Thermodynamic Analysis of Multi-Pollutant Removal in Electrostatic Precipitation Applied to Small-Scale Combustion

1 1Thermodynamic Analysis of Multi-Pollutant Removal in 2Electrostatic Precipitation Applied to Small-Scale Combustion 3 Oleksandr Molchanov *1, Kamil Krpec 1, Jiří Ryšavý 1 41Energy Research Center, Technical University of Ostrava, 17. listopadu 15/2172, 708 33 5 Ostrava–Poruba, Czech Republic 6 [email protected], [email protected], [email protected] 7 *Corresponding Author: [email protected], tel +420773286102 8Highlights 9ESP solved a multi-pollutant emission from small-scale biomass combustion 10 Simultaneous removal of PM (>99%), NOx (78%), and hydrocarbons (90%) achieved 11 Corona discharge thermodynamics revealed for real biomass combustion gases 12 Ion-induced nucleation cooling vs. Joule heating creates distinct thermal regimes 13 Thermodynamic insights enable the optimised design of intensified emission control 14 Abstract 15 This manuscript presents novel insights into the thermodynamic behaviour of electrostatic 16 precipitators (ESPs) used for a 5-kW residential biomass combustion system to simultaneously 17 remove PM, NOx, and hydrocarbons. The ESP was operated with different energisation regimes 18 with positive and negative discharge polarities. This study reveals, for the first time, that corona 19 discharge in ESPs exhibits competing thermodynamic processes: cooling through ion-induced 20 nucleation, ensuring the NOx removal, versus Joule heating growing with ESP energisation. 21 Distinct operational regimes were revealed. At specific input energy (SIE) < 1 J/L, electrostatic 22 precipitation alone achieved >99% PM removal without affecting gaseous pollutants. At SIE 23 below 2.64/2.85 J/L for positive/negative corona, NOx reduction was 20-40 %, and nucleation24 driven cooling dominated, reducing gas temperature by 1.8-2.3°C. SIE in the range 2.64-4.6/2.8525 7.27 J/L for positive/negative corona ensured the more efficient DeNOx of about 40-60 % and 90 26 % removal for hydrocarbons; within this range, Joule heating compensated nucleation cooling, 27 creating the transition regime with thermal instability as competing mechanisms balance. Above 28 7 J/L, Joule heating prevails, raising temperature by 1.5/2.4°C for positive/negative corona while 29 enabling maximum pollutant removal: >99% PM (reducing concentrations to about 0.15 µg/Nm3), 30 78% NOx, and 92% total hydrocarbons. Mechanistic analysis quantitatively confirmed this 31 thermodynamic competition through energy balance modelling. These findings transform our 32 understanding of corona discharge processes and offer practical pathways for developing efficient, 33 compact multi-pollutant control technologies for residential heating applications. 34 Keywords 35 electrostatic precipitator; multi-pollutant control; biomass combustion; DC corona 36 Used symbols and constants Cc - Cunningham correction factor, 𝐶𝑐 = 1 + 𝜆 2𝑟 ∙ ( 2.514 + 0.8 ∙ 𝑒 ― 0.55 ∙ 𝜆 2𝑟 ) 𝑐 𝑝 [J/(kg×K)] Specific heat capacity of combustion gases 𝐶 𝑜𝑛(𝑜𝑓𝑓) [mg/m3]/[#/cm3] Concentration: ESP on(off)-regime, mass/number Dp [nm] The particle cut-off diameter 𝐸 [V/cm] Electric field strength 𝐽 [#/(s3×cm3)] Nucleation rate 𝐽 𝑖𝑜𝑛𝑠 [A/m2] Current density 𝐽 𝑖𝑜𝑛𝑠 = 𝑛 𝑖 𝑢 𝑖 𝑞 𝑒 𝐸 ∆𝐻 [J/mol] Nucleation energy I [mA] Electric current in ESP k [W/m*K] Combustion gas thermal conductivity, k=0.0296 This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 2 kb [J/K] Boltzmann constant 1.3806488(13)×10−23 𝑛 𝑖 [#/cm3] ions density ∆𝐿 [J/mol] Heat of condensation per cluster R [cm] Distance from discharge wire to collecting electrode 𝑟 [cm] Distance from discharge electrode 𝑟 0 [cm] Radius of discharge electrodes T [K] Absolute gas temperature U [kV] Voltage in ESP ui [cm2/kV×s] Ion mobility V [m3/s] Volume flow rate of combustion gases 𝜂 [%] ESP efficiency  0 [F/m] Electric constant (vacuum permittivity)  0 = 8.85 × 10−12 I [mA] Electric current in ESP t [s] Time variable U [kV] Voltage in ESP ui [cm2/kV×s] Ion mobility 𝑞 𝑒 [C] Elementary (electron) charge qe = 1.6·10–19 C 𝜇 𝑒 [cm2/V×s] Electron mobility 37 1INTRODUCTION 38 Residential biomass heating contributes to over 2.8 million premature deaths annually 39 through particulate matter (PM), nitrogen oxides (NOx), and volatile organic compound (VOC) 40 emissions [1]. Recent epidemiological studies confirm that proximity to residential heating sources 41 amplifies cardiovascular and respiratory disease rates to levels comparable to those from major 42 industrial sources [2]. With residential heating accounting for up to 70% of primary PM2.5 43 emissions in urban areas during winter months [3] and projected 40% biomass use to increase by 44 2030 in developing regions, this crisis demands innovative emission control technologies 45 specifically designed for small-scale applications. 46 Conventional Industrial NOx control methods cannot always be successfully scaled down to 47 residential systems, facing significant limitations: selective catalytic reduction requires high 48 temperatures [4] and can generate secondary emissions [5] ncluding N2O and NH3 slip, while 49 chemical methods demand substantial reagents [6] and produce waste requiring additional 50 processing [7]. These fundamental incompatibilities between industrial solutions and residential 51 constraints have created a critical technology gap. 52 Electrostatic precipitators (ESPs) offer unique potential for residential applications through 53 their ability to simultaneously remove multiple pollutants. ESPs use a corona discharge, which 54 ensures effective PM removal [8] from combustion gases by charging the particles and removing 55 them from combustion gases by Coulomb's forces. In addition, the corona discharge environment 56 generates a non-thermal plasma (NTP) [9], where highly energetic electrons initiate a cascade of 57 chemical reactions that convert NOx [10] and VOC [11] into aerosols that are precipitated 58 alongside with initial fly ash. However, despite decades of ESP application, a fundamental 59 knowledge gap remains: the thermodynamic interactions governing corona discharge performance 60 in real combustion environments remain unquantified and poorly understood. 