Underground Diesel Exhaust Wet Scrubbers: Current Status and Future Prospects

: Diesel engines release a range of harmful components into the environment in the form of gases, liquids, and particulate matter (PM). These components have a direct and indirect impact on human health and climate change. Wet scrubbers are used to clean diesel exhaust emissions, by bubbling them through a liquid (usually water) to reduce their temperature and remove some soluble components and particles. Then, these emissions pass through a ﬁlter to remove further diesel particulate matter. The PM-capturing mechanism, heat transfer mechanism, and ﬂuid mechanism of a wet scrubber are reviewed. Several parameters have a major inﬂuence on wet scrubber performance, such as inlet gas velocity. Modeling of a wet scrubber can be conducted through thermodynamics analysis, heat transfer analysis, and computational simulation. These investigations may lead to optimizing wet scrubber performance, and then to reducing both humidity and temperature at the scrubber exit. This humidity reduction increases ﬁlter life and reduces maintenance costs.


Introduction
Atmospheric air contains pollutants that have a short-and long-term effect on human health [1] and climate change such, as nitrogen dioxide (NOx), ground-level ozone (O 3 ), and particulate matter (PM). In 2015, nearly 39% of nitrogen dioxides produced in the European Union was from the transportation sector. Significant nitrogen monoxide emissions [2] and 50% of PM are generated by diesel engines [3]. To clarify, diesel engine emissions can be divided into gaseous precursors (NOx, H 2 SO 4 , SO 3 , SO 2 , H 2 O, low-volatile, and semi-volatile organic compounds), and solid carbonaceous material such as PM [2][3][4].
PM is a suspended mixture in air, consisting of solid and liquid particles [5,6]. Its particles have different morphologies, sizes, and compositions. The diameter of PM can be measured using different methods based on their suitability. These methods are classified as: gravimetric, smoke opacity/smoke number, Laser Light Scattering Photometry (LLSP), Tapered Element Oscillating Microbalance (TEOM), and Scanning Mobility Particle Sizer (SMPS) [7]. Another measurement method was developed by Volkwein et al. [8] to estimate the PM from engines, based on the pressure increment across the dry filter.

Background
Experts around the world have developed a range of studies concerning wet scrubber development, in order to reduce PM. Mainly, there are two types of wet scrubbers: those based on liquid droplets, and those based on gas bubbles. One example of a gas bubble based wet scrubber is the diesel exhaust wet scrubber. The diesel exhaust wet scrubber consists of an inlet exhaust gases pipe, with an outlet inserted beneath the water surface, as shown in Figure 1. The exhaust gas stream goes through the liquid, breaking into bubbles in different shapes and sizes, based on their velocities and locations. These air bubbles leave the water surface, then the scrubber, through the gas outlet towards the DPF, with a lower temperature and higher humidity than the inlet conditions. This design has several advantages, such as strong transfer (for heat and mass), and ease (for operation and construction). Moreover, the absence of moving parts leads to low maintenance costs [21], and reduced wear and tear [22]. To clarify, the DPF (also known as a particulate trap) is defined as a simple device where particles are trapped.
Wet scrubbers have various responsibilities, in particular, the elimination of sparks before they make contact with the surrounding environment, the filtration of PM, and the reduction of exhaust temperatures [7]. Furthermore, the wet scrubber is more effective than other types of scrubbers, even if it is relatively small. Moreover, it can be used for scrubbing different materials, including those that are sticky, hygroscopic, combustible, explosive, or corrosive. Therefore, it can be used in several engineering applications [19]. For instance, Gabriel et al. [23] converted a wet scrubber into a bio-trickling filter, by developing a ten-step procedure. Their experiments confirmed that a bio-trickling filter effectively removes H 2 S, regardless of its concentration. the DPF, with a lower temperature and higher humidity than the inlet conditions. This design has several advantages, such as strong transfer (for heat and mass), and ease (for operation and construction). Moreover, the absence of moving parts leads to low maintenance costs [21], and reduced wear and tear [22]. To clarify, the DPF (also known as a particulate trap) is defined as a simple device where particles are trapped.  Although there are several positive aspects of wet scrubbers, they also have negative impacts. Firstly, the increased collection efficiency can lead to cost increments due to a pressure drop across the scrubber. Secondly, there are limits for both the temperature and the flow rate of exhaust gases. Moreover, a sludge waste is generated, which requires treatment or disposal. Another disadvantage is the presence of moisture in the gas stream, causing plume visibility or corrosion in the downstream system [19].

