Calculation and Analysis of the Thermodynamic Properties of Air-Aerosols Mixtures

Wepari Charles Yaguibou^1*, Aly Rachid Korbeogo², Ibrahim Pafadnam³, Niessan Kohio⁴, Abdoul Karim Kagone⁵, Zacharie Koalaga⁵

¹Centre Universitaire de Dori, Université Thomas Sankara, Ouagadougou, Burkina Faso.
²Ecole Polytechnique de Ouagadougou, Ouagadougou, Burkina Faso.
³UFR Science et Technologie, Université Thomas Sankara, Ouagadougou, Burkina Faso.
⁴Ecole Normale Supérieure, Ouagadougou, Burkina Faso.
⁵UFR Science et Technologie, Université Joseph Ki-Zerbo, Ouagadougou, Burkina Faso.

DOI: 10.4236/ampc.2025.155005                

Abstract

Circuit breakers and other electrical equipment are often exposed to operational challenges caused by dust contamination, particularly short-circuit failures. These issues are frequently linked to the deposition of aerosols containing compounds such as aluminium oxide (Al₂O₃), calcium oxide (CaO), iron oxide (Fe₂O₃), and silicon dioxide (SiO₂) on critical components. While previous research has examined the influence of individual dust species—especially silica—on circuit breaker performance, these studies primarily focused on isolated effects, neglecting the combined thermodynamic impact of multiple aerosol constituents. In reality, environmental dust often comprises a mixture of species, including Al₂O₃, CaO, Fe₂O₃, and CO, which can vary significantly depending on the geographical context. This study aims to assess the influence of such aerosols on the thermodynamic properties of air plasma under atmospheric pressure and local thermodynamic equilibrium conditions, across a temperature range of 2000 K to 30,000 K. The properties, including mass enthalpy, specific heat at constant pressure, sound velocity, and mass density, are computed directly from the population densities of the relevant species. Results reveal that the presence of aerosol mixtures alters the thermodynamic behaviour of the arc plasma during circuit interruption. Notably, reductions in mass enthalpy, specific heat, and sound velocity are observed with increasing temperature, while specific heat increases at temperatures below 7000 K. Additionally, mass density is found to increase with temperature. These findings suggest that aerosol contamination during the interruption phase can degrade circuit breaker performance, potentially resulting in residual leakage currents or fire risks due to incomplete arc quenching.

Keywords

Composition, Density, Enthalpy, Plasma, Heat, Sound, Aerosol

1. Introduction

Dust is an environmental factor that can accelerate the ageing and malfunction of electrical equipment. The West African region, situated within the intertropical zone, extends from 4˚N to the southern edge of the Sahara (~20˚N) and from 18˚W to 20˚E (eastern border of Lake Chad) [1]. This region is a significant source of desert aerosols, which include dust particles, sand, pollen, volcanic ash, and sea spray. The transport of these particles across West Africa is largely influenced by regional atmospheric dynamics, particularly the Harmattan and monsoon winds [1]-[4].

The chemical composition of aerosols in West Africa varies according to soil characteristics. Typically, they are composed of oxides of aluminium, calcium, iron, and silica (Al₂O₃, CaO, Fe₂O₃, and SiO₂, respectively) [5]-[12]. Desert aerosols often mix with urban pollutants like hydrocarbons [13] [14] and accumulate on electrical equipment, particularly circuit breakers. Through vent holes, the mixture enters circuit breakers and deposits on the electrodes and within the breaking chamber [15] [16]. Figures 1-2 show dust episodes and accumulation on circuit breakers. Previous studies have demonstrated the impact of dust particles, such as silica, on circuit breaker performance. Silica significantly alters molar fractions, forming solid and liquid SiO₂ phases that condense on the gas generator surfaces. This process modifies the arc’s dynamic viscosity and speed [15] [16]. Aerosols can degrade electrical circuits and components within circuit breakers. However, prior studies have not addressed the combined effects of various species, including Fe₂O₃, CaO, Al₂O₃, and CO, which may be present in dust deposits depending on regional conditions. This study aims to investigate the effects of aerosols on the thermodynamic properties of plasma in the West African region.

The remainder of this paper is organised as follows: Section 2 outlines the methods for computing thermodynamic properties; Section 3 discusses the effects of aerosols on these properties; and Section 4 presents the conclusions.

Figure 1. Dust storm in Niger in 2020 (https://sciencepost.fr).

Figure 2. Dust deposition on circuit breakers [15].