61 Previous studies have identified isolated thermodynamic phenomena without recognising 62 their interconnected nature. Yanallah et al. [12] observed an increase in gas temperature from Joule 63 heating in the corona discharge but did not consider competing cooling mechanisms. Concurrently, 64 Liu et al. have documented that ion-induced nucleation– the fundamental process that converts 65 gaseous pollutants into precipitable aerosols – extracts latent heat from the surrounding 66 environment, introducing distortions in the thermodynamic equilibrium [13]. These opposing 67 thermodynamic processes coexist in ESP corona discharge, yet their competition and its This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 3 68 implications for pollutant removal have never been investigated. 69 In addition, the complexity of real combustion gases—containing water vapour (8-15%), 70 varying oxygen levels (6-15%), temperature fluctuations (100-200°C), and hundreds of trace 71 species—creates a dramatically different environment from the simplified conditions studied in 72 laboratory investigations. 73 To address the knowledge gap, this study presents the first comprehensive thermodynamic 74 analysis of corona discharge in ESPs treating real biomass combustion gases. Our specific 75 objectives are: 76 1. Quantify the thermodynamic competition between cooling by ion-induced nucleation and 77 Joule heating across the full range of corona discharge operating conditions, identifying critical 78 transition points and their governing parameters; 79 2. Establish the mechanistic relationships linking thermodynamic behaviour to 80 simultaneous removal of PM, NOx, and VOCs, elucidating how thermal dynamics influence 81 chemical kinetics and particle formation; 82 3. Compare discharge polarities to determine how positive and negative corona create 83 different thermodynamic landscapes and removal efficiencies under identical conditions; 84 4. Develop practical design principles that exploit thermodynamic insights to optimise ESP 85 performance for residential biomass combustion systems. 86 To provide mechanistic insight into the observed temperature dynamics, we developed a 87 simplified analytical framework. While this model cannot capture the full complexity of the 88 system, it highlights the fundamental interplay between nucleation cooling and Joule heating. 89 This study presents novel insights that have not been previously reported. The integration of 90 plasma physics, aerosol science, and chemical engineering perspectives provides a holistic 91 understanding previously lacking in the literature. The findings have immediate practical 92 applications while contributing to the fundamental understanding of plasma-assisted pollutant 93 removal processes. 94 2EXPERIMENTAL METHODOLOGY 95 2.1 Experimental setup 96 The ESP performance was evaluated using the experimental setup shown in Figure 2. A 597 kW wood pellet domestic heat source with automatic feeding generated combustion gases, which 98 were removed with a fan. A constant negative pressure of 15 Pa in a heating unit outlet was 99 maintained automatically. The chemical composition of the wooden pellets can be found in [14]. 100 A specialised ESP with honeycomb collecting electrodes was used. The collecting electrodes 101 comprised 20 hexagonal cells with a side length of 25 mm and an active height of 1000 mm. 102 Discharge electrodes were presented by stainless-steel wire with a diameter of 0.35 mm and 103 installed along the central axis of each hexagonal cell. The DC corona discharge was generated in 104 ESP by an XP Glassman high-voltage power unit (Model PS/030R040-22), capable of delivering 105 a maximum output voltage of 30 kV and a current of 40 mA. 106 This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 4 107 108 Figure 1. Experimental setup 109 The monitoring and analysis system included gas analysis using ABB continuous analysers 110 and particle sampling with size distribution detection by a Dekati® Electrical Low-Pressure 111 Impactor (ELPI) with sample conditioning by a Dekati® FPS-4000 dilution system. In compliance 112 with EN 303–5:2013, all sampling points were positioned downstream of the ESP within a straight 113 section of the exhaust duct. 114 2.2 Measuring methods 115 2.2.1 Gas analysis 116 Combustion gases were sampled with a flow rate of 2.0 L/min. A 0.1 μm PTFE membrane 117 filtered each sample, and moisture was removed by a Peltier cooler. To prevent condensation, each 118 sample line was heated to 180 °C. To prevent condensation, each sample line was heated to 180 °C. 119 The concentrations of oxygen, carbon monoxide, and carbon dioxide were determined using 120 an ABB AO2020 Series Multi-Gas Analyser. This instrument used a paramagnetic detector for O2 121 concentrations and a Non-Dispersive Infrared (NDIR) detector for CO and CO2. The analyser 122 offered an accuracy of ±1.5% for concentrations ranging from 0 to 500 ppm. 123 Nitrogen oxides were measured using a Horiba PG-350E chemiluminescence analyser 124 (CLA) equipped with a NOx converter. The measurement accuracy was better than ±1.5% over 125 the range of 0–500 ppm. 126 A flame ionisation detector (FID), configured for a concentration range of 0–500 ppm, was 127 used to obtain the content of total hydrocarbons (THC). The FID range was adjusted using propane 128 (C3H8) so that overall measurement uncertainty was ±2%. 