Capturing Mechanisms of Pollutants in Wet Scrubbers
The method of dissolving at least one component of a gas mixture into a liquid is called absorption, which is a feature of the wet scrubber. Two processes occur within this method. The physical process includes dissolving the components by solvent, which is controlled by the solvent and gas properties (viscosity and density), and the pollutant-specific temperature (equilibrium solubility and diffusivity depend on this). The chemical process represents the reaction between these components and the solvent. Most solvents are liquids, such as water, aqueous solutions, and some types of oils, namely, mineral and nonvolatile hydrocarbon. For economic feasibility, the solvent used to remove pollutants should be low in cost, viscosity and vapor pressure, and high in gas solubility. For this reason, water is considered to be the most suitable solvent for most applications [24].
Both chemical and physical processes increase if the contact area between the two phases increases. This contact area depends on bubble size at a constant gas flow rate. Passing gas through an orifice into a liquid pool leads to it breaking up into singular bubbles. Bubbles sizes and shapes are dependent on different factors, such as orifice (size and shape), fluid properties, and gas velocity. Bubble shapes can generally be classified into three different shapes: spherical, elliptical, and spherical cap. The transition from spherical to elliptical, and then to spherical cap, results from an increase in the gas flow rate within the system. Moreover, bubble size can also increase due to increasing orifice size, viscosity, and dissolving electrolyte concentration in the water. Bubble size decreases by decreasing surface tension by adding another liquid (such as alcohol) to water [25]. Furthermore, the liquid height above the orifice has a minor influence on bubble size [26].

Heat Transfer Mechanism in Wet Scrubbers
The design and operation principle of the wet scrubber is similar to the bubble column reactor. The bubble column reactor is a system containing a large number of gas bubbles, in direct contact with the continuum liquid. Moreover, the gas phase contains some soluble components, which are transferred to the liquid phase [27,28]. This reactor is suitable for various engineering applications [21]. These similarities concern flow type, analysis, gas inlet, and system types, as shown in Figure 2. To explain, Davidson & Schüler [29] experimentally investigated the bubble formation at an orifice fitted inside a viscous liquid. Several forces limited both the bubble motion and their positions, such as drag, buoyancy, surface tension, and inertia. It was observed that these forces had various influences on the detaching bubble volume based on the gas volume flow rate. Increasing liquid density created smaller bubbles, and increased the bubble rising velocity. Different types of heat transfer are found in wet scrubbers: evaporation, condensation, and convection. Evaporation occurs at the contact area between the liquid phase and the gas phase above. Condensation and boiling exist in most heat transfer cases of flowing fluid [30]. The phase changes from liquid to gas and vice versa, causing liquid evaporation, in addition to heat and mass transfer. The hydrodynamic behavior of the wet scrubber is also complex due to significant density compressibility differences in the fluid phases [19].
Heat transfer coefficients depend on multiple factors, in particular, the liquid properties (temperature variation changes the viscosity) and bubble size [31]. In other words, bubble motion depends mainly on this heat transfer rate and vice versa, due to direct interactions between bubbles and other structures within the fluid. Indeed, a high heat transfer rate could be achieved by adding particles to the liquid phase [32].
Gandhi and Joshi [33] analyzed the heat transfer coefficient of the bubble column. It was found that the Support Vector Regression (SVR) correlation was better than empirical and semi-empirical correlations, the main reason being that its prediction was more accurate and enhanced for different systems: gas-liquid, a large variety of operating pressures, a wide range of operating temperatures, most velocities of gas and liquid, different column diameters, and various liquid heights. Furthermore, Jhawar and Prakash [34] used fast response probes in a bubble column to study local heat transfer and dynamics. The authors claimed that this reactor should be operated in a heterogeneous regime, for high rates of achievement of heat transfer.

