Developments in Unipolar Charging of Airborne Particles : Theories , Simulations and Measurements

Charging of airborne particle is an important process in both scientific studies and industrial applications, of which the unipolar charging takes up the major part due to higher charging efficiency. In order to understand the charging mechanism of airborne particles, accordingly to predict the efficiency of unipolar chargers, different theoretical models have been proposed and investigated in all regimes. Numerical techniques have been also adopted by researchers to analyze the charging process of airborne particles and thus to model the unipolar chargers. On the other hand, with the advent and application of various measuring techniques, the electric charges measurement of airborne particles was made possible for researchers. In this work, we mainly present a summary of these models, numerical techniques and experimental results on unipolar charging in all regimes, as well as the recent developments in the design of unipolar chargers, trying to briefly overview the development in this research field.


INTRODUCTION
Airborne particles, also known as particulate matter (PM) or particulates, are commonly referred to the particles that are able to suspended in the atmosphere, which can be as respirable suspended particle (RSP; particles with diameter of 10 µm or less), fine particles (diameter of 2.5 µm or less) and ultrafine particles.Airborne particles consist of diverse composition including nitrates, sulfates, elemental and organic carbon, polycyclic aromatic hydrocarbons (PAHs), biological compounds, and metals (Cheruiyot et al., 2015;Kim et al., 2015), which causes severe impacts on climate and human health (Li et al., 2015), fine particles have been extensively studied in diverse fields (Aurela et al., 2015;Malaguti et al., 2015).Among them, the charging process of particles plays an essential part in many applications.For instance, some particle size measurement instruments by electrical differential mobility analysis require the particles to be unipolarly charged with a known charge distribution (Kulkarni et al., 2011), related instruments of which are differential mobility analyzers (DMA) and aerosol particle mass analyzer (APM).Similarly, particle measurement by electrical low-pressure impactors (ELPI) also requires particles to be charged in a corona charger, therefore faradic current produced by charged particles of each channel can be measured (Marjamaki et al., 2000).In addition, particle charging is an important process in gas purification facilities such as electrostatic precipitators (ESPs) (Kim et al., 2012;Qi and Kulkarni, 2012;Liang et al., 2013;Luond and Schlatter, 2013;Clack, 2015) and filtration facilities (Sambudi et al., 2016).Compared with bipolar charging, unipolar charging of airborne particles has attracted particular attention, primarily due to its higher charging efficiency, since the recombination of charged particles with ions of opposite polarity are avoided.
Depending on the mechanisms used to generate gaseous ions for charging, most unipolar chargers can be classified into three types: corona, radioactive, and photoelectric.Corona dischargers are most commonly used to produce highconcentration ions (Hernandez-Sierra et al., 2003;Alguacil and Alonso, 2006;Intra, 2012).The discharging corona is usually produced in a non-uniform electrostatic field, either in a corona-wire or corona-needle configuration.When the field strength is high enough somewhere, ambient air or other gases will undergo an ionization process, and a large amount of gaseous ions and free electrons are generated for charging process.Ionizing radiation is another technique commonly adopted by researchers (Chen and Pui, 1999;Vivas et al., 2008a).Radioactive sources, such as 241 Am and 210 Po, were used to emit bipolar charged ions, and unipolar ions for charging were separated with an imposed electric field.Photoelectric effect also found its application in airborne particle charging (Han et al., 2003;Hontañón and Kruis, 2008;Kim et al., 2011), when the frequency of the incident radiations, like soft X-ray or ultraviolet (UV) lights, exceed a certain threshold value, electrons can be emitted from the surface of particles, and irradiated particles thus become positively charged.In latest research, soft Xray chargers are also used in fine particle pre-charging and removal in ESPs (Choi et al., 2016).Recently, new types of chargers such as ion beam aerosol charger (IBAC) (Seto et al., 2003;2005), surface-discharge microplasma aerosol charger (SMAC) (Kwon et al., 2005;2007;Manirakiza et al., 2012) and carbon fiber ionizers (Han et al., 2008;Park et al., 2011b) were also introduced as the alternatives of traditional unipolar chargers, with higher charging efficiency for ultrafine particles, controlled ion concentration and less ozone generation, which reduced environmentally hazardous by-products and guaranteed chemical or biological analysis accuracy.
To better describe the unipolar charging process of airborne particles under different circumstances, and more precisely predict and further improve the efficiency of chargers in different applications, numerous charging models have been developed and compared with experimental studies as well.In this article, a summary of typical models and numerical techniques, as well as representative experimental results on unipolar particle charging are presented, aiming to summarize the development of researches concerning the unipolar charging process of airborne particles.

THEORETICAL MODELS ON UNIPOLAR CHARGING
Existing models for unipolar airborne particle charging are primarily classified into three regimes according to their application range (Fig. 1), which is indicated by the Knudsen number (Kn = 2λ/d p , the ratio of mean free path of gaseous charging ions to the diameter of charged particles).Respectively, the three regimes are continuum regime (Kn << 1), transition regime (Kn ~1) and free-molecular regime (Kn >> 1).This section reviews the progress on theoretical charging model research and compares the theories, hypothesis and application regimes of different models, which are concluded in Table 1.