129 A K-type Class 1 thermocouple monitored the temperature of combustion gases; 130 measurement accuracy was better than ±1.5 °C across a temperature range of −40 °C to +375 °C. 131 2.2.2 Particle analysis 132 Particulate emissions were evaluated both gravimetrically (PM) and numerically (PN). 133 PM concentrations were determined via isokinetic sampling, following an adapted version 134 of the standard [15], adapted for small-scale combustion units as specified in the standard [16]. 135 Gravimetric analysis was performed with an accuracy tolerance of ±10%. 136 PN concentration and particle size distribution were measured using the ELPI, which 137 operates by pre-charging particles and classifying them across a cascade impactor with 14 138 aerodynamic size channels, covering diameters from 6 to 5300 nm. This enabled real-time 139 determination of both total particle number concentration and size-resolved distribution, with a 140 measurement uncertainty of approximately ±5%. Detailed information on ELPI operation is 141 available in [17]. 142 Dekati® FPS-4000 fine particle sampler allows to avoid problems associated with clogging 143 and condensation in downstream equipment; therefore, it was used to adapt the samples to the ELPI Fan t,°C Diluter FPS 4000 Ambient air Compressor Dilution air (4 bar) HEPA filtr XP Glassman CO2 Boiler CO2 ESP PG-350 NO VA-5000 NOx Converter CO, CO2 O2 This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 5 144 ELPI operating capabilities: samples were diluted with ambient air, pumped with a compressor, 145 and then filtered through a HEPA filter. The dilution ratio was settled at 1:80 and verified by 146 comparing the CO2 concentrations in the flue gas and the sample. 147 2.2.3 Electrical measurements 148 The applied voltage and current in the electrostatic precipitator (ESP) were monitored using 149 an XP Glassman high-voltage power supply. The unit provided current measurements with better 150 than ±1% accuracy and voltage measurements accurate to within ±2% of the output value. It 151 featured a recovery time of 1 ms to within 0.1%. 152 2.3 . Operation regimes Experimental procedures 153 The heating unit was operated at a constant output of 5 kW to ensure stable and reproducible 154 conditions throughout the experimental campaign. The investigation followed a systematic 155 protocol, beginning with baseline measurements taken with the ESP switched off. After a two156 hour stabilisation period to allow the system to reach steady-state operation, reference samples 157 were collected. 158 The ESP was tested through five alternating on/off cycles, each lasting 10 minutes. During 159 these intervals, key parameters—including voltage, current, gas composition and temperature— 160 were continuously monitored. Particle number concentrations and size distributions were also 161 recorded. 162 The ESP "on" mode was tested across a discharge current range of 0.1 to 40 mA. Discharge 163 current values were incremented as follows: from 0.1 to 1 mA in 0.1 mA steps; from 1 to 10 mA 164 in 1 mA steps; and from 10 to 40 mA in 5 mA steps. The high-voltage power supply automatically 165 adjusted the applied voltage to maintain the desired current setpoint. To evaluate the effect of 166 current magnitude and polarity, tests were conducted under both positive and negative discharge 167 conditions. 168 2.4 Quality Control Measures 169 Each ESP test was conducted five times for every energisation level, with each test 170 consisting of five alternating ESP on/off cycles. During each cycle, the steady-state operation was 171 verified by monitoring the flue gas temperature, CO concentration, and current-voltage 172 characteristics of the ESP. 173 Before each experimental series, all gas analysers were calibrated. Calibration procedures 174 included zero calibration using ultra-high purity nitrogen (99.999%) and span calibration with 175 certified reference gases for CO, CO2, and NOx. 176 The ELPI is highly effective for monitoring purposes, with its measurement accuracy for 177 particle size distribution supported by SMPS data on particles emitted from small-scale 178 combustion [18], and by FMPS measurements [19] for ultrafine airborne particles. The ELPI's 179 accuracy in the measurement of total particle number concentration has been validated through 180 CPC measurements [20] within the concentration range of 103 to 105 #/cm3. However, its accuracy 181 is subject to certain limitations related to particle detection thresholds: particles at low 182 concentrations may fall below the ELPI’s detection limit, making precise quantification 183 challenging [21]. This detection limit varies by particle size, approximately 130 particles/cm3 at 184 50 nm, 4 particles/cm3 at 500 nm, and 0.4 particles/cm3 at 5000 nm. Additionally, measurements 185 of fine particles can be influenced by particle losses occurring across impactor stages [22]. Finally, 186 variations in the surface conditions of impactor stages can also introduce measurement 187 inconsistencies [19]; to mitigate these effects, bare steel was used, as it provides reliable results 188 for particles with roughly spherical geometry. 