The Fluid Mechanism in Wet Scrubbers
Three types of flow patterns have been observed in wet scrubbers: homogeneous (bubbly), transitional, and heterogeneous (churn-turbulent). Based on the operation conditions, the most frequently encountered flow regime is the churn-turbulent flow [22]. The flow pattern depends mainly on inlet gas velocity, scrubber diameter, the height to diameter ratio, and the nature of the gas-liquid system such as pressure, temperature, viscosity, surface tension, solid loading, orifice size, and preformation pitch [22,35,36], as shown in Figure 3. This figure explains how increasing the inlet gas velocity changes the flow regime from bubbly to churn-turbulent, for a given scrubber size. Different types of heat transfer are found in wet scrubbers: evaporation, condensation, and convection. Evaporation occurs at the contact area between the liquid phase and the gas phase above. Condensation and boiling exist in most heat transfer cases of flowing fluid [30]. The phase changes from liquid to gas and vice versa, causing liquid evaporation, in addition to heat and mass transfer. The hydrodynamic behavior of the wet scrubber is also complex due to significant density compressibility differences in the fluid phases [19].
Heat transfer coefficients depend on multiple factors, in particular, the liquid properties (temperature variation changes the viscosity) and bubble size [31]. In other words, bubble motion depends mainly on this heat transfer rate and vice versa, due to direct interactions between bubbles and other structures within the fluid. Indeed, a high heat transfer rate could be achieved by adding particles to the liquid phase [32].
Gandhi and Joshi [33] analyzed the heat transfer coefficient of the bubble column. It was found that the Support Vector Regression (SVR) correlation was better than empirical and semi-empirical correlations, the main reason being that its prediction was more accurate and enhanced for different systems: gas-liquid, a large variety of operating pressures, a wide range of operating temperatures, most velocities of gas and liquid, different column diameters, and various liquid heights. Furthermore, Jhawar and Prakash [34] used fast response probes in a bubble column to study local heat transfer and dynamics. The authors claimed that this reactor should be operated in a heterogeneous regime, for high rates of achievement of heat transfer.

The Fluid Mechanism in Wet Scrubbers
Three types of flow patterns have been observed in wet scrubbers: homogeneous (bubbly), transitional, and heterogeneous (churn-turbulent). Based on the operation conditions, the most frequently encountered flow regime is the churn-turbulent flow [22]. The flow pattern depends mainly on inlet gas velocity, scrubber diameter, the height to diameter ratio, and the nature of the gas-liquid system such as pressure, temperature, viscosity, surface tension, solid loading, orifice size, and preformation pitch [22,35,36], as shown in Figure 3. This figure explains how increasing the inlet gas velocity changes the flow regime from bubbly to churn-turbulent, for a given scrubber size. Each flow regime has hydrodynamic characteristics completely different from others, resulting in different mixing as well as mass and heat transfer rates. The homogeneous flow regime occurs at lowto-moderate inlet velocities of the gas phase. The characteristics of this regime are small bubbles of uniform size, traveling vertically with minor transverse and axial oscillations. There is a narrow bubble size distribution with no bubble breakup and coalescence. By comparison, heterogeneous flow occurs at high inlet velocities of the gas phase. Both small and large bubbles are generated in this flow regime, as a result of the intensity of coalescence and breakup, causing wide bubble size distribution. It is called a churn-turbulent regime because the large bubbles churn through the liquid. The slug flow regime occurs for small columns where bubble size becomes very close to column size when a void fraction is larger than 30% [22]. Up flow occurs in the central region of the bubble column, while down flow occurs near the walls in this flow type [35].
Various experimental techniques have been outlined by Shaikh and Al-Dahhan [22], to determine the flow regime transition, from bubbly flow to slug flow (due to bubble coalescence), in the bubble column. Also, in their worthwhile review Besagni et al. [28] explained in detail all the possible flow regimes in the bubble column and which parameters could affect it. For example, flow characteristics might be measured using various techniques such as the photographic method [5], X-ray [7], PIV [10,37], optical fiber probe [38], conductivity probe [39], pressure transducer [20,[40][41][42], electrical capacitance tomography [43], and acoustic probe [44,45].

