On the other hand, it has been predicted that the application of FM in aquafeeds will be dropped to under 10% in some most popular aquaculture species such as omnivorous (*e.g.* carp, catfish and tilapia, 1-2% FM) and carnivorous fish species (*e.g.* marine fish, salmon and trout, 5-10% FM) [9]. Such tremendous shift from FM to APS in aquafeeds has resulted in new challenges in performance, feed utilization, welfare, and final product quality of cultured aquatic animal species [6].

Among alternative plant protein sources (APPS), legumes are the most abundant protein rich ingredients for applying in aquafeeds [10]. However, these APPS have several drawbacks such as a wide range of protein contents, EAA imbalances or inadequacies (*e.g.* sulfur amino acids including cysteine, methionine and taurine), low bioavailability of some minerals or microelements as they bounded with phytic acid (*e.g.* phosphorous, iodine, calcium and selenium) and the presence of high amounts of various ANF (*e.g.* antitrypsin factors, phytates, saponins, and polyphenols), which consequently impose some challenges in their use in aquafeeds formulations [8, 11]. Although some processed protein derivatives of legumes such as soy protein concentrate, soy protein isolate or pea protein isolate contain high protein levels (65-90%) and have low ANF concentrations, but they are too expensive to be used in most aquafeeds. In addition, the agriculture industry also restricted to develop production of these APPS without putting extra stress on land, water, and phosphorous resources. In this chapter it was aimed to highlight the opportunities and challenges in application of legumes as APPS and providing some strategies for enhancing their efficiency in aquafeeds.

#### **2. Legumes, alternative protein sources for aquafeeds**

The family Fabaceae (Leguminosae) or commonly named legumes are the third largest family of flowering plants with almost 770 genera and over 19,500 species [12, 13]. The largest and the most important economically subfamily of the legumes, are the Faboideae, which are the source of primary crops including dry seeds (*e.g.* lentils, broad beans, beans and peas), flavoring plants (*e.g.* carob and lupins), fodder plants (*e.g.* alfalfa) and oilseeds (*e.g.* peanut or groundnut and soybeans). The seeds are the most important part of the legumes that used as ingredients for aquafeeds manufacturing. In this section, it has been tried to introduce the most

important legumes used in the aquaculture industry. In 2020, the global production of some legumes such as peanut, dry pea, chick pea, cow pea, lentil and lupins were 48.757, 48.75, 14.184, 14.246, 8.786, 5.734 and 1.01 MT, respectively [14].


**2.2 Lead and lead compounds**

Lead and its derivatives are industrial toxic substances that have been widely used by humans for centuries and therefore play an important role in environmental pollution. Lead is a metal found in nature. It is a bluish gray metal that is rarely found in the earth's crust. It occurs mainly as lead ore, and the most important ore is lead sulfide (galena). It is found in a variety of compounds such as lead, lead acetate, lead chloride, lead chromate, lead nitrate, and lead oxide. While pure lead is insoluble in water, the solubility of lead compounds in water varies. The chemical symbol of lead is Pb and its atomic weight is 207.2 g/mol. Its vapor pressure is 1.77 mm Hg at 1000°C [18]. In nature, pure metal or its oxides, inorganic salts such as carbonate, sulfate, nitrate and acetate, and organic compounds such as lead tetraethyl exist. The primary use of lead is in the manufacture of batteries. In addition, it is widely used in in the production of paint, alloys and metal products (lead-antimony and lead-tin) in industry, electronic conductors, rubber, sheet lead, waterproof plates (roofing) or sound and radiation insulation, linoleum, solder, pipes, ammunition and toys. Its use for ceramic glazes, paint and pipe soldering has