Continuum Regime (1) Field Charging
'Field charging' was the first model proposed for particle charging.Based on a rather comprehensive physical view, it was theoretically studied by Pauthenier and Moreau-Hanot (1932).In the model, charged particle is simplified as a conducting sphere suspending in the electric field, and gaseous ions are assumed to be transported to the particle surface along the field lines.As the charging process continues, the particle acquires more electric charges and field lines are gradually repelled from the surface (as shown in Fig. 2).
Under these assumptions, the number of ions deposited on the particle surface is calculated using electrostatic principles.And by integrating the ion current around the particle surface, the overall charging rate in an external electric field E is given by, After integration with starting condition t = 0, q = 0: where d p is the particle diameter, N i is the concentration of ions above the surface, e the elementary unit of charge, E is electric strength, Z is the electrical mobility of ions, q s is saturation charge, equals to (3ε s /(ε s + 2))πε 0 d p 2 E 0 , τ is the time constant of field charging, equals to 4ε 0 /(N i eZ).The formula is applicable for conductive and dielectric particles with different specific dielectric constant.
However, in real cases, the applied electric field is not always uniform, particle charging models in non-uniform fields should be paid attention to.Kim and Yoon (1997) derived a simple expression for the field charging rate of a spherical particle in a linear electric field, while Adamiak (1997) and Samuila et al. (1998) studied the charging process of particles in an alternating electric field.Experimental investigations and numerical simulation showed that particles could be charged up to a level close to the saturation value, as predicted by the Pauthenier formula, however, the charging process is not continuous but proceeds only in the time intervals in which the external electric field is stronger than the field produced by the charges already accumulated on the particle.In rest of the time, the resultant electric field repels the ionic bombardment and the particle charge remains unchanged.Lackowski (2001) performed similar numerical calculation, and compared the results with experimental ones, which confirmed the validity of field charging model.
In another aspect, Zevenhoven (1999) analyzed the effect of particle surface conductivity on the unipolar charging process.By allowing for a non-uniform distribution of free charges, the author obtained an expression for the electric current on the particle surface and results showed that a surface charge non-uniformity would lead to a rotation of a particle for a typical field charging case.Similarly, Alisoy et al. (2005) investigated the charging of spherical dielectric particles in an electric field, and demonstrated that a stationary particle acquired less charge than a rotating particle.Koseoglu and Alisoy (2011) extended the theory into a stationary and rotational cylindrical dielectric particle in unipolar corona field.Furthermore, Alisoy et al. (2010) made the analysis on the effect of particle concentration and mobility on the charging process, and illustrated that the ion density variation and the particle drift velocity could significantly affect the field charging kinetics. (

2) Diffusion and Combined Charging
Although 'field charging' mechanism is generally considered to be predominant for particles with larger than 0.5 µm (White, 1951), it becomes less effective as the particle size decreases.In the cases where low-intensity electric field is applied or smaller particles are adopted, the chaotic motion of gaseous ions thus cannot be ignored.To better describe this charging mechanism of airborne particles, a 'diffusion charging' theory was proposed by Fuchs (1947) and Bricard (1949), respectively.Based on solving the continuum transport equation of ion concentration around a single spherical particle, the ion current in the vicinity of particle surface is calculated by, where D i is ionic diffusion coefficient (equals to Z(k/e)T), d p is the particle diameter, N i is the ion concentration, e the elementary unit of charge, x is the ration of r and a, r is distance from the center of the particle, a is the radius of the particle, ε 0 is the vacuum dielectric constant, ε s is the dielectric constant of particle.White (1951) later derived a simpler expression for diffusion charging from gas kinetics theory, which was later pointed out to be also valid in free molecular regime (Gentry and Brock, 1967;Liu et al., 1967b).The diffusion charge is expressed by, Table 1.A comparison of theoretical models on unipolar particle charging.

Maxwellian
Transition and free molecular Charge distribution Boisdron and Brock (1970)   * * ln 1 where t is time, q * is particle charge constant, τ * is the time constant of diffusion charging, d p is the particle diameter, N i is the ion concentration, e the elementary unit of charge, ε 0 is the vacuum dielectric constant, m i is ion mass, Z is the ion mobility, k is the Boltzmann constant and J is current density.Thus, to take both charging mechanisms into account, researchers have made different approaches to combine these two models in a reasonable way.Murphy (1959) made the first trial but ended up only in qualitative analysis.Another method was taken by Liu and Ye (1968) who divided the entire charging process into two time steps.Before reaching the saturation charge limit, the particle is subject to both charging mechanisms, while after that, it is only 'diffusion charging' that works.Similar but more complex model was obtained by Smith and McDonald (1975), who identified three regions on the particle surface, and calculated the overall charging rate as the sum of them.Till now, a most commonly used model was developed by Lawless (1996), which has been extensively used in the numerical simulations of electrostatic precipitators (Long and Yao, 2012;Guo et al., 2013;Lancereau et al., 2013).The charging rate is expressed in a dimensionless form as: where v = qe/2πε 0 d p kT is the dimensionless particle charge, w = (ε s /ε s + 2)(Ed p e/2kT) is the dimensionless electric field strength, and t = (ρ s b i t/ε 0 ) is the dimensionless charging time.