The Governing Parameters of Wet Scrubbers
The interrelated bubble parameters, such as bubble velocity, gas-liquid interfacial area, and bubble frequency, have a major influence on wet scrubber performance. Other factors affecting scrubber performance include scrubber design (geometry and size), operation condition (flow rates, temperatures, pressures), and physical properties [19]. Furthermore, particle changes (coagulation and volatility) could occur as a result of their passing through the exhaust system, after passing through the engine cylinders [46]. Moreover, the amount of water (high or low) in addition to equipment could affect wet scrubber performance [38]. Most importantly, dimensionless numbers can be used to describe the flow and heat transfer mechanisms, to make the equation independent of the specific equipment shape or size, viscosity, density, and so forth. Seven different dimensionless numbers can be Each flow regime has hydrodynamic characteristics completely different from others, resulting in different mixing as well as mass and heat transfer rates. The homogeneous flow regime occurs at low-to-moderate inlet velocities of the gas phase. The characteristics of this regime are small bubbles of uniform size, traveling vertically with minor transverse and axial oscillations. There is a narrow bubble size distribution with no bubble breakup and coalescence. By comparison, heterogeneous flow occurs at high inlet velocities of the gas phase. Both small and large bubbles are generated in this flow regime, as a result of the intensity of coalescence and breakup, causing wide bubble size distribution. It is called a churn-turbulent regime because the large bubbles churn through the liquid. The slug flow regime occurs for small columns where bubble size becomes very close to column size when a void fraction is larger than 30% [22]. Up flow occurs in the central region of the bubble column, while down flow occurs near the walls in this flow type [35].
Various experimental techniques have been outlined by Shaikh and Al-Dahhan [22], to determine the flow regime transition, from bubbly flow to slug flow (due to bubble coalescence), in the bubble column. Also, in their worthwhile review Besagni et al. [28] explained in detail all the possible flow regimes in the bubble column and which parameters could affect it. For example, flow characteristics might be measured using various techniques such as the photographic method [5], X-ray [7], PIV [10,37], optical fiber probe [38], conductivity probe [39], pressure transducer [20,[40][41][42], electrical capacitance tomography [43], and acoustic probe [44,45].

The Governing Parameters of Wet Scrubbers
The interrelated bubble parameters, such as bubble velocity, gas-liquid interfacial area, and bubble frequency, have a major influence on wet scrubber performance. Other factors affecting scrubber performance include scrubber design (geometry and size), operation condition (flow rates, temperatures, pressures), and physical properties [19]. Furthermore, particle changes (coagulation and volatility) could occur as a result of their passing through the exhaust system, after passing through the engine cylinders [46]. Moreover, the amount of water (high or low) in addition to equipment could affect wet scrubber performance [38]. Most importantly, dimensionless numbers can be used to describe the flow and heat transfer mechanisms, to make the equation independent of the specific equipment shape or size, viscosity, density, and so forth. Seven different dimensionless numbers can be investigated in wet scrubber performance, namely: Bo, Ec, Nu, Pr, Re, St, and We. For these reasons, any study of wet scrubber performance should consider all the related parameters.

The Effect of Inlet Gas Velocity
A change in gas volume flux has a significant effect on wet scrubber performance [7]. It was found that 19% absorption of carbon dioxide was caused by increasing the gas flow rate. Another 10% to 14% increment of absorption was achieved by heating carbon dioxide, which was based on the heat energy generated from the reaction between water and carbon dioxide. Under a certain amount of hydrogen chloride (HCl) concentration, increasing the inlet gas flow rate would result in a reduction in HCL removal [37]. Therefore, choosing a wet scrubber size depends mainly on the exhaust gas flow rate, as it limits the amount of scrubbing liquid [38].
Increasing the inlet gas velocity increases the mixing of the liquid phase, reduces bubbles size due to high bubble breakup [21], and leads to wider bubble size distribution [40]. Nevertheless, at low inlet gas velocities, bubble breakup and coalescence were weak, in addition to a narrow distribution being observed [40]. However, the excessive turbulence and high inlet gas flow rate lead to more water ejection at the scrubber exit. This could result in damages to the post-scrubber diesel particulate filter, in addition to increasing the maintenance time required [39]. Usually, diesel equipment for underground mining operates in continually varied operating conditions. Therefore, all these parameters can be expected.