decreased significantly. In addition, it is used in the composition of some ointments (lead acetate), diluted lead acetate (as abortive) is used infrequently in treatment under the name white water and as an insecticide (lead arsenate) in agriculture. Tetraethyl lead was used as a gasoline additive to increase the octane rating, before the EPA banned its use in gasoline in 1996 in the USA. Leaded gasoline is still used for propeller planes and some race cars [1, 19]. Metallic lead is a bluish, gray-silver soft metal. It melts at 327°C, is quite dense and can easily stretch (can take the form of a wire). It is not affected by dilute hydrochloric acid and sulfuric acid. It forms concentrated sulfuric acid and hot lead sulfate. Lead melts even in cold temperatures, forming lead nitrate and nitrous vapors. Organic acids (acetic acid, citric acid, etc.) affect lead slowly and cause the formation of their respective salts. It emits steam at temperatures above 500°C and harmful metallic dust. Lead is slightly soluble in water and may be the source of toxicity in some drinking water. Lead oxides usually form from water-insoluble compounds. PbO "oxide" (yellow masikot) forms yellow-orange lead oxide (lilac) when heated and is used for glass, enamel, accumulators, etc. in industry. PbO2 "bioxide" is the red oxide of lead and is an energetic oxidizer. Pb3O4 "minium" (cinnabar, plombi orthoplumbus) is a red-colored compound added to antirust paints and used in the varnish, enamel, crystal and battery industries. It is formed by heating lead oxide in air flow at 500°C. Lead sulfide is the substance that forms the mineral galena in its natural state. It is insoluble in water. It is found in the combination of yellow-colored varnishes used in ceramics and pottery, and color changes to dark brown when manganese oxide is added or green when copper oxide is added. These varnishes continue to be used in many countries today. It can be dissolved with organic acids. Food or acidic liquids (vinegar, wine, lemon juice, etc.) should not be placed in containers painted with this type of varnish. Lead hydrocarbonate is mixed with linen oil and used to obtain white paint. However, these dyes darken with the effect of hydrogen sulfide in the air and also have toxic effects. Although its use is prohibited in many countries, residues in old settlements can cause some poisoning cases. Arsenate lead was formerly used as insecticide in agriculture, including in Turkey, before being banned in many countries because of its toxicity. However, some residues from past use can be found in the soil due to its durability. Lead chromate is also called "chrome yellow" and can be used to obtain yellow dye. Lead stearate is used to reinforce some plastic materials. The basic iodide and acetate of lead -lead iodide and lead acetate (soluble in water)- are used in dermatology to benefit from solubilizing effect in the form of a solution. Basic lead acetate is a compound made by neutralizing lead acetate with lead oxide (PbO). Lead naphthenate is used as an additive in some moisturizing drugs. Alcoholic derivatives of tetraethyl-lead and tetramethyl-lead are organic derivatives of lead that are added to gasoline as an antidetonante (0.5%). Often ethylene dibromide and ethylene dichloride compounds are added to engines to prevent metallic lead build-up. Exhaust fumes from cars operating with leaded gasoline contain lead halides and oxides as well as a small amount of undissolved lead-alcohol (1–10%). In many countries, the proportion of lead in gasoline is legally limited (0.5 g/l) and unleaded gasoline vehicles are now produced. These organic lead derivatives added to gasoline play an important role in air pollution (especially in big cities) [1, 20].

Lead is taken into the organism generally through digestion (in the form of food, liquid drinks, vapor or particles) and through the respiratory tract. It is a highly toxic metal that enters biological systems by mixing with respired air and nutrients from the air, water and soil. Up to 90% of the lead in the atmosphere in solid and gaseous form is absorbed by the lungs. Small lead dust or vapor, especially in the air, cause lead compounds (oxides or salts) to enter the organism by inhalation. Very small particles can reach the alveoli, while large particles are discharged from the

upper respiratory tract or can be reabsorbed by entering the digestive tract through sputum and saliva. When organic lead compounds contaminate the skin, they can be absorbed significantly, especially from lesioned areas. When the carcinogenic effect is examined, human studies are insufficient regarding lead exposure and increased cancer risk. In animal studies, kidney tumors were reported in rats and mice orally exposed to lead. Lead is assessed as B2 (possible human carcinogen - based on evidence of adequate carcinogenicity in animals) according to the Guidelines for Carcinogenic Risk Assessment (US EPA, 1986) [1, 21].


**2. Abiotic stresses and relationship to virus outbreaks**

Earlier we introduced the definition of general stress response (GSR) which is an advanced subject describing multiple gene expression, mutation, protein transcription, mRNA translation, intracellular endoplasmic reticulum repair, DNA recombination and repair, epigenetic imprinting and motility [23]. It also includes specific RNA polymerases, such as in alphaproteobacteria, where the GSR is under the transcriptional control of the alternative sigma factor EcfG. EcfG regulates genes for proteins that are associated with the regulation of motility (escape) and biofilm formation (adhesion), by binding to the RNA polymerase to redirect general protein transcription towards stress response genes [12]. The stress response can include conversion from non pathogenic to pathogenic mechanisms to acquire

*Trajectories of RNA Virus Mutation Hidden by Evolutionary Alternate Reality Thermodynamic… DOI: http://dx.doi.org/10.5772/intechopen.100481*

nutrients under harsher, more competitive conditions. Infections prepare the nowpathogenic bacteria to withstand diverse host environments [24] defined by any range of abiotic stresses, whether in acidity, alkalinity, radioactivity, temperature extremes, nutrient and resource scarcity, drought or any mixed combinations of stresses and durations. Viruses may exploit the presence of these stress responses, including the RNA-dependent RNA polymerases for replication of their genomes or, in retroviruses, the reverse transcriptase to produce new viral DNA which can be integrated into the host DNA under its integrase function [25]. Interestingly, the arrival of virulence and infection of genes at specific, appropriate times, frequencies and sites also stimulates patterns that resemble wide-sweeping oscillations of outbreaks (**Figure 2**) [24, 26].