Transition and Free Molecular Regime (1) Limiting Sphere Model
In the non-continuum regime, where the diameter of particles is in the same magnitude or even smaller than the mean free-path of gaseous ions, the image force induced by the charged particle cannot be ignored.Therefore, previous charging models for airborne particles in continuum regime no longer fit here.
The charging model in transition regime was first proposed by Natanson (1960), and later developed by Fuchs (1963) as the 'limiting sphere' model.It assumes that the particle charging region is separated by an imaginary sphere concentric to the particle.Inside the sphere, the ions are supposed to travel without collisions with gas molecules (shown in Fig. 3), so the number of ions striking the particle in unit of time is given by: where δ is the limiting-sphere radius, n(δ) ion concentration on the limiting sphere, c ̅ the mean thermal velocity of the ions, and α the fraction of all the emerging ions which finally reaches the particle surface.(Fuchs, 1963).Natanson (1960) calculated the overall probability α of the collision between ions and the airborne particle, given by: where φ(ρ) is the potential of the ion, b distance from O to the tangent drawn to the trajectory at point A, and b m the minimum value of b.Outside the sphere, the charging process is described by the classic diffusion theory of ions.
To match the two fluxes at the surface of the limitingsphere, the charging rate of a single particle is derived.Marquad (2007) extended the model into a 2D form to include the presence of external electric field.As a result of imposed electric field force, the collision probability α is no longer constant for ions striking from different angle, but turned out to be a function of azimuthal angle, expressed as α(θ).Similarly, the electrostatic potential map around the limiting sphere is recomputed with the existence of external electric field, and continuum convective-diffusion equation is solved for the ion concentration profile on the limiting sphere at different angle.In this way, by integrating the ion current around the limiting sphere surface, the overall ion current is obtained according to, where β i equals to I/(eN i,∞ ), integral combination coefficient.I is the current through the limiting sphere.where q is the particle charge, n ∞ the ion concentration at infinity, and thus extended the limiting sphere theory into a more elaborate 2D model with wider application in the transition regime.
(2) Boltzmann Equation and BGK Model Nevertheless, due to the mean velocity assumption employed in the limiting sphere model, it will probably underestimate the acquired charge of finer particles under certain conditions.Gentry and Brock (1967) took a different approach, trying to illustrate the unipolar charging mechanism with a first order approximation of Boltzmann equation.
Since the ion concentration is sufficiently low that ion-ion interactions can be neglected, the gas system can be described by the Boltzmann equation.The equations for the ions i and neutral gas j have the following forms, where f i and f j are the velocity distribution functions of ions and neutral gas molecules in the neighborhood of the particle, X is the spacial vector, v i and v j represent velocity vectors of ions and neutral gas molecules, Γ i and Γ j are the appropriate collision operators, and F i is the force vector per unit mass acting on an ion owing to the presence of charge on the particle.
The net flux of ions to a particle is determined from the moments of the velocity distribution functions of ions striking and reflecting from the particle surface respectively.A rather complicated expression is found for the net radial flux of ions to a conducting particle.Later, Gentry (1972), Marlow and Brock (1975) modified the theory, and took the image force into account, while Huang (1990) took Van der Waals force into consideration as well.More recently, Lushnikov (2005) further developed the BGK model in the free molecular regime.Based on a solution of the collisionless kinetic equation about ion transport in the presence of force fields created by the particle charge and the image force, they used the exact free-molecule ion distribution over coordinates and velocities to calculate the rate of ion deposition onto neutral and charged dielectric particles, which is applicable for particles with the size much smaller than the ion mean free path. (

3) Charge Distribution Model
Previous descriptions of the unipolar charging processes for airborne particles were largely averaged or deterministic in nature, whereas, Boisdron and Brock (1970) pointed out that such descriptions are inadequate for charging process.
Apparently, collision of an ion or radioactive atom with a particle is a random event, thus resulted a statistical distribution of ions on the poly-disperse particles or even mono-disperse ones.Combining Natanson's (1960) expressions on the ion fluxes with the Boltzmann-like equations of the concentrations of the particles, the equations can be re-written in the expanded form: where N p,n is the concentration of airborne particles with n elementary charges, N i is the ion concentration, and β n is the combination coefficient of ions with airborne particles carrying n elementary charges.Together with the initial boundary conditions, the steady-state charge distribution on airborne particle clusters is determined.However, this set of equations neglects both ion and particle losses and supposes that ions and particles are uniformly mixed in the charging region.Recently, a revised charging model based on the birth-and-death theory was developed.In the work of Kimoto et al. (2010), they estimated the effect of electrostatic dispersion on particle losses in the charging chamber with the assumption that particles are completely mixed with unipolar ions in the charging chamber and compared the calculated results with experimental results.Furthermore, Domat et al. (2014a) proposed a revised model including both diffusional and electrical losses for airborne particles and ions.The electrical loss is modeled with the inclusion of a radial electric field which is considered constant throughout the charging region, while the diffusional one is expressed by a loss factor determined from the ratio between the total volume occupied by the ions and the surface area where they are probably loss.In this way, this model can be used to more precisely predict the charge distribution in real unipolar chargers, as well as to obtain the ion concentration and mean radial electric field from the measured charge distribution fractions, without additional measurements.