The Effect of Bubble Size
Wet scrubber performance is dependent on bubble size because a larger bubble surface area transfers more heat. As a case in point, Higuera and Medina [41] investigated bubble generation and coalescence in quiescent inviscid liquid, using the formulation of potential flow. A constant gas flow rate was injected vertically upward into the liquid. Their results show that bubbles have a constant volume at a low Weber number because bubble growth depends on inertia and buoyancy forces. At a high Weber number, on the other hand, this growth was led by the interaction among the bubbles. Moreover, increasing the inlet gas velocity reduces the average bubble diameter [47]. Conversely, bubble size could be reduced as a result of a pressure increment [43]. In a wet scrubber, the gas phase is injected underneath the liquid-phase surface at a non-constant rate, so the bubbles have non-uniform shapes with the continuous breakup and coalescence. Thus, investigating this particular parameter is extremely complex.

The Effect of Particle Density
PM loading is known as dust loading, and it is defined as the mass of PM per unit volume at the scrubber inlet. Removal efficiency decreases as the fly-ash loading increases [47]. Furthermore, Guo and Gao [48] used a wet scrubber to remove both SO 2 and NO 2 ; using limestone slurry including several operating parameters, namely, the reaction temperature, oxygen amount in flue gas, and inlet concentration of SO 2 and NO 2 . It was found that minimizing the concentration of the inlet NO 2 , the amount of O 2 in the flue gas, and the reacting temperature, caused a reduction in the removal efficiency of SO 2 . Nevertheless, the absorption of NO 2 was increased due to increasing the concentration of the inlet SO 2 and reducing the reaction temperature and the flue gas oxygen. Furthermore, the collection efficiency depends on the particle size. Therefore, higher efficiency could be achieved with large particle sizes [19,47]. In summary, for underground diesel equipment, PM depends on fuel type [14] and equipment operating conditions.

The Effect of the Liquid Thermal Properties on Pollutant Removal
Pollutant diffusion occurs when the liquid has less pollution than the gaseous component [24]. For instance, Bhadra et al. [49] experimentally tested a wet scrubber, using a water solution and other components to collect solid particles. Their experiments were conducted by wetting solid particles through direct contact with the liquid. After absorption, the solid particles were dissolved in the liquid or created a colloidal form that settled down. It was observed that mixing carbonate of calcium (limestone) with exhaust gases from the engine gave a higher emission reduction. In another example, Talaia [44] experimentally tested the bubble rising velocity in a single column using two different liquids (water and glycerol). It was confirmed that this velocity depends mainly on drag force rather than buoyancy.
The most suitable absorption liquid can be chosen after considering several factors, particularly availability, cost, pollutant concentrations, removal efficiency, requirements for handling exhaust gas capacity, and the recovery value of pollutants. Adding coolants such as urea ((NH 2 ) 2 CO) to the scrubbing liquid will increase its boiling temperature and life. Indeed, the removal efficiency increases for a limited time [49]. Therefore, it is key to consider this effect in any underground diesel exhaust wet scrubber investigation.

The Effect of Liquid Volume
High water levels in the wet scrubber lead to a 25% reduction in PM emissions [11]. However, increasing the water level inside the scrubber also leads to more water exiting [45]. The investigation of underground diesel exhaust wet scrubber performance should consider this factor to determine which one of these two options is more important.

Scrubber Outlet Conditions (Particularly Temperature and Humidity)
Lowering the exhaust gas temperature is the main role of the wet scrubber. Its lesser role is to eliminate the sparking possibility at the exhaust [42]. Indeed, increasing the outlet gas temperature reduces the corresponding relative humidity. Equally importantly, the water evaporation causes most of the water transportation from the scrubber. This evaporation depends on the inlet gas-phase temperature, while a low amount of water leaves the scrubber due to the aerodynamic process. Another 2-8% water generates from the combustion, and is carried by exhaust gas. This percentage is not constant; it is affected by both engine load and speed [7]. Exit temperature and relative humidity increase with operation time, and any type of thermal energy leaving or entering the scrubber depends on engine rpm. The increment in the absolute humidity was also found to occur at a high evaporation rate [22].