189 To reduce particle measurement errors introduced by the dilution system, ambient air was 190 pre-filtered with a HEPA filter, reducing background particle concentrations to below 200 191 particles/cm3. The actual dilution ratio was verified by comparing CO2 concentrations in the raw 192 flue gas and diluted sample within the mixing chamber. This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 6 193 All sampling was conducted isokinetically, with probes positioned at the centreline of the 194 flue gas duct. The sampling location was in a straight, horizontal section of the duct with a constant 195 diameter of 150 mm, at a distance of at least five duct diameters from any bends or disturbances, 196 maintaining an isokinetic tolerance within ±20%. This setup complies with the requirements of 197 EN 13284-1:2017. 198 2.5 Data normalisation and evaluation 199 The measured values of combustion gaseous compounds and particle concentrations were 200 normalised to the volume unit of dry gas at 101.325 kPa, 0 °C, and reference O2 at 10%. 201 PN concentration data are presented as total number concentration and as differential 202 concentrations dN/dlog(Dp), where dN is the particle count within each size bin, and dlog(Dp) 203 represents the logarithmic width of each particle diameter interval. This format allows for direct 204 comparison between instruments with different binning schemes. 205 Total NOx concentration was calculated as [NOx]=[NO2]+1.529×[NO] due to ISO 206 10849:2022. 207 The ESP removal efficiency was determined considering the concentrations for each 208 contaminant during on/off regimes: 209 𝜂 𝑚 = ( 1 ― 𝐶 𝑜𝑛 𝐶 𝑜𝑓𝑓 ) 100% (1) 210 The specific input energy SIE [J/L], or Becker parameter, was evaluated as follows 211 𝑆𝐼𝐸 = 𝐼  𝑈 𝑉 (2) 212 3RESULTS AND DISCUSSION 213 3.1 Experimental conditions 214 Fuel was dosed periodically to the boiler at regular intervals, resulting in the combustion 215 process going through three distinct stages: (i) initial combustion, characterised by unstable 216 thermal conditions and improper air settings; (ii) steady-state combustion, marked by an optimal 217 air-to-fuel ratio; and (iii) the smouldering, associated with incomplete oxidation. 218 The particle size distribution at the ESP-off regime was obtained for each combustion stage 219 and presented in Figure 2. The size distribution of emitted particles was unimodal, with a mode 220 range between 33 and 98 nm. The combustion stage slightly affected the emitted particle size 221 distribution: during the initial combustion stage, the proportions of ultrafine (≤6 nm) and large 222 (≥1 µm) particles were decreased, while the smouldering phase demonstrated a distinct peak for 223 33-nm particles. This supports the findings from [23], who reported that smouldering conditions 224 in a wood-chip-fired appliance produced fewer but larger particles compared to efficient 225 combustion modes. The latter research [24] supports this conclusion. 226 227 Figure 2. Size distribution of emitted particles 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 6 13.8 19 33.3 50.7 98 169 315 590 910 1630 2470 3660 5370 dN/dlog(Dp) [/cm3) Dp [nm] Nominal combustion Smouldering Initial combustion This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 7 228 General information on experimental conditions is given in Table 1, with weighted average 229 measured values [25]. 230 Table 1. Combustion gas parameters Parameter Unit Value Temperature °C 129 Gas flow rate m3/h 36.0 Content of N2/CO2/O2/H2O vol % 64.0/14.5/13.0/8.5 Content of CO mg/m3 210 Content of NOx mg/m3 200 Content of THC mg/m3 9 PM mg/m3 35 PN [/cm3] 107 231 Both the combustion gas parameters and emission characteristics of the tested stove are 232 consistent with those commonly observed in small-scale heating systems [26], so the measurement 233 results can be considered representative. 234 Figure 3 presents the data on the ESP with SIE obtained through Equation (2). The 235 combustion stages slightly affected the combustion gases' properties and were associated with only 236 minor fluctuations in the electrical operating parameters of the ESP. 237 The minimal current of 0.1 mA corresponded to a voltage of 5.0 kV and 7.7 kV at negative 238 and positive polarity, respectively. Sparks and breakdown events within the ESP restricted the 239 operation of the positive corona to a maximum voltage of 11.9 kV, corresponding current of 30 240 mA. In contrast, the negative corona discharge remained stable up to 12 kV but was limited at 40 241 mA by the current capacity of the XP Glassman. 242 243 Figure 3. SIE and the electric current of ESP with applied voltage 244 Generally, the current-voltage characteristics of the ESP were typical for DC corona 245 discharge with current and voltage values similar to those previously published [8]. 246 3.2 Changes in NOx concentration 247 Figure 4 reflects changes in weighted average NOx and NO concentrations in the 248 background of fluctuations. Although initial NOx concentrations varied across different 249 combustion stages – namely, lower NOx formation during the early stage due to reduced 250 temperatures, and changes in NO/NO2 ratios during the smouldering phase resulting from 251 incomplete combustion - no systematic variations in NOx emissions were identified in relation to 252 the combustion phases. 