Formalisms in statistical mechanics and thermodynamics have been used previously in order to describe the lifecycle of pathogenic viruses, from mutation to evolution and infection [5].

Viral mutation rates are caused by a number of processes including:

Retroviruses are viruses with RNA-containing virions and a cellular DNA stage [27]. Para-retroviruses are viruses with DNA-containing virions and a cellular RNA stage [20]. Both mutate and evolve at rates similar to riboviruses. Riboviruses are non-reverse transcribing RNA viruses [28].

#### **Figure 2.**

*Comparison of drought and non-drought virus infection patterns, where drought represents an example of abiotic stress impact on infectiousness-patterns: Circles represent cycles of growth, and cycles of nutrient (gas) exchange between symbiont species in a given habitat; Drought triggers vertical (chronic re-infection of a host), likely due to the limited host-population growth in times of drought-related resource limitations. Horizontal infection results in chronic virus re-infection, and can include host DNA to virus transfer. Source: the author, F.H. Campbell.*

In general, the list of habitat stresses on bacterial mutation rates can result in:

In Drake et al., mutation-rate calculations for DNA-type viruses are based on the effective genome size *Ge* for transforming a mutant frequency *f* into a mutation rate, where *f* is measured for large populations that had accumulated mutants in the putative absence of selection. In Zhao et al., the mutation rate in the SARS-CoV genome was estimated to be 0.80–2.38 � 10–3 nucleotide substitution per site per year, well within the magnitude of RNA viruses. The most recent common ancestor of the 16 sequences was inferred to be present as early as the spring of 2002, the outbreak of SARS [37]. Khailany et al. describe the current SARS-CoV-2 with genome size between 29.8 kb to 29.9 kb and 116 mutations implicated in the severity of infection and spread - including the three most common mutations: 8782C > T in ORF1ab gene, 28144 T > C in ORF8 gene and 29095C > T in the N gene [38]. For comparison, examples of mutation rates for non-SARS viruses in general are shown in the table below (**Table 1**).

Pathogenic RNA viruses that encode complex RNA-dependent RNA polymerase bearing a 30 exonuclease domain will mutate slowly [40, 41] and indeed, the SARS-CoV-2 viruses mutate in four months in order to accumulate knowledge about the infective host [19] and successfully bypass the host immunity, including those who were early-vaccinated such as with mRNA, mod-mRNA vaccines and possibly

*Trajectories of RNA Virus Mutation Hidden by Evolutionary Alternate Reality Thermodynamic… DOI: http://dx.doi.org/10.5772/intechopen.100481*

#### **Table 1.**

*Mutation rates of non-SARS pathogenic viruses and genome size. Adapted from Sanjuán et al. [39].*

others will inevitably show success by activation of cellular anti-viral proteins known as zinc antiviral proteins (ZAP) and APOBEC-3. ZAP and APOBEC-3 diminish a virus by detecting its foreign CG-dinucleotide before it infects, simply by comparing it to its own native RNA as part of natural innate immunity response. However, the slow-rate (four months) SARS mutations allow the virus to successfully bypass this antiviral protein in mass-vaccinated humans.

Thermodynamic models in the research all consistently recognize that a cell is infected with one or more virus particles, and that each infecting genome is copied iteratively such that complementary strands accumulate in the host, eventually producing final strands of the same polarity as the infecting strand, so that these final strands are then packaged and released throughout the host [30]. It is assumed that "final" strands rarely (or never) re-enter the beginning of the cycle within a single infection. In this way, the mutation frequency *f* is the same as the mutation

rate *μ* per replication. And so, if *n* number of complementary strands are copied from a template and if *μ* is the mutation rate per copying event, then the number of mutations will be *nμ*, and *f* ¼ *nμ=n* ¼ *μ*.

But, thermodynamic research of habitats does not establish relationships between mutations and spreadrate /infectiousness locations in a habitat and what drives the location: Is it just the population dysbiosis? Is it just the habitat stress?

For example, *J* might represent a infectious spread rate and *N j* the infected population, the number of mutations occurring in a pathogenic outbreak could be described an effective infection rate *μij* per habitat.

*Ji* ¼ P*n j*¼1*μijN j* for pathogenic virus infection spread rate requiredwhere, *μij* is the

infection matrix which in the limit as *lim N j*!0 *∂Ji ∂Ni* � � and is symmetric when *μij* ¼ *μji* and

which could be crudely integrated over an entire habitat per host-species nonhomogeneously over time. However, this sort of model evaluation is largely unable to describe the wavelike nature of outbreaks in the infections caused by virus mutation following an ecological threat. In addition, no part of it satisfactorily allows sensitivity to the interaction between the host and virus, as a thermodynamic instability which would result in the oscillatory periodic moment of spread. We need a method to include entropy production *∂s ∂t* þ ∇*Js* ¼ *σ*; *σ* ≥0 and the flux of pathogenic virus throughout a habitat in response to a habitat stress, resulting in a non-uniform infectiousness.