Removal Efficiency
The removal efficiency depends strongly on the scrubber configuration and the scrubbing liquid [42]. It is defined as the number of molecules of a compound removed or destroyed in a system relative to the number of molecules that entered the system: where: C in is the concentration of any component that enters the system, and C out is the concentration of any component that leaves the system. Or [50]: f iltertion e f f iciency = Particles downstream trap Particles upstream trap × 100%.
Researchers have studied this parameter extensively to reduce the emission at the scrubber exit. For instance, Tokumura et al. [51] effectively removed indoor air pollutants using a wet scrubber coupled with the photo-Fenton reaction. To clarify, this reaction consists of a series of chain reactions between H 2 O 2 at acidic value and Fe(II)/Fe(III) [52]. Indeed, the high increment in removal efficiency was achieved using this technique [53,54]. Also, D'Addio et al. [55] experimentally tested an electronic wet scrubber by spraying tap water to remove both fine and ultrafine particles from combustion gases. By system charging, there was an increment of approximately 30% achieved in removal efficiency. Therefore, the hydrodynamic interaction was less effective than electrostatic interaction. More importantly, high removal efficiency is achieved due to bubbles bursting [27].

A Thermodynamic Model of the Diesel Exhaust Wet Scrubber
An energy balance can be applied to a wet scrubber with thermodynamic analysis. It balances inlet and outlet masses, in addition to inlet and outlet energies, as shown in Figure 4 [39]: where: . E in is the inlet energy of exhaust gases from the diesel engine (kW), . E out is the outlet energy leaving the scrubber from its exit (kW), . E ∆ν is the lost energy because of the water volume changing (due to evaporation) (kW), Q L is the heat transfer from the scrubber to the surrounding environment through all of its sides (kW), and . E w is the amount of storage energy inside the scrubber (kW). where: is the inlet energy of exhaust gases from the diesel engine (kW), is the outlet energy leaving the scrubber from its exit (kW), is the lost energy because of the water volume changing (due to evaporation) (kW), is the heat transfer from the scrubber to the surrounding environment through all of its sides (kW), and is the amount of storage energy inside the scrubber (kW). The calculations of inlet energies and outlet energies would be based on the components of the exhaust gases, which consist of carbon dioxide, water vapor, oxygen, and nitrogen, as shown in Equation (4) Therefore, inlet energy consists of the inlet energy of each component as:  The calculations of inlet energies and outlet energies would be based on the components of the exhaust gases, which consist of carbon dioxide, water vapor, oxygen, and nitrogen, as shown in Equation (4): Therefore, inlet energy consists of the inlet energy of each component as: .
Similarly, the outlet energy from the wet scrubber exit represents the entire mixture: .
where: m . is the mass flow rate (kg/s), c p in is the specific heat capacity at the scrubber inlet temperature (kJ/kg·K), c p out is the specific heat capacity at the scrubber outlet temperature (kJ/kg·K), T in is the temperature at the scrubber inlet (K), and T out is the temperature at the scrubber exit (K). Moreover, by combining the energy loss due to water evaporation, with the liquid phase that is leaving the wet scrubber because it is carrying some energy, the energy loss due to changing water volume is calculated by: where: h f g is the water vaporisation latent heat (kJ/kg), dW dt is the water mass change rate (kg/s), and c p f is the liquid specific heat capacity (kJ/kg·K).
Water temperature increases as a result of heat transfer from inlet gases, and this energy stores in water, therefore, it can be calculated as: where dT w dt is the water temperature changing rate (K/s). The heat loss through the scrubber body can be calculated as: dT above dt + %A below m scrub. c p scrub. dT below dt + (m w c p f dT w heat loss dt ), (9) where %A is the scrubber surface area percentage, above or below the liquid surface, and scrub. refers to the scrubber. The enthalpy-based calculation is another method to calculate the energies instead of heat capacity mentioned in Equations (5)- (7). Finally, the liquid balance technique calculates the evaporation rate through the scrubber, as follows: where E is the evaporation rate (kg/s), . m w in is the average inlet liquid mass flow rate (kg/s), and . m w out is the average outlet liquid mass flow rate (kg/s).