Non-Spherical Particle Charging Model
Despite the varieties of charging models for airborne particles mentioned above, none of them is applicable to non-spherical particles.A charging model towards arbitrarily shaped particles was first developed by Laframboise and Chang (1977).The model also assumes that the charge transport to the particle is governed by the continuum transport equation and ions have a sticking probability per collision with the particle surface.Chang (1981) re-examined the theory and provided simpler equations depending on the Kn ion .The mean charge of airborne particle obtained from unipolar diffusion charging is governed by the following equations: In continuum regime (Kn ion → 0), and in free molecular regime (Kn ion → ∞), where n p is the mean charge of airborne particle, C p is the electrical capacitance, ϕ p is the non-dimensional surface potential eV p /(kT), V p is the electric potential of a particle relative to the potential at large distance, S p is the geometric surface area of particle.
Most recently, Gopalakrishnan (2013) applied a different method, trying to describe the charging process with collision kernel based equations.The charging rate for airborne particles with p number of charges is calculated as: where N p and N i are the airborne particle and ion number concentrations, and β p;i is the collision rate coefficient or kernel of ions and particle.To obtain the collision kernel for airborne particles with arbitrary shape, Gopalakrishnan utilized a dimensional analysis method to identify different shapes with two dimensionless number: the Coulomb potential energy ratio, and the image potential energy ratio.
With the examination of molecular dynamics (MD) and Brownian dynamics (BD) calculations, an expression for collision kernel was found applicable for particles of any shape.The simulation results also indicated that this model could provide more accurate predictions in the transient regime than the limiting sphere model.

Numerical Techniques on Unipolar Charging Process (1) Monte-Carlo Simulation
Despite the comprehensive physical pictures embedded in those models above, few of them are able to capture the charging characteristic of particles with complex shapes.In an effort to describe the charging process of such airborne particles, a Monte-Carlo code has been developed by Filippov (1993), and was later developed and extended to wider applications by Biskos (2004).
The Monte-Carlo method is well-known and widely used in modeling and describing transport phenomenon, by using large numbers of realizations to compile the average behavior.As illustrated in Fig. 4, the simulation volume consisted of uniformly distributed particles and ions that move randomly according to their thermal velocities.Since the particles are significantly more massive compared to ions, they are considered to be fixed in the simulation volume.In the simulation process, as is mentioned before, the ions are assumed to move in straight paths between ion-particle collisions far off the charged particles.But when an ion gets close enough to a charged particle, the velocity is significantly altered by the ion-particle interaction force, and the speed distribution departs from Maxwellian.Solving the dynamic equation of ions numerically along the free path accordingly results in the ion trajectories near the particle.After large numbers of iterations, the averaged charge acquired is determined.For agglomerates, the total charge number is the sum of that on every elementary particle.Filippov (1993) developed the first Monte-Carlo simulation code on unipolar charging process, and particles with diameters between 5 and 80 nm were adopted in the calculation.The calculation results were compared with previous experimental data of Adachi et al. and other researchers (Adachi et al., 1985;Romay and Pui, 1992), as well as the predictions of limiting sphere model.As is shown in Fig. 5, Monte-Carlo method and the limiting sphere model gave relatively close results, which agreed fairly well  with experiments in the entire diameter range.Likewise, Biskos (2004) also examined the Monte-Carlo method for particles in the size range of 5 to 1000 nm, and further extended it into non-spherical particles charging, where rectangular shape particles, chain aggregates and 3D crossshape aggregates were employed.A close agreement was found between Monte-Carlo method and the charging models for spherical particles.As for non-spherical airborne particles, however, the charging behavior exhibited significant divergence compared with theoretical predictions, which calls on further studies on this topic. (

2) Numerical Modelling of Unipolar Chargers
Apart from the Monte-Carlo simulations on theoretical charging processes, researchers also developed numerical techniques to analyze the charging process in unipolar chargers.Aliat et al. (2008;2009) presented a twodimensional numerical model on airborne particle charging in a negative wire-tube corona charger with the combination coefficients of negative ions and electrons to airborne particles calculated by Fuchs's model, the numerical results of which showed good agreement with experimental data of Marquard (2005).Alisoy (2012) also developed a numerical method to investigate the charging kinetics of poly-disperse particles in a coaxial electrode system, where a previous charging model considering ion concentration and particle mobility was adopted (Alisoy et al., 2010).Alonso (2009) investigated and compared the effects of four different initial mixing state on the charging process, which is often ignored by other researchers.
Besides, particle and ion loss to the walls by diffusion and electrostatic dispersion were also taken into account in the calculations (Alonso andAlguacil, 2003, 2007).Numerical results show that the charger's extrinsic charging efficiency (the percentage of neutral particles which acquire charges in the conditioner and make the exit of charger) strongly depends on the initial mixing state, and the maximum efficiency is achieved when a core of ions is surrounded by airborne particles, a state which has been in practice by injecting ions and particles into the charger through two coaxial cylinders.Kimoto et al. (2010) compared the experimental results with the calculations results and the results showed that particle loss caused by electrostatic dispersion was reduced by use of the small volume charging chamber.
Towards the practical application of numerical techniques, Chien et al. (2011Chien et al. ( , 2013) ) developed a two-dimensional (2D) numerical model to predict the charging process in real unipolar chargers with complex geometries, which contains the fully coupled calculation of flow field, electric potential and ion concentration fields, and the charging dynamics of airborne particles.Methods for calculating the fields is based on the work of Lin and Tsai et al. (2010), while the charging model developed by Marlow and Brock (1975) was adopted to calculate the particle charging efficiency, and good agreement between the predicted and experimental charging efficiencies was obtained.The numerical results also showed the advantage of using sheath air on minimizing the charged particle loss, which is accordingly able to facilitate the design of unipolar chargers for airborne particles.
In addition, Huang andAlonso (2011, 2012) investigated the trajectories and charging dynamics of particles and electrostatic loss within a corona needle charger by solving the governing equations on flow field, electric field, and particle motion.Simulation results showed that the number of charges acquired per particle depends on the parameters of particle diameter, radial position from the symmetry axis, applied voltage, Reynolds number, and axial distance along the charger.A similar 2D numerical model on a corona needle charger was also developed and evaluated by Park et al. (2011a).However, some of researchers employed the charging models only in continuum regime, which may cause some error towards the modelling of nanoparticle charging.
Finally, to evaluate different charging models, Long and Yao (2010) used a numerical model of the electrostatic precipitator and nine particle charging models including field charging theory, diffusion charging theory and combined field-diffusion theory were compared against experimental data based on the particle charge, particle motion and particle collection efficiency.The results showed that prediction results of the constant charging models were better than that of the non-constant models but differed little for the submicrometer particles and a first choice of model was given for numerical models of the particle dynamics in electrostatic precipitators