0 10 20 30 40 50 5 6 7 8 9 10 11 12 ESP current [mA] ESP voltage [kV] Positive corona Negative corona 0 10 20 30 40 50 SIE [J/L] This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 8 253 254 Figure 4. Changes in NO and NOx concentrations with SIE 255 NOx concentrations remained unchanged until the applied voltage in the ESP reached 256 approximately 7.8 kV for negative polarity and 8.4 kV for positive polarity, corresponding to SIE 257 values exceeding 1 J/L. Beyond this threshold, NOx concentrations began to decrease with 258 increasing voltage. At 12 kV, the initial NOx concentration was reduced to 44 /45 mg/m3 for 259 positive/negative corona, respectively. The maximum NOₓ removal efficiency of 78% was 260 achieved under negative polarity operation, with corresponding SIE values of 35.7 J/L for positive 261 and 48.4 J/L for negative corona discharge. 262 The energy consumption of NOx removal in the studied ESP was compared to previously 263 published data on NOx abatement in the DC corona, as shown in Table 2 264 Table 2. Studies on DENOx in DC Corona Study NOx Removal [%] SIE (J/L) Key Conditions [27] 90 72 10% humidity, 380 ppm NOx [27] 90 542 190 ppm NOx, mixed gas [28] 70 249 - 918 250 ppm NO, mixed gas [29] 48 81 - 894 250 ppm NO, mixed gas [30] 78 80 120 ppm NO mixed gas 265 The referenced studies primarily focus on synthetic gas mixtures at room temperature, while 266 the present study examines actual combustion gases. The resulting differences in gas composition, 267 along with variations in experimental setups and ESP operating conditions, complicate direct 268 comparisons. Nevertheless, the overall energy efficiency of the ESP investigated here is generally 269 consistent with findings from previous research. 270 The performance of the studied ESP can be evaluated in comparison with other NOx control 271 technologies based on removal efficiency, energy consumption, and operational requirements. 272 Chmielewski et al. [31] investigated an industrial-scale electron beam technology for NOx 273 abatement, achieving up to 70% removal efficiency with energy consumption ranging from 28.8 274 to 43.2 J/L. While this method shows strong potential due to its advanced radiation-based treatment 275 capabilities, it is limited by complex system design and demanding operational needs. 276 Bhowmick et al. [7] demonstrated a two-step process involving low-temperature oxidation 277 via ozone injection followed by wet scrubbing. This approach achieved up to 95% NOx removal 278 but requires a separate scrubbing unit to eliminate the oxidised species and incurs high 279 operational costs due to ozone generation. 280 Mok et al. [32] employed a two-stage system combining a pulsed corona plasma reactor with 281 a monolithic V2O5/TiO2 catalyst. The 80-% NOx reduction was achieved. However, the system 282 consists of multiple components, which increased both complexity and cost and was not able to 283 remove particulate matter. 284 While the studied ESP here demonstrated slightly lower NOx removal efficiency, it offers 285 notable advantages: lower energy consumption, a compact and integrated design, and simpler 0 20 40 60 80 100 120 140 160 180 200 220 0 0 1 10 100 Concentration [mg/m3] SIE[J/L] NOx (negative corona) NOx (positive corona) NO (negative corona) NO (positive corona) Initial NO concentration Initial NOx conentration This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 9 286 operation. Combined with its high particle removal efficiency, these characteristics make the ESP 287 a suitable solution for small-scale combustion systems, where space, cost, and energy efficiency 288 are key priorities. 289 The DeNOx process in DC corona can be explained as follows [10]. Corona discharge 290 produces free electrons, which collide with neutral gas molecules, triggering dissociation and 291 producing reactive species such as OH radicals and oxygen atoms; the latter further react to form 292 ozone. These reactive species interact with NOx, resulting in the formation of nitrous acid (HNO2) 293 and nitric acid (HNO3) vapours. The corona discharge environment facilitates ion-induced 294 nucleation, converting acid vapours into liquid aerosols. These newly formed particles 295 subsequently precipitate along with the original fly ash. 296 Nucleation is the process by which small clusters of molecules aggregate to form droplets 297 from a gas or vapour. For nucleation to succeed, a molecular cluster must overcome a significant 298 energy barrier, primarily associated with surface tension. In the absence of electric charges, the 299 change in the system's free energy is governed by the interplay between two oppositely directed 300 factors: surface energy, required to create the interfacial boundary between the liquid and the 301 surrounding vapour, and volume energy released to the surrounding gas as vapour condenses into 302 liquid. The droplet formation can lead to a local decrease in temperature, which in real conditions 303 depends on the rate of heat removal from the system and the size of the formed droplets. 304 The presence of ions significantly intensifies this process by altering the energetic and 305 kinetic conditions that govern nucleation. Ions create local electric fields that attract nearby polar 306 or polarisable molecules, thereby promoting the formation and stabilisation of molecular clusters. 307 This attraction lowers the energy required to form a stable nucleus. Consequently, nucleation can 308 proceed under lower supersaturation levels than would be necessary without ions. Moreover, ions 309 enhance the frequency and efficiency of molecular collisions through electrostatic forces: charged 310 clusters draw neutral molecules more effectively than neutral clusters, accelerating cluster growth. 