Bubble Heat Transfer Model
Heat transfer analysis of the wet scrubber should directly investigate the bubbles in the scrubber, their formation mechanism, variation of growth with time and height, and finally the heat transfer mechanism between the bubbles and their surrounding liquid. The bubble heat transfer coefficient greatly depends on the two-phase flow regime [36,56]. One of the several classifications of two-phase mixtures is based on their combinations of gas, liquid, and solid phases, in addition to the possibility of plasma. In a diesel exhaust wet scrubber, all these types exist except the plasma. Furthermore, variations in the two-phase flow occur due to phase combinations and varied interface structures [57].
For a thorough investigation, the influence of all forces acting on bubbles must be considered. Single bubbles do not exist in wet scrubbers, due to the nature of the high gas-phase flow rate. However, the heat transfer model of a wet scrubber could begin by studying a single bubble, then expanding to multiple bubbles with various sizes and shapes.
Forces that affect the bubble vertically are drag force, buoyancy, virtual mass force, and gravity [36,58,59]. These forces equal bubble mass multiplied by its acceleration, according to Newton's second law of motion, as follows: where P is the pressure force, F D is the drag force, F V is the virtual mass force, F G is the gravity force, and all in (N), m is the bubble mass (kg), and a is the bubble acceleration (m/s 2 ). Pressure forces direct an object upward in liquid, due to the pressure difference between the top and the bottom of that object. It is equal to the fluid weight displaced by the body: where V b is the bubble volume (m 3 ). The liquid resistance to bubble movement is called drag force, and it can be calculated as: where C D is the drag coefficient due to drag force, and s a is the bubble front face area (m 2 ). Rising bubbles accelerate the surrounding liquid and generate another virtual mass force. This force increases inertial mass effectiveness, and interrupts the continuous phase acceleration. However, the virtual mass force could be neglected if the dispersed phase density far outweighs the continuous phase: Finally, the gravity force is calculated as:

Bubble Size
Bubble motion depends mainly on its volume [58]. Therefore, it is important to investigate this factor to improve wet scrubber performance. Indeed, bubble volume is calculated from the force balance mentioned in the previous section. On the other hand, the gas flow rate has no effect on bubble volume in a static regime (at a small gas flow rate), due to neglecting the two-phase momentums. In the turbulent regime, large bubbles shatter into small ones, because they cannot survive against the gas turbulence [59]. Table 1 demonstrates some correlations of both dimensional and non-dimensional bubble diameter. This table could be valuable for bubble diameter estimation in a scrubber. In particular, the correlation proposed by Levich [60] concerns a churn-turbulent regime, and that developed by Martinez-Bazan et al. [61] concerns turbulent flow. At a constant inlet gas velocity, Davidson and Schuler's equation [62] could calculate bubble diameter without including the fluid properties. Bubble shape can be assumed to be spherical or elliptical based on the flow type. For a constant flow rate at the orifice without including the inviscid liquid properties and surface.
3 Levich (1962) [60] d max ≈ 3.63σ Churn-turbulent flow regime. 4 Wallis (1969) [64] 1 3 When the diameter of the orifice is comparable with the radius of the bubble, that is Moalem and Sideman The breaking up of injected bubbles into fully developed turbulent flows based on Kolmogorov's concept. Following the idea of Levich [60]. The unsteady motion of single bubbles rising freely in a quiescent high viscous liquid. The volumetric gas rate and the number of generated bubbles per unit time were used to calculate the bubble volume based on spherical shape assumption.

Bubble Rising Velocity
The rising velocity of a single bubble depends on buoyancy and drag forces, which are functions of gravity, fluid properties, and equivalent diameters. Dynamic viscosity has a strong effect on terminal velocity [44]. The bubble acceleration affects the total drag coefficient [68]. Similarly, a slip occurs at the liquid-vapor interface, and the liquid cleanliness can be determined by measuring small bubbles [69]. Also, bubble velocity increases due to the bubble size increment. Moreover, the bubble drag coefficient and aspect ratio decrease with an increasing Reynolds number [70]. For more details, Table 2 shows several correlations to predict bubble rise velocities. It contains some of the most widely used correlations [71]. Indeed, some correlations should be examined carefully for their suitability for a wet scrubber, especially those on Line 3-5, and 8 in Table 2. For this purpose, three-dimensional bubble movement should be considered to achieve more accurate results. Collapse for un-pure vapor radius-dependent rising velocity was obtained using a simple energy balance by assuming a quasi-steady state.