Comparison of Experiments with Theoretical Models
With the advent and application of various measuring techniques, the electric charge measurement of airborne particles was made possible for researchers.To examine the accuracy and applicability of particle charging models, numbers of experiments on unipolar charging of particles have been conducted by researchers.In this section, we present a brief summary of the relevant work, which is concluded in Table 2.
(1) Continuum Regime Pauthenier and Moreau-Hanot (1932) performed one of the first measurements on particle charging of continuum regime.In the experiment, metallic and insulating spheres with diameter ranging from 10 to about 200 µm were released in a negative corona field.By analyzing the trajectories of particles, the charges on each particle were obtained and results showed the agreement with the 'field charging' model.Different from case of solid spheres adopted above, Fuchs et al. (1936) measured the acquired charge of oildroplets ranging from 0.5 to 3 µm in radius, and good agreement was also obtained between averaged measured charges and theoretical predictions by 'field charging' model for all sizes of droplets studied (Fig. 6).
More elaborate measurement was conducted by Hewitt (1957) using a cylindrical mobility analyzer, and he took a charge-mass-ratio method as a comparison.He obtained convincing data on the charging process of particles with diameters ranging from 0.07 and 0.66 µm, which was later verified to agree with the combined field and diffusion charging model by Liu and Kapadia (1978).Regarding the diffusion charging of particles, Liu et al. (1967a) examined the model at low pressures with a cylindrical mobility analyzer, and a reasonable agreement was found between the experimental data and the formula derived by White.Similarly, Kirsch andZagnit'Ko (1981, 1990) also conducted several experiments to verify the diffusion charging model in the presence of a weak electric field and vapors of different liquids, and results showed that the acquired charges of di-2-ethylhexyl sebacate (DES) and dibutyl phthalate (DBP) particles with radius between 0.05 and 1.5 µm agree fairly well with Fuchs's diffusion charging theory.
Towards the examination of combined charging models, McDonald et al. (1980) performed an experiment in the continuum regime using Millikan cell.Experimental results showed agreement with the combined charging model by Smith and McDonald (1975) for positive corona while indicating a certain variance for negative corona at higher temperature, which was possibly attributed to the 'free electron charging mechanism'.Frank et al. (2004) measured the electric charges on droplet particles of 0.1-20 µm in diameter with three different methods, and results showed that the average charge agreed fairly well with the prediction of combined charging model by Lawless (1996).Most recently, Long and Yao (2010) summarized different kinds of charging models in continuum regime and reexamined them with the experimental data of Hewitt (1957), which indicated that Lawless model should be the first choice relatively for modelling particle charging dynamics in electrostatic precipitators. (