But how can we forecast thermodynamic stability of a habitat in this equation? What are the specific thermodynamic limits and how is this represented or accommodated in mutation responsive virus nature?

We might try to show that, when an ecosystem's resources are severely constrained, a higher re-infection rate occurs. This requires investigation of models from the research to do with the replication conditions in RNA viruses that predominate poststress outbreaks. If so, we find from Drake et al. and Pathak and Temin [32, 42]:

	- a. Transcription by the host RNA polymerase produces one RNA genome.
	- b. Reverse transcriptase then catalyzes two replications in order to generate a DNA-based chromosome that integrates into the host chromosome,

including of a different cell for packaged retroviruses, or of the same cell in the case of a retrotransposon.

c. Thereafter it assumes a far lower mutation rate so that the resulting mutant frequency is the sum of the mutation rates of all three steps. Drake [43] notes that retro-element rates are roughly an order of magnitude lower than the RNA-virus rates and that retroviral mutation rates do not appreciably reduce specific infectivity and render more resistance to increased mutation rates (e.g., Spleen necrosis virus, which is obliterated only after a roughly 13-fold increase.)

After obtaining the entropy production and mutation rates for given species of infectious viruses, we need an understanding of the host immunity resistance proteins and their interactivity with virus mutability [41, 44]. Mutability of the viruses is correlated inversely with genome size [30, 41]. Unfortunately the solution for modeling becomes much more complex because each host immunity resistance proteins are transient in very short intervals of expression and mutating virus variants are population-wide processes rather than merely intracellular-driven [41].

It is worthwhile to insert a comment here: For example, SARS-CoV-2 viruses colonize specifically anaerobic proteobacteria commonly found in the gut of livestock. These bacteria likewise have a range of mutations according to abiotic environmental stress related gene-signaling. They include *Prevotella* (found in the gut of bovine, ovine, swine, avian livestock); Streptococcus (bovine, ovine and camel), *Bacterioides* (gut of swine, and hind-gut of avians) and *Mycoplasma pneumoniae*, *Haemophilus influenzae and Pseudomonas aeruginos,* which can be hosted by all the previously listed livestock. It is interesting to observe that livestock experience the most significant of stresses in rapid successive seasonal intervals (every six and nine months) when livestock are brought in large herds to be slaughtered. The slaughter process supports full resistance mutation processes resulting in the pathogenic conversion of these bacteria: animal confinement stress, heat-stress, food-stress (particularly before slaughter), dehydration stress, anxiety-panic stress, and trauma to the tissue from slaughter (and related death practices, such as live-animal steaming) and, of course, maternal stress towards offspring also butchered en measles. Vascular swelling from butchering [45–47] is part of the explosive discharge of gut-related bacterial organisms from slaughterhouse events into the ambient environment: This explains the relatively constant high pergenome mutation rate observed (0.003 per round of copy) [41] and at levels of 1,000,000 animals per week per slaughterhouse neighborhoods and livestock postbutchering products are all visibly the same location where COVID19, dementia, gastrointestinal diseases outbreaks are their absolutely highest [45, 48, 49]. In the period of 2019 through the year of this chapter's writing, COVID19 disease outbreaks were consistently describable as oscillatory or wavelike with dense centers and radiating lines of trajectory between the centers [50–52]. The locations did not repeat but also showed a pattern of shifting so that new outbreak locations or "hotspots" were observed. In mapping these outbreaks, the author noticed a clever relationship to mathematical lissajous-like oscillations. Would it be possible to describe the relationship between infectious spread so-called waves of outbreaks as a lissajous parametric trajectory?


3.1. Effect of deformed bubble shape variations on the pressure and surface energy required for bubble breakage

To illustrate the influence of pressure energy control breakup, theoretical predictions of the surface energy and the pressure energy requirements for the breakage of ellipsoidal and spherical-capped bubble are shown, respectively, in Figure 6. It can be clearly seen from Figure 6 that the energy requirement for ellipsoid bubble shifts from pressure energy to surface energy with an increase in the breakup volume fraction. This may be attributed to a higher dynamic pressure being required inside a smaller bubble for resisting the surrounding eddy pressure in order to sustain its own existence. However, the spherical bubble requires most of the surface energy for its breakage. This may mainly be due to the contribution of the large front surface of spherical-capped bubbles.

The surface energy requirement for bubble breakage in Figure 6 has taken into account the bubble shape variations. To further illustrate the significance of considering the variation of bubble shapes, a theoretical comparison of the increase in surface energy for the breakage of the original spherical bubbles versus various shapes of bubbles has been shown in Figure 7.

Figure 6. Two competitive control mechanisms of the breakage of ellipsoidal bubbles (deq,i = 16 mm) and spherical-capped bubbles (deq,i = 32 mm).