311 This accelerates the cluster's growth, increasing the probability of reaching critical stability before 312 evaporation. Additionally, the electrostatic forces between the ion and attached molecules stabilise 313 the growing cluster, preventing premature fragmentation. 314 3.3 Changes in particle concentration 315 PM concentrations in the ESP-off regime were measured at 35 mg/Nm3. However, under the 316 lowest energisation (SIE of 0.048/0.08 J/L for negative/positive corona respectively) the 30317 minute sampling did not provide sufficient data for an accurate evaluation of precipitation 318 efficiency: after each of the five sampling sessions, the mass increase on the filter runs was 319 comparable to the uncertainty of the equipment. This likely resulted from the effective removal of 320 larger particles—which constitute the majority of the PM mass—even at minimal ESP energisation 321 levels. Consequently, PM concentrations in the treated flue gas were considered statistically 322 insignificant and were excluded from further analysis. 323 The ELPI demonstrated average values of the total PN concentration of approximately 324 1.65×107 #/cm3. Changes in total PN concentration in Figure 5 demonstrate the high particle 325 precipitation efficiency of ESP for both discharge polarities: the minimal ESP energisation regime 326 of 0.7/0.48 J/L for positive/negative corona ensured the removal of 97/95% of the total particle 327 number. Increasing the ESP energy further enhanced performance, so with maximal SIE values of 328 35.7 J/L for positive and 48.4 J/L for negative corona, a total PN concentration of about 329 1.8×10⁴ particles/cm3 was achieved. This value is comparable to ambient air levels during the 330 campaign, which ranged between 1.4×10⁴ and 2.1×10⁴ particles/cm3. This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 16 509 Considering the above, ion-induced nucleation represents energy extraction highly localised 510 around phase transitions, where latent heat removal creates thermodynamic "sinks". 511 Generally, the growth in discharge energisation intensifies the nucleation rate through higher 512 ion concentrations, thus intensifying the release of latent heat from the surrounding gas during 513 phase transition. Concurrently, the corona discharge generates Joule heating that raises the gas 514 temperature, with heating intensity proportional to discharge power. The net temperature effect 515 depends on the balance between these competing processes. 516 When a generated cluster becomes critically stable, overcoming the maximum Δ𝐺, it 517 continues to grow by adding molecules, and each added molecule contributes to releasing the 518 condensation heat 𝑄 𝐶(𝑟) . 519 The steady-state energy equation for thermal balance in an adiabatic DC corona in 520 cylindrical coordinates can be : 521 1 𝑟 𝑑 𝑑𝑟 ( 𝑟𝑘 𝑑𝑇 𝑑𝑟 ) = 𝑄 𝐽(𝑟) ― 𝑄 𝑁(𝑟) + 𝑄 𝐶(𝑟) (11) 522 Further boundary conditions are suggested: the temperature on the surface of the collecting 523 electrode is equal to the baseline gas temperature 𝑇 𝑔 , while on the discharge wire surface, the gas 524 is assumed to be in thermal equilibrium. Therefore 525 𝑇 (𝑅) = 𝑇 𝑔 , 𝑑 𝑇 ( 𝑟 0 ) 𝑑𝑟 = 0 (12) 526 It is evident that this distributed internal energy of combustion gases can create multiple 527 thermodynamic zones within the discharge volume - electrode-proximate heating zones, 528 intermediate mixed-effect regions, and bulk cooling zones where nucleation dominates. As a 529 result, the spatial decoupling between heating and cooling mechanisms creates complex 530 thermodynamic landscapes. 531 As energisation increases, the balance between these zones shifts dramatically. Initially, 532 distributed cooling zones dominated the thermal landscape. However, as Joule heating intensifies, 533 the electrode-proximate heating zones expand, eventually overwhelming the distributed cooling 534 capacity and establishing net heating throughout the system. This can explain the temperature 535 progression with rapid cooling and consequent heating with growing ESP energisation for both 536 polarities. 537 Solving this equation (11) with boundary conditions (12) requires strong mathematical 538 resolvents, which are not available now. Moreover, the accurate modelling of condensation heating 539 requires the particle precipitation to be considered, which additionally complicates the solution. 540 Therefore, some argued simplifications can be applied. 541 Firstly, when ions transfer momentum to neutral gas molecules, they generate an ionic 542 wind—a jet-like flows, that in usual ESPs can reach velocities of a few meters per second, 543 depending on ESP energisation [18]. This allows consider the ion distribution to be uniform. 544 Secondly, the generation of HNO3 in the discharge region is nearly uniform, with slight 545 concentration peaks near the discharge electrodes at a distance of approximately 3 mm for both 546 polarities (Figure 12). This, together with uniform distribution of ozone– the primary DeNOx 547 reagent [10], allows for simplifying HNO3 distribution as homogeneous. 548 Thirdly, as previous works show [13], the formed particles are formed with a small diameter, 549 in the size of units of nanometers and already carry a single charge. The drift velocity of such 550 particles, considering the Cunningham correction factor, can achieve several tens of meters per 551 second. This suggests that these particles are rapidly precipitated and do not introduce significant 552 distortion, reasonably excluding the condensation heating from further consideration, and thus 553 allowing 𝑄 𝐶 = 0 . 