2) Transition and Free Molecular Regime
In non-continuum regime, measurement on the airborne particle charging was first performed by Adachi et al. (1985) using zinc chloride (ZnCl 2 ) and di-2-ethyl hexyl sebacate (DEHS) particles of 4-100 nm in diameter.Mono-disperse particles were obtained at the exit of differential mobility analyzer (DMA), and then get charged by unipolar ions produced by α ray from Am-241.Results showed that the charged fraction of particles was in quite good agreement with the prediction of limiting sphere model.Pui et al. (1988) also examined the unipolar charging models in non-continuum regime.Mono-disperse, uncharged silver (Ag) and sodium chloride (NaCl) particles with diameter ranging from 4 to 75 nm were exposed to unipolar ions produced by a corona discharge.The results (Fig. 7) indicated that the BGK model by Marlow and Brock (1975) best predicted the combination coefficient in the entire size range, while above 10 nm, the data approached the limiting sphere model, which was consistent with Adachi's experiment above.
Apart from those concerns on charged fraction, Biskos et al. (2005) employed a TDMA system to investigate the mean charges and actual charge distributions on airborne particles in transition regime.Mono-disperse particles with diameter between 10-300 nm were adopted, while the measurements showed fairly good agreement with limiting sphere theory and the charge distribution model.Similarly, Alguacil and Alonso (2006) also measured the charge distribution on airborne particles in diameter below 35 nm, by employing tandem differential mobility analyzer (TDMA) setup.The average charges per particle predicted by limiting sphere theory was in relatively good agreement with the experimental results despite the existence of high intensity electric field in the charging region.
Besides, Oh et al. (2004) studied non-spherical particle charging experimentally for the first time.TiO 2 agglomerates were produced by thermal decomposition of titanium tetraisopropoxide (TTIP) vapor, charged by the indirect photoelectric charger and the average charge of particles was measured by particle electrometer and condensation particle counter.Experimental results showed that aggregates with a low fractal dimension have about 30% more charges than spherical particles since particles with a lower fractal dimension have larger surface area and self-capacitance.Shin et al. (2010) further studied the effect of particle morphology on unipolar diffusion charging of particle agglomerates, and found that the experimental data was in good agreement with estimates of Chang's theory.
In respect of other factors in particle charging process, Shin et al. (2009) investigated the material dependence of the charging process experimentally.The examined particles (10-200 nm) covered a wide range of dielectric constant with almost the same spherical or compact morphology.Measurements of both charged fraction and mean charge per particle showed very small differences among different materials.And the level of the small difference was consistent with the estimation by limiting sphere model.Qi et al.

Recent Progresses in Unipolar Charger Design
In addition to the above-mentioned proving charging experiments, in practical applications, however, the charging efficiency is the most important index evaluating the performance of unipolar charger.In order to achieve higher charging efficiency and less electrostatic loss with nanosized particle charging, researchers have been dedicated in promoting new designs of unipolar chargers for years.Another key a parameter to describe the operation effect of unipolar charger is the N i t product, i.e., the multiplication of mean ion number concentration and particle residence time.To improve particle charge, the N i t product should be enlarged.Therefore improvement of ion concentration and residence time is necessary for improving particle charge.However, as for a practical charger, particle loss due to electrostatic dispersion and particle diffusion.What's more, both negative and positive discharging can be used in unipolar dischargers.However, ozone can be generated as a common by-product in negative discharging while positive discharging won't have the problem.Positive discharging is used in areas such as particle measurement instruments (ELPI) and air cleaner while negative discharging is widely used in industry facilities such as ESPs.Intra andTippayawong (2009, 2011) reviewed the historical development of unipolar chargers.In this session, we will mainly focus on the most recently developed unipolar chargers, and respective applicable charging models.The ion properties used in the calculation of unipolar chargers designs are concluded in Table 3 and comparison of parameters in different unipolar particle chargers is shown in Table 4. Han et al. (2008) developed a novel kind of unipolar charger using carbon fiber ionizers, which consisted of a bundle of approximately 300 carbon fibers with the diameter of about 5-10 µm.In the experiment, a positive DC voltage of 2.3-4.0 kV was applied to the carbon fiber ionizers, and as shown in Fig. 8, an extrinsic charging efficiency of about 60% was achieved for 20 nm particles at 2.3 kV, showing good agreement with calculated the intrinsic charging efficiency based on limiting sphere charging theory with ion properties from previous studies (Han et al., 2003).