Figure 7. Normalized increase in the surface energy for the breakage of original spherical bubbles and various shapes of bubbles.

(r/R < 0.6), while underestimation is shown near the column wall for both the original breakup model and the improved breakup model. Since the standard k˜ε turbulence model is still applied in this study, the underestimation of gas holdup may be due to the slight poor prediction of the turbulence dissipation rate. The issue of underestimation on the gas holdup distribution has also been addressed by Chen et al. [27], in which case the breakup rate was artificially increased by a factor of 10 to obtain a "better" agreement with the

Figure 8. Comparison of the original breakup model and the improved breakup model for the prediction of the gas

Modelling of Bubbly Flow in Bubble Column Reactors with an Improved Breakup Kernel Accounting for Bubble…

http://dx.doi.org/10.5772/intechopen.76448

79

Figure 9 shows the radial distribution of the time-averaged turbulence dissipation rate for Case 1. The turbulence dissipation rate distribution predicted by the standard k˜ε model is smaller than the result obtained by the RNG k˜ε model. This is because the RNG k˜ε model has a specific contribution from the local strain rate as the correction to the turbulence dissipation rate. The tendency of the standard k˜ε model to underestimate the turbulence dissipation rate can also be seen in the studies carried out by Laborde-Boutet et al. [28], Chen [29] and Jakobsen et al. [30]. As a result, the standard k˜ε model is insufficient to properly estimate the turbulence dissipation rate in the regions with rapidly strained flows, which most likely corresponds to the near wall region in the bubble columns. It can be seen from Eq. (19) that the breakup rate ΩB˜ε1=3 exp ε2=3 , which is at least equivalent to the dissipation rate ε of the order of 1/3. Therefore, the equilibrium state of bubble coalescence and breakup phenomena cannot be reasonably addressed with an inaccurate estimation of the turbulence dissipation rate and inevitably affect the predictions of gas holdup. Also, as the predicted coalescence rate is about one order of magnitude higher than the predicted breakup rate, the bubble coalescence and

experimental data.

holdup profile in the radial direction for Case 1.

The generation of spherical bubbles due to eddy collision with large ellipsoidal or sphericalcapped bubble is not covered, as the breakage volume fraction will be far smaller than 0.05. The generation of small spherical bubbles occurs more frequently due to the interaction of the shed eddies with the bubble skirt. This phenomenon was concisely described and explained by numerical modelling work carried out by Fu and Ishii [26]. It is shown in Figure 7 that the maximum increase in surface energy for ellipsoidal bubbles and spherical-capped bubbles is different. As binary breakage is assumed, a large ellipsoidal bubble breaks into two smaller ellipsoidal bubbles in most cases. The maximum increase in surface energy is demonstrated when equal-size breakage occurs, which suggests that the parent ellipsoidal bubble has been through a large deformation process itself. However, the spherical-capped bubble can break into different combinations of daughter bubble types, including one ellipsoidal and one spherical-capped bubble, two ellipsoidal bubbles, or two spherical-capped bubbles. The maximum increase in surface energy for the breakage of a spherical-capped parent bubble is found with the largest volume fraction of ellipsoidal daughter bubble. This result coincides with the existing experimental observations: the ellipsoidal bubble has a more stable structure that is able to resist bombarding eddies from both the front and the rear, whereas the sphericalcapped bubble can only resist eddies hitting from the front but is easily and rapidly ruptured by eddies hitting from the rear.

Figure 8 compares the time-averaged gas holdup predicted by the original breakup model and the improved breakup model. It can be found that the improved breakup model has achieved results very similar to the experimental data at the core region of the column

Modelling of Bubbly Flow in Bubble Column Reactors with an Improved Breakup Kernel Accounting for Bubble… http://dx.doi.org/10.5772/intechopen.76448 79

Figure 8. Comparison of the original breakup model and the improved breakup model for the prediction of the gas holdup profile in the radial direction for Case 1.

(r/R < 0.6), while underestimation is shown near the column wall for both the original breakup model and the improved breakup model. Since the standard k˜ε turbulence model is still applied in this study, the underestimation of gas holdup may be due to the slight poor prediction of the turbulence dissipation rate. The issue of underestimation on the gas holdup distribution has also been addressed by Chen et al. [27], in which case the breakup rate was artificially increased by a factor of 10 to obtain a "better" agreement with the experimental data.