554 Solving the analytical solution (11) considering the above simplifications results in the 555 distribution of temperature in radial distance: 556 𝑇 ( 𝑟 ) = 𝑇 ( 𝑅 ) + 𝐼𝑈 𝑘𝜋𝑘𝐿 ∙ 𝑙𝑛 ( 𝑅 𝑟 0 ) ― 𝐽 0 ∆ 𝐻 𝑛𝑢𝑐 2𝑘 ( 1 ― 𝑟 2 𝑅 2 ) (13) This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 17 557 Consequently, the volume-averaged temperature can be obtained 558 𝑇 = ∫ 𝑅 𝑟 0 𝑇 ( 𝑟 ) ∙ 𝑟 𝑑𝑟 ∫ 𝑅 𝑟 0 𝑟 𝑑𝑟 (14) 559 560 561 Figure 13. The changes in average temperature with ESP energisation 562 The temperature distribution was predicted due to Formula (13), then averaged through 563 Formula (14) for energisation ranges for positive and negative corona. The changes in average 564 temperature with ESP energisation are presented in Figure 13. The comparison between model 565 predictions and experimental observations reveals divergences across operating regimes. 566 In the ESP regimes where nucleation dominates, the model predicts a temperature decrease 567 of 1.4/1.8 °C for positive /negative corona, which varies considerably from the measured result in 568 Table 3. In addition, the limits of the transition regime, where cooling and heating effects balance, 569 demonstrate quite a disagreement between theory and experiment: the model predicts this 570 transition at a specific input energy of 18.2 J/L/24.5 J/L positive /negative corona, while 571 experiments show the crossover occurring between 6.5 and 8.0 J/L. At high specific input energies 572 where Joule heating dominates, the model predicts a temperature rise of 3.2/5.4 °C; experimental 573 observations, however, range from 1.5°C to 2.4°C. 574 The divergences are not random but follow systematic patterns that reflect the underlying 575 physical mechanisms omitted from the simplified analysis. Perhaps most significantly, the model 576 assumes perfect spatial uniformity in temperature distribution, while experiments consistently 577 reveal spatial temperature variations of ±1.5°C across the ESP volume. This spatial non-uniformity 578 cannot be captured by the radially symmetric model and represents a fundamental limitation of the 579 approach. The measured variations likely result from three-dimensional flow patterns, non580 uniform corona distribution along the wire length, and inter-cell coupling effects in the multi-cell 581 ESP configuration. 582 Despite the divergence from the measuring results, the simplified modelling successfully 583 captures the essential physics of competing thermal processes. Model supports that the negative 584 corona's higher current density at equivalent voltages creates more rapid Joule heating 585 accumulation, explaining the earlier thermal crossover and more pronounced high-energy heating 586 effects. 587 However, negative corona also demonstrates higher initial cooling, likely due to more 588 efficient reactive species generation and enhanced ionisation rates, which led to more intensive 589 nucleation. This creates a light deeper cooling, but also a sharper thermal transition once Joule 590 heating begins to dominate. 591 The temporal response differs significantly between processes. Joule heating responds 592 instantaneously to current changes, while nucleation cooling involves multi-step kinetic processes 593 - ion formation, molecular clustering, and phase transition. This temporal mismatch creates 594 transient regimes where rapid energisation increases can temporarily suppress nucleation before 595 steady-state ionic concentrations establish sufficient cooling capacity. In addition, nucleation 596 cooling is a reversible process – clusters can evaporate if conditions shift – while Joule heating 597 irreversibly raises the system’s thermal energy. This, together with the effect of combustion stages 598 on gas temperature and composition, can support the fluctuations in measured temperatures. -2 -1 0 1 2 3 4 0 5 10 15 20 25 30 35 40 ∆T [℃] SIE [J/L] measured predicted -3 -2 -1 0 1 2 3 4 5 0 5 10 15 20 25 30 35 40 45 50 ∆T [℃] SIE [J/L] This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 18 599 3.7 Practical relevance of research findings 600 ESP demonstrated the potential of multi-pollutant control ability, and this integration is 601 particularly valuable in residential heating applications where spatial, financial, and energy 602 constraints are of high importance. However, advanced emission control in corona discharge 603 requires a balanced approach to the structural design and operating parameters of the ESP. Several 604 practical considerations essential for engineering optimisation can be highlighted. 605 One key finding is the identification of an SIE threshold that marks the transition from net 606 cooling—driven by ion-induced nucleation—to net heating dominated by Joule dissipation. 607 Operating below this threshold not only aids in pollutant removal but also contributes to thermal 608 management by supporting condensation and reducing thermal stress. Beyond this point, however, 609 Joule heating becomes dominant and can raise the flue gas temperature. Understanding this 610 thermodynamic competition provides a useful operational reference and opens the door to 611 advanced control strategies aimed at maintaining favourable thermal conditions across a broader 612 energisation range. 