In another study, a corona-discharge based, unipolar mini-charger was developed by Qi et al. (2008), which is only 25 mm in length and 12.5 mm in diameter, consisting of an outer metallic case and a pointed tungsten needle electrode as the discharge module.Despite of its compact size, it has demonstrated good intrinsic and extrinsic charging efficiencies for particles ranging from the submicron (higher than 80%) down to 5 nm (about 60%) in a low flow rate (0.3 L min -1 ).Whereas, higher extrinsic charging efficiency was achieved in a high flow rate of 1.5 L min -1 since lower particle losses in the charging zone.However, the agreement between the experimental and calculated charge distributions was not satisfactory, which may be attributed to the nonuniform distribution of ion concentration and electrical field.Tsai et al. (2010) developed a unipolar charger containing multiple gold discharging wires in a tube, and investigated the charging performance of nano-sized particles.By shortening the residence time in the charging region, the optimal extrinsic charging efficiency was obtained and the charger's extrinsic charging efficiency increased from 2.86% to 86.3% in the charger as the particle diameter increasing from 2.5 to 50 nm.Moreover, particle charge distribution at the exit was analyzed using TDMA system, and results showed that most particles are singly charged or uncharged for diameter smaller than 10 nm while the fraction of multiply charged particles becomes higher for particles larger than 20 nm.
Additionally, Vivas et al. (2008b) reported their effort on optimizing an existing diffusion charger developed by Büscher et al. (1994) to reduce the multiple charging of submicron airborne particles.By imposing an ion-driving  voltage on the grid between the ion-generation and charging chambers, as well as minimizing the grid length and duty cycle of imposed voltage, the multiple charging of the particles of 250 nm was greatly reduced.For a flow rate of 1.5 L min -1 , the extrinsic charging efficiencies of 19% and 63% are attained with the corona charger for particles of, respectively, 50 and 250 nm.Comparison between the analytical solution given by Biskos et al. (2005) and experimental extrinsic efficiency showed reasonably good agreement.Park et al. (2009) designed a new type of diffusion charger for determining the geometric standard deviation of particle sizes as well as the geometric mean diameter and the total number concentration of particles, which consisting of discharge zone, mixing and charging zone, three flow channels, and ion trap zone.we introduce a methodology.In this work, the estimated N i t product for 3.5 to 5 kV of applied voltage was within 1-6 × 10 6 s cm -3 , and the particle losses were below 12% for particle in all channels.The author also evaluated the average charge and charged fraction of particles in three different channels based on TDMA system, and results showed that the calculation based on charge distribution model acquired good agreement with the experimental data.
Moreover, as shown in Fig. 9, a small mixing-type unipolar charger (SMUC) for airborne particles was developed by Kimoto et al. (2010).The charger has a small charging chamber of only 0.5 cm 3 volume to reduce particle loss caused by electrostatic dispersion, and the High-Pressure Corona (HPC) ionizer described by Adachi et al. (2004) and Whitby (1961) was used as a unipolar ion generator.The average charging time was 0.025 s when the flow rates of ions and particle were 0.2 and 1 L min -1 , and the optimum discharge conditions were achieved when the applied voltage is +8 or -9 kV.Under such conditions, the measured extrinsic charging efficiencies are 0.46-0.66and 0.59-0.71for negative and positive charging, respectively, in the particle size range of 5-40 nm.Since the negative ion mobility in air in higher than that of positive ions, resulting in higher ion loss due to electrostatic dispersion and particle diffusion, therefore the extrinsic charging efficiency of positive corona discharge is higher than that of negative discharge.Measurement results also showed that the experimental charging efficiencies agree well with the results calculated without considering electrostatic dispersion, suggesting that particle loss due to electrostatic dispersion is reduced by the use of small-volume charging chamber.
Li and Chen (2011b) also designed a DC-corona based charger (Fig. 10), consisting of a tungsten needle as discharging electrode, and a cylindrical grounded metal case.The charging experiment was conducted at a flow rate of 3 L min -1 and an ion-driving voltage of 600 V.It is reported the extrinsic charging efficiency is higher than 60% for particles of diameters larger than 15 nm.The birth-anddeath charging model was used to obtain the calculated charge distributions of particles, and reasonable agreement was achieved when compared with the measured charge distributions.The authors (2011a) also investigated the charging performance of an particle charger based on pentype UV-lamps ,which was a quartz tube about 7 inches long surrounded by four low pressure Hg lamps with a 6 inches lighted length.Results showed the extrinsic charging efficiency of the charger was higher than 80% for particles of diameters larger than 15 nm, and a comparatively good agreement was also obtained between the experimental and calculated charge distributions in the study.
Besides, Domat et al. (2014b) investigated the effect of electrode gap on the performance of a corona charger with separated corona and charging zones.Similarly, the ion chamber is concentric to the outer casing and surrounded by the particle flow, which was shown in a theoretical study (Alonso et al., 2009) to be the best configuration for unipolar diffusion chargers.Due to its flexible design on the gap between electrode and outer casing, the charger is able to vary the onset voltage and ion concentration over a wide range, therefore the intrinsic and extrinsic charging efficiencies and charged particles loss.Experimental results indicated that varying the electrode gap distance is an efficient way to regulate the ion concentration, as well as the charging performance.Most recently, Alonso and Huang (2015) designed an electrical charger based on a point-to-plate DC corona discharge for particle charging below 10 nm.diameter below 10 nm.In spite of its simple design, the specific design allowed relatively small diffusion and electrostatic losses since the small effective charging volume in comparison with other typical designs.As a consequence, the extrinsic charging efficiency attainable was higher than published similar devices of Chen and Pui (1999), Tsai et al. (2010), Chien et al. (2011), etc. for particle size in the range 5-10 nm while for smaller particles the charging efficiencies was slightly lower than those attainable chargers with sheath air to reduce particle diffusion losses.