The generation of spherical bubbles due to eddy collision with large ellipsoidal or sphericalcapped bubble is not covered, as the breakage volume fraction will be far smaller than 0.05. The generation of small spherical bubbles occurs more frequently due to the interaction of the shed eddies with the bubble skirt. This phenomenon was concisely described and explained by numerical modelling work carried out by Fu and Ishii [26]. It is shown in Figure 7 that the maximum increase in surface energy for ellipsoidal bubbles and spherical-capped bubbles is different. As binary breakage is assumed, a large ellipsoidal bubble breaks into two smaller ellipsoidal bubbles in most cases. The maximum increase in surface energy is demonstrated when equal-size breakage occurs, which suggests that the parent ellipsoidal bubble has been through a large deformation process itself. However, the spherical-capped bubble can break into different combinations of daughter bubble types, including one ellipsoidal and one spherical-capped bubble, two ellipsoidal bubbles, or two spherical-capped bubbles. The maximum increase in surface energy for the breakage of a spherical-capped parent bubble is found with the largest volume fraction of ellipsoidal daughter bubble. This result coincides with the existing experimental observations: the ellipsoidal bubble has a more stable structure that is able to resist bombarding eddies from both the front and the rear, whereas the sphericalcapped bubble can only resist eddies hitting from the front but is easily and rapidly ruptured

Figure 7. Normalized increase in the surface energy for the breakage of original spherical bubbles and various shapes of

78 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

Figure 8 compares the time-averaged gas holdup predicted by the original breakup model and the improved breakup model. It can be found that the improved breakup model has achieved results very similar to the experimental data at the core region of the column

by eddies hitting from the rear.

bubbles.

Figure 9 shows the radial distribution of the time-averaged turbulence dissipation rate for Case 1. The turbulence dissipation rate distribution predicted by the standard k˜ε model is smaller than the result obtained by the RNG k˜ε model. This is because the RNG k˜ε model has a specific contribution from the local strain rate as the correction to the turbulence dissipation rate. The tendency of the standard k˜ε model to underestimate the turbulence dissipation rate can also be seen in the studies carried out by Laborde-Boutet et al. [28], Chen [29] and Jakobsen et al. [30]. As a result, the standard k˜ε model is insufficient to properly estimate the turbulence dissipation rate in the regions with rapidly strained flows, which most likely corresponds to the near wall region in the bubble columns. It can be seen from Eq. (19) that the breakup rate ΩB˜ε1=3 exp ε2=3 , which is at least equivalent to the dissipation rate ε of the order of 1/3. Therefore, the equilibrium state of bubble coalescence and breakup phenomena cannot be reasonably addressed with an inaccurate estimation of the turbulence dissipation rate and inevitably affect the predictions of gas holdup. Also, as the predicted coalescence rate is about one order of magnitude higher than the predicted breakup rate, the bubble coalescence and

Figure 9. Radial distribution of time-averaged turbulence dissipation rate for Case 1.

breakup phenomena cannot be reasonably addressed under this scenario and will inevitably affect the predictions of gas holdup. In addition, as pointed out by Jakobsen et al. [30], despite the accuracy of calculating the local turbulence dissipation rate from the k˜ε turbulence model, this turbulence dissipation rate merely represents a fit of a turbulence length scale to singlephase pipe flow data. Therefore, the contribution of turbulence eddies that are induced by the bubbles has not being included. More importantly, the mechanism of bubble breakage caused by the interactions of bubble-induced turbulence eddies with the subsequent bubbles, which may be dominant in the core region of the bubble column, cannot be revealed through the breakage kernels that are very sensitive to the turbulence dissipation rate.

Figure 10 shows the radial distribution of time-averaged gas holdup at different cross sections in the axial direction. The results are obtained by using the improved breakup model. It can be seen clearly from Figure 10 that the predicted time-averaged gas holdup in the fully developed region (H/D > 5) has achieved self-preserving characteristics regardless of the axial positions. It appears that the inlet conditions have a weak influence on this selfpreserving nature in the bubble columns, which is a result concurring with some previous experimental findings [31, 32].

Figure 11 presents the unit volume-based interfacial area in the bulk region for each bubble class. Due to the large differences in size from the smallest to the largest bubble class, the y-axis is shown in a log10 scale. Interfacial area is a key parameter that largely affects the prediction of heat and mass transfer between gas and liquid phase in the bubble columns. Although the differences in the simulated interfacial area between the improved breakup model and the original breakup

model are not significant when the bubble size is relatively small, the influence of the bubble shapes is gradually reflected when the shape of the bubbles transforms from ellipsoid to spheri-

cal-cap, resulting in much larger interfacial areas for spherical-capped bubbles.

Figure 11. Comparison of the simulated interfacial area in the bubble column for Case 2.

Figure 10. Radial distribution of time-averaged gas holdup at different axial positions.