613 Another important consideration is the choice of corona polarity. While both positive and 614 negative discharges demonstrated high pollutant removal efficiencies, they exhibited different 615 thermodynamic responses. Negative corona produced stronger initial cooling effects and more 616 intense heating at high discharge levels, whereas positive corona offered more gradual thermal 617 changes. This distinction can inform the selection of discharge polarity based on the thermal 618 sensitivity of the system and desired emission outcomes. 619 The research also points to opportunities for improvement in power supply strategies. The 620 observed temporal mismatch between Joule heating and nucleation-driven cooling suggests that 621 pulsed or intermittent energisation could be used to take advantage of transient cooling phases 622 while avoiding excessive heating. Such approaches could enhance system stability and energy 623 efficiency under dynamic combustion conditions. 624 In terms of physical design, modifications to the electrode configuration offer promising 625 avenues for improving thermal performance. Adjusting the geometry of discharge and collecting 626 electrodes could redistribute heating zones and create conditions that favour sustained nucleation, 627 even under higher energisation regimes. Moreover, recent innovations such as water-filled 628 collecting electrodes for heat transfer enhancement [44] or a heat storage device with liquid-filled 629 collection electrodes [45] present practical solutions for managing heat accumulation and 630 improving long-term thermal stability. 631 4CONCLUSIONS 632 This research provides novel insights into the thermodynamic behaviour of corona discharge 633 in electrostatic precipitators applied to small-scale biomass combustion systems. The ESP was 634 applied to real combustion gases from 5-kW domestic heating and demonstrated the ability to 635 solve complex emission control in biomass combustion by abating gaseous, volatile and particulate 636 hazardous: 637 - The baseline particle concentration was reduced to around 97 % even at minimal 638 energisation of 0.48/0.7 J/L for negative/positive corona, while total particle concentrations were 639 reduced to levels comparable to ambient air (1.8×104 particles/cm3) at maximum energisation of 640 35.7 J/L for positive and 48.4 J/L for negative corona; 641 - Effective NOx removal begins at SIE values exceeding 1 J/L for both discharge polarities. 642 Maximum NOx removal efficiency of 78% was achieved with operation at SIE of 48.4/35.7 J/L, 643 under negative/positive polarity, thus reducing NOx concentrations from 200 mg/m3 to 44-45 644 mg/m3. The removal mechanism involves corona-generated reactive species (OH radicals, oxygen 645 atoms, ozone) that convert NOx into nitrous and nitric acid vapours, which subsequently undergo 646 ion-induced nucleation to form precipitable aerosols; 647 - ESP confirmed the ability of corona discharge to decontaminate VOC by reducing total This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=5393018 Preprint not peer reviewed 19 648 hydrocarbon content from 9 mg/m3 to 0.6 mg/m3 under both polarities; 649 Such a high ESP performance was reflected in the combustion gases’ thermodynamics. The 650 study reveals a fundamental competition between two opposing thermodynamic processes: ion651 induced nucleation cooling and Joule heating. At low specific input energy levels (SIE < 2.85 J/L), 652 ion-induced nucleation dominates by extracting latent heat during phase transitions, resulting in 653 measurable gas cooling of 1-2 °C. However, as SIE increases beyond 7 J/L, Joule heating 654 overwhelms the nucleation cooling effect, leading to net temperature increases up to 2.4 °C above 655 baseline conditions. 656 Negative corona demonstrates superior initial cooling efficiency due to higher ion 657 concentrations and more intensive nucleation processes. However, it also exhibits sharper thermal 658 transitions and more pronounced high-energy heating effects due to higher current densities. 659 Positive corona shows more gradual thermal responses but achieves comparable NOx removal 660 efficiency at slightly lower SIE values. 661 This study advances the understanding of thermodynamic processes in corona discharge 662 environments and provides practical tools for optimising ESP design and operation, supporting the 663 development of sustainable emission control solutions for residential heating applications. 664 Understanding these competing thermodynamic mechanisms opens pathways for advanced 665 ESP control strategies and contributes to the development of more efficient and cost-effective 666 emission control technologies for small-scale combustion systems. 667 The implications extend beyond emission control. Understanding these thermodynamic 668 interactions could revolutionise applications ranging from indoor air purification to industrial 669 process optimisation. The principles discovered here may apply to any plasma-chemical system 670 where phase transitions compete with electrical heating, including semiconductor manufacturing, 671 materials processing, and atmospheric chemistry. 672 While this study focused on a single 5-kW unit, the fundamental thermodynamic principles 673 should apply across scales. The specific transition energisation regime may shift with system size 674 due to changes in surface-to-volume ratios and residence times. Future work should validate these 675 findings across 1-50 kW systems. 676 ACKNOWLEDGEMENTS 677 This work was supported by OP JAK under the project "INOVO!!!" CZ.02.01.01/00/23 678 021/0008588 and project LIFE18 IPE/SK/000010. 679 680 REFERENCES 681 [1] P.J. Landrigan, R. Fuller, N.J.R. Acosta, O. Adeyi, R. Arnold, N. Basu, A.B. 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