Bubble Heat Transfer
Bubble heat transfer rate is influenced by various factors, such as bubble size, bubble orientation, temperature, and the physical properties of both gas and liquid phases [33]. Heat transfer increases with increasing gas-phase inlet velocity, and working pressure [43]. Simply, the heat transfer can be calculated from the energy balance at the interface of the bubble, by assuming the bubble to have a spherical shape; it can be expressed mathematically as [29]: Subsequently, the heat transfer coefficient can be calculated from correlation [79]: The heat transfer coefficient can become more complex during rising motion, so [79]: where h c is the heat transfer coefficient, and t k is the condensation time (s). Moreover, the heat transfer can be calculated using other correlations. Some of them were reported by Reference [33], as explained in Table 3. The most suitable correlations for wet scrubbers are the Line 6-7, 9 and 14-15 of Table 3 due to flow and system similarities.
Large rising vapor-gas bubble condensation in a hypothetical core. 8 Deckwer et al.  For bubble column using a fine and a coarse gas distributor: The 1st correlation is for ug g ≤ 0.3 m/s The 2nd correlation is for ug g > 0.3 m/s. 16 Leong et al. (2017) [90] q = h f g ρ 1 2 g [σ(ρ l −ρ v )] 1 4 1+cos β 16 Critical heat flux for pool boiling by adopting the force balance approach including the effects of capillary wicking force and the modified Taylor wavelength.

Computational Simulations
Two-phase flow analysis usually starts with general principles that govern all matter behavior in a particular mass, momentum, and energy conservation, because they can be expressed in mathematical form at any time and in any position [91]. Additionally, Wallis [64] is considered to be the first scientist who used the one-dimensional drift flux to analyze the fluid flow.
Several studies focused on simulating bubble columns. Indeed, different computational fluid dynamics methods were used to study the bubble column hydro-dynamically. For example, Direct Numerical Simulations (DNS) represent the whole physics of the flow, using the Volume of Fluid (VOF) approach in software such as FLUENT [92], and OpenFOAM [93]. Therefore, special algorithms are necessary for fluid interfaces, tracing between continuous and particle, as well as a very fine mesh grid to garner all time and length scales.
The interface motion can be modeled using different methods [94]. For example, such methods include the Eulerian-Lagrangian (E-L) method, the two-dimensional and transient study of a single particle [95], and the Eulerian-Eulerian (E-E) method. Different turbulence models adopted the E-E method, such as the Reynolds Stress Model (RSM), large eddy simulation [96], explicit algebraic Reynolds stress model, baseline models [97], and multi-fluid turbulence model [78]. By solving the motion equations for individual bubbles, or bubble tracking, the gas phase can be described [98].
For the wet scrubber, there is currently no simulation available due to the complex churn-turbulent flow, and its extremely complex design compared to a bubble column. As a starting point, simulation for simple cases of flow inside a wet scrubber can be achieved using ANSYS Fluent with several assumptions included.

Conclusions
The performance of a diesel exhaust wet scrubber depends on several parameters, including the scrubber design and operating conditions. It is important to reduce the humidity at the scrubber exit, to prolong the DPF life after the scrubber. This will produce two benefits: increasing the operating time, and reducing the maintenance cost. Few studies have focused on this type of wet scrubber. Therefore it is advantageous to have an up-to-date and informative database about this device, in particular for countries with mining sites, or which have mining equipment production. To reduce the time that might be spent on such studies, careful consideration of bubble column studies should be made to find the most suitable investigative approach, especially using computational simulation, as wet scrubbers have almost the same design and operating principles as bubble columns. Finally, experiments and three appropriately-developed models, thermodynamics, heat transfer, and computational simulation, can be used to investigate the performance of diesel exhaust wet scrubbers.