Modelling of Bubbly Flow in Bubble Column Reactors with an Improved Breakup Kernel Accounting for Bubble…

http://dx.doi.org/10.5772/intechopen.76448

81

Modelling of Bubbly Flow in Bubble Column Reactors with an Improved Breakup Kernel Accounting for Bubble… http://dx.doi.org/10.5772/intechopen.76448 81

Figure 10. Radial distribution of time-averaged gas holdup at different axial positions.

breakup phenomena cannot be reasonably addressed under this scenario and will inevitably affect the predictions of gas holdup. In addition, as pointed out by Jakobsen et al. [30], despite the accuracy of calculating the local turbulence dissipation rate from the k˜ε turbulence model, this turbulence dissipation rate merely represents a fit of a turbulence length scale to singlephase pipe flow data. Therefore, the contribution of turbulence eddies that are induced by the bubbles has not being included. More importantly, the mechanism of bubble breakage caused by the interactions of bubble-induced turbulence eddies with the subsequent bubbles, which may be dominant in the core region of the bubble column, cannot be revealed through the

Figure 10 shows the radial distribution of time-averaged gas holdup at different cross sections in the axial direction. The results are obtained by using the improved breakup model. It can be seen clearly from Figure 10 that the predicted time-averaged gas holdup in the fully developed region (H/D > 5) has achieved self-preserving characteristics regardless of the axial positions. It appears that the inlet conditions have a weak influence on this selfpreserving nature in the bubble columns, which is a result concurring with some previous

Figure 11 presents the unit volume-based interfacial area in the bulk region for each bubble class. Due to the large differences in size from the smallest to the largest bubble class, the y-axis is shown in a log10 scale. Interfacial area is a key parameter that largely affects the prediction of heat and mass transfer between gas and liquid phase in the bubble columns. Although the differences in the simulated interfacial area between the improved breakup model and the original breakup

breakage kernels that are very sensitive to the turbulence dissipation rate.

Figure 9. Radial distribution of time-averaged turbulence dissipation rate for Case 1.

80 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

experimental findings [31, 32].

Figure 11. Comparison of the simulated interfacial area in the bubble column for Case 2.

model are not significant when the bubble size is relatively small, the influence of the bubble shapes is gradually reflected when the shape of the bubbles transforms from ellipsoid to spherical-cap, resulting in much larger interfacial areas for spherical-capped bubbles.

### 3.2. Effect of deformed bubble shape variations on the interfacial mass transfer across bubble surfaces

The interfacial area obtained by the improved breakup model is based on the statistical model of bubble shapes. The results will be slightly different when a more realistic model, which considers the dynamic deformations that occur during bubble motions, is implanted into the simulations. Indeed, the current results have implied that assuming all bubbles to be of a spherical shape may lead to significant underestimation of the interfacial area and hence affect the predictions of the heat and mass transfer rate when chemical reactions are considered in the bubble column reactors. To further address this issue, the volumetric mass transfer coefficient, kLa, estimated based on the improved breakup model for each bubble class is presented in Figure 12.

The convective mass transfer film coefficient can be defined by Eq. (37)

$$k\_{\rm L} = \frac{\overline{D}}{d}Sh\tag{37}$$

Re in Eq. (38) is the bubble Reynolds number and Sc is the Schmidt number. The Schmidt

Modelling of Bubbly Flow in Bubble Column Reactors with an Improved Breakup Kernel Accounting for Bubble…

Sc ¼ υ

According to the analogy between heat and mass transport phenomena, a similar method can be applied to calculate the Nusselt number by simply replacing the Schmidt number with the Prandtl number. By doing so, the ratio of convective heat transfer to conductive heat transfer

It is observed that the volumetric mass transfer coefficient is greatly increased due to the contribution of ellipsoidal and spherical-capped bubbles. However, the peak value obtained based on the improved breakup model may be attributed to the predicted number density of the corresponding bubble class. As illustrated in Figure 7, the improved breakup model requires a higher increase in surface energy at the boundary of ellipsoidal and sphericalcapped bubbles, which makes the smallest spherical-capped bubbles more difficult to break. The results for this particular bubble class may not be a good reflection of the physical phenomenon in reality, but the overall enhancement of the mass transfer coefficient is still very significant. The predictions on the overall mass transfer coefficient are shown in Figure 13. Figure 14 presents the local mass transfer coefficient at different cross sections along the height of the bubble column. It can be seen from Figure 14 that the mass transfer rate estimations based on Luo and Svendsen model and the improved breakup model are obviously very different. The results based on the Luo and Svendsen model may imply that the mass transfer is mainly associated with the regions where the larger Sauter mean bubble diameter has been predicted. The results based on the improved breakup model suggest that the mass transfer is

Figure 13. Volumetric mass transfer coefficient predicted using both the improved breakup model and Luo and Svendsen

D (39)

http://dx.doi.org/10.5772/intechopen.76448

83

number is the ratio of momentum diffusivity to mass diffusivity, defined by Eq. (39)

can be characterized.

model [3].

where D is mass diffusivity, d is the bubble diameter and Sh is the Sherwood number. The Sherwood number represents the ratio of the convective mass transfer to the rate of diffusive mass transfer. It can be determined by using the Frossling equation described by Eq. (38)

$$Sh = 2 + 0.552 \text{Re}^{\frac{1}{2}} \text{Sc}^{\frac{1}{3}} \tag{38}$$

Figure 12. Comparison of the volumetric mass transfer coefficient for each bubble class.