SUMMARY AND FUTURE WORK PROSPECT
Unipolar charging is one of the most important techniques applied in airborne particle studies in laboratories and industrial applications.In this work, a historical development of theoretical models and numerical methods of unipolar particle charging are reviewed, and relevant experimental results are summarized and compared with theoretical ones.
In the continuum regime, the field/diffusion charging models act as primeval models with only limited application range, while combined charging models may yield quite satisfying predictions universally.However, in the noncontinuum regime, when the particle size approaches the mean free path of gas molecules, charging models become more detailed and require much more precise description on the charging process.Limiting sphere and BGK model both provide applicable solutions in non-continuum regime within certain range.Moreover, charging models towards the charge distribution and non-spherical particles have been also proposed and verified by researchers.
As the development of theoretical models, the numerical techniques in modelling the particle charging process are also advancing in recent years.The Monte-Carlo method has been successfully used in predicting the average acquired charge number of arbitrarily shaped particles, as well as the charge distribution on the spherical particles.Moreover, researchers also developed different numerical techniques to analyze the ion density distribution and particle charging process in unipolar chargers.While the previous simulations were largely based on chargers of coaxial configuration, unipolar chargers with complex geometries were also numerically modelled and investigated in recent studies.Numerical predictions on charging efficiencies showed good agreement with the experimental values, and the models are thus able to facilitate the design of unipolar chargers for airborne particles.
Towards the recent developments on the design of unipolar chargers, in order to increase extrinsic charging efficiencies and minimize the electrostatic loss of charged particles, it is concluded that structural designs such as separating corona and mixing chambers have been used, and novel discharging electrodes have been developed and evaluated, specific flow rates and sheath air have been adopted.Furthermore, with the assistant of charged particle measurement techniques such as traditional trajectory analysis and Millikan cell as well as online measurement techniques based on different mobility analyzers, such as DMA and TDMA systems, the extrinsic charging efficiencies were adopted to evaluate the charging effects, most of which have been proved consistency with theoretical results.With the developed unipolar charger, the measurement accuracy of particle measurement instruments such as DMA, APM, etc. is improved since errors caused by particle loss due to electrostatic dispersion and particle diffusion is eliminated and corrected by sheath air, which also has the function as dilution air to reduce particle concentration and to expand applicable scope.
Despite those remarkable progresses made by researchers in the past decades, some important aspects in the unipolar particle charging still remain undercover: • Some researchers (Penney and Lynch, 1957;McDonald et al., 1980;Aliat et al., 2008;2009) once suggested a 'free electron charging' mechanism at high Ni-t products, or high temperature ionizations, which have not widely accepted by researchers.• Ion properties are the key parameters in the calculation of models listed in this paper, however, the values of ion mobility and mass reported in the aerosol charging literature lie within a considerable wide range of values.And large variations may exist between the calculation NOMENCLATURE Roman a particle radius, m b distance in Eqs. ( 8) and ( 9), m c ̅ the mean thermal velocity of the ions, m s -1 C p electrical capacitance in Eqs. ( 17) and ( 18), F d p particle diameter, m D i ionic diffusion coefficient, equals to Z(k/e)T, m 2 s -1 e elementary unit of charge, ≈1.602 × 10 -19 C E electric strength, V m -1 F i the force vector per unit mass acting on an ion owing to the presence of charge on the particle in Eqs. ( 14) and ( 15), N f i the velocity distribution functions of ions in the neighborhood of the particle in Eqs. ( 14) and (15) f j the velocity distribution functions of neutral gas molecules in the neighborhood of the particle in Eqs. ( 14) and (15) I current through the limiting sphere, A J current density, A m -2 k Boltzmann constant, 1.3806 × 10 -23 J K -1 Kn Knudsen number, equals to 2λ/d p m i ion mass, kg N p particle concentration, 1 m -3 N p,n concentration of airborne particles with n elementary charges, 1 m -3 N i ion concentration, 1 m -3 N i,∞ ion concentration at infinity, 1 m -3 N i (δ,q,θ) ion concentration in the limiting sphere as a function of δ, q and θ, in Eq. ( 13), 1 m -3 N i t a parameter to describe the operation effect of a charger, equals to mean ion number concentration × aerosol residence time, s m -3 n p mean number of charge of airborne particle in Eq. ( 18) q particle charge, C q s saturation charge, equals to (3ε s /(ε s + 2))πε 0 d p 2 E 0 , C r distance from the center of the particle, in Eq. ( 3), m S p the geometric surface area of particle in Eq. ( 18), m 2 t discharging time, s T temperature, K v equals to qe/2πε 0 d p kT, the dimensionless particle charge in Eq. ( 7) v i velocity vectors of ions in Eqs. ( 14) and ( 15), m s -1 v j velocity vectors of neutral gas molecules in Eqs. ( 14) and ( 15), m s -1 V p the electric potential of a particle relative to the potential at large distance, V w equals to w = (ε s /ε s + 2)(Ed p e/2kT) is the dimensionless electric field strength in Eq. (7) X the spacial vector in Eqs. ( 14) and (15) x equals to r/a in Eq. (3) Z electrical mobility of ions, m 2 (Vs) -1 Greek α the fraction of all the emerging ions reaches the particle surface β i integral combination coefficients in equation 13, equals to I/(eN i,∞ ), m 3 s -1 β n combination coefficient of ions with airborne particles carrying n elementary charges in Eq. ( 16) β p;i collision rate coefficient or kernel of ions and particle λ mean free path of gas, m ε 0 vacuum dielectric constant, 8.85 × 10 -12 F/m ε s specific dielectric constant, F/m δ the limiting-sphere radius, m φ(ρ) the potential of the ion ϕ p non-dimensional surface potential, equals to eV p /(kT), in Eq. ( 18) Γ i the appropriate collision operators of ions in equation Eqs. ( 14) and (15) Γ j the appropriate collision operators of neutral gas molecules in Eqs. ( 14) and ( 15) REFERENCE Adachi, M., Kousaka, Y. and Okuyama, K. (1985).Unipolar and bipolar diffusion charging of ultrafine aerosol particles.J. Aerosol Sci.16: 109-123.Adachi, M., Kusumi, M. and Tsukui, S. (2004).Ioninduced nucleation in nanoparticle synthesis by ionization

Fig. 2 .
Fig. 2. Electric field line around a particle (a) an uncharged particle (b) a particle with saturation charge.
where f(w) is the fraction of surface covered by diffusion band,

Fig. 10 .
Fig. 10.Schematic diagram of the DC-corona based charger developed by Li and Chen (2011b).

Table 2 .
Experimental results and comparison on unipolar particle charging.

Table 3 .
Ion properties used in the calculation of unipolar chargers designs.

Table 4 .
Comparison of parameters in different unipolar particle chargers.