Re in Eq. (38) is the bubble Reynolds number and Sc is the Schmidt number. The Schmidt number is the ratio of momentum diffusivity to mass diffusivity, defined by Eq. (39)

3.2. Effect of deformed bubble shape variations on the interfacial mass transfer across

82 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

The convective mass transfer film coefficient can be defined by Eq. (37)

Figure 12. Comparison of the volumetric mass transfer coefficient for each bubble class.

The interfacial area obtained by the improved breakup model is based on the statistical model of bubble shapes. The results will be slightly different when a more realistic model, which considers the dynamic deformations that occur during bubble motions, is implanted into the simulations. Indeed, the current results have implied that assuming all bubbles to be of a spherical shape may lead to significant underestimation of the interfacial area and hence affect the predictions of the heat and mass transfer rate when chemical reactions are considered in the bubble column reactors. To further address this issue, the volumetric mass transfer coefficient, kLa, estimated based on the improved breakup model for each bubble class is presented

kL ¼ D

where D is mass diffusivity, d is the bubble diameter and Sh is the Sherwood number. The Sherwood number represents the ratio of the convective mass transfer to the rate of diffusive mass transfer. It can be determined by using the Frossling equation described by Eq. (38)

Sh ¼ 2 þ 0:552Re1

2Sc1

d Sh (37)

3 (38)

bubble surfaces

in Figure 12.

$$S\mathcal{c} = \frac{\upsilon}{\overline{D}}\tag{39}$$

According to the analogy between heat and mass transport phenomena, a similar method can be applied to calculate the Nusselt number by simply replacing the Schmidt number with the Prandtl number. By doing so, the ratio of convective heat transfer to conductive heat transfer can be characterized.

It is observed that the volumetric mass transfer coefficient is greatly increased due to the contribution of ellipsoidal and spherical-capped bubbles. However, the peak value obtained based on the improved breakup model may be attributed to the predicted number density of the corresponding bubble class. As illustrated in Figure 7, the improved breakup model requires a higher increase in surface energy at the boundary of ellipsoidal and sphericalcapped bubbles, which makes the smallest spherical-capped bubbles more difficult to break. The results for this particular bubble class may not be a good reflection of the physical phenomenon in reality, but the overall enhancement of the mass transfer coefficient is still very significant. The predictions on the overall mass transfer coefficient are shown in Figure 13. Figure 14 presents the local mass transfer coefficient at different cross sections along the height of the bubble column. It can be seen from Figure 14 that the mass transfer rate estimations based on Luo and Svendsen model and the improved breakup model are obviously very different. The results based on the Luo and Svendsen model may imply that the mass transfer is mainly associated with the regions where the larger Sauter mean bubble diameter has been predicted. The results based on the improved breakup model suggest that the mass transfer is

Figure 13. Volumetric mass transfer coefficient predicted using both the improved breakup model and Luo and Svendsen model [3].

Acknowledgements

Nomenclature

support of EPSRC (Grant no. EP/G037345/1).

a long half axis length of a ellipse, m c short half axis length of a ellipse, m

D bubble column diameter, m

deq equivalent bubble diameter, m

Eo Eötvös number, dimensionless

es increase in surface energy, kgm2

ē mean turbulence kinetic energy, kgm2

fV breakage volume fraction, dimensionless

kL convective mass transfer film coefficient, m/s

H distance from the bottom surface, m

D mass diffusivity, m2

d bubble diameter, m

FD drag force, N/m3 FLift lift force, N/m3

FVM virtual mass force, N/m3

g gravity acceleration, m/s2

k turbulence kinetic energy, m2

dV length of virtual axis, m

This work was supported by the National Natural Science Foundation of China (Grant no. 91534118). Weibin Shi would also like to acknowledge the Ph.D. scholarship of the International Doctoral Innovation Centre (IDIC) of University of Nottingham Ningbo China and the

Modelling of Bubbly Flow in Bubble Column Reactors with an Improved Breakup Kernel Accounting for Bubble…

http://dx.doi.org/10.5772/intechopen.76448

85

This chapter is an extension of a conference paper that was presented at the 13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2017) and was nominated for invitation into the HEFAT2017 Special Issue of Heat Transfer Engineering based on its designation as a high-quality paper of relevance to the modelling of fluids based systems.

CD effective drag coefficient for a bubble around a swarm, dimensionless

/s2

/s2

/s2

/s

Figure 14. Distribution of estimated volumetric mass transfer coefficient at different cross sections in the bubble column for Case 2. (a) Luo and Svendsen model; (b) improved breakup model. (from top to bottom: H = 0.6, 0.5, 0.4, 0.3 and 0.2 m.).

more uniformly distributed, in which case the enhanced overall mass transfer estimation comes from the statistical sum of the contributions of each bubble class.