2. Methods and Materials

In West Africa, the period from February to April is characterised by large emissions of desert dust from the Saharan and local areas. However, the wet period from June to September and the period from December to January are characterised by small emissions of dust [17]. The most abundant chemical species in aerosols are silicon, calcium, iron, and aluminium oxides. The carbon oxide species are derived from biomass fires and fossil-fuel production. Further, silicon oxides account for up to 60% of the total mass. After silica, the most abundant oxides are aluminium (Al₂O₃) and ferric oxides (Fe₂O₃) [9] [10]. These proportions are directly linked to the texture of the soil itself. They’re typically derived from analyses conducted in various studies across a sub-region. It’s important to understand that these proportions are not static; they can vary significantly from one area to another due to differences in geology and topography. The composition and proportion of the chemical components of aerosols vary depending on the area. The mass proportions reflect desert sandstorms, regional soil composition, and human activity, with SiO₂ as the dominant species. The red colour of the dust in Ouagadougou indicates the presence of Fe₂O₃. Moreover, CaO has remarkable proportions, but less than Fe₂O₃ in Ouagadougou. The presence of Al₂O₃ is remarkable. We have not yet encountered work that establishes a clear composition of aerosols. Studies typically focus on mass fractions and specific chemical species based on the region [1] [3] [8]-[10].

A circuit breaker may need to operate in a polluted environment over a long duration. Our study found that aerosols were composed of silicon oxides, iron oxides, aluminium oxides, calcium oxides, and carbon monoxide. We assume that 1 g of aerosol contained the following mass percentages: 50% SiO₂, 20% Fe₂O₃, 10% Al₂O₃, 5% CO, and 15% CaO. This work is entirely theoretical because we do not have the equipment for experiments.

The mass fractions of the chemical elements of aerosol species that constitute the basic elements of the plasma were calculated using Equation (1) below:

$\text{\%}A=\text{\%}air*\text{\%}{A}_{air}+\text{\%}aero\left(\begin{array}{l}\text{\%}{A}_k{C}_l\left(\frac{k{M}_A}{M_{A_k{C}_l}}\right)+\text{\%}{A}_x{D}_z\left(\frac{x{M}_A}{M_{A_x{D}_z}}\right)+\\ \text{\%}{A}_{\gamma }{E}_{\beta }\left(\frac{\gamma M_A}{M_{A_{\gamma }{E}_{\beta }}}\right)+\text{\%}{A}_{\nu }{F}_{\theta }\left(\frac{\nu M_A}{M_{A_{\nu }{F}_{\theta }}}\right)\end{array}\right)$ (1)

where A, B, C, D, E, and F represent chemical elements; A_iB_j represents the chemical species of air of mass percentage %air; $A_{\nu }{F}_{\theta }$ , $A_k{C}_l$ , $A_x{D}_z$ , and $A_{\gamma }{E}_{\beta }$ represent the species brought by aerosols of mass percentage %aero; $M_{A_k{C}_l}$ , $M_{A_x{D}_z}$ , $M_{A_{\gamma }{E}_{\beta }}$ , $M_{A_{\nu }{F}_{\theta }}$ , $M_A$ , $M_B$ , $M_C$ , and $M_D$ represent the molar masses of the species considered; and i, j, k, l, x, z, 𝜃, 𝜈, β, and γ represent the numbers of atoms. From Equation (1), we obtain the mass percentages of the basic elements of our plasma, as listed in Table 1. The initial step in calculating the thermodynamic properties and transport coefficients is determining the equilibrium composition of the gas mixture using the principle of minimisation of the Gibbs free energy of the mixture [16] [18]-[21]. To this end, the specific chemical potential of all plasma particles must be determined [20]. Smoothed and tabulated thermodynamic data from Bonnie and Bendjebbar are used to calculate specific thermodynamic properties. The specific heat capacity, specific enthalpy, and specific entropy are obtained by Equation (2) [22] [23]:

$\{\begin{array}{l}\frac{C_P^0\left(T\right)}{R}=a_1{T}^{-2}+a_2{T}^{-1}+a_3+a_{4}T+a_5{T}^2+a_6{T}^3+a_7{T}^4\\ \frac{H^0\left(T\right)}{RT}=-a_1{T}^{-2}+a_2\frac{\ln \left(T\right)}{T}+a_3+a_4\frac{T}{2}+a_5\frac{T^2}{3}+a_6\frac{T^3}{4}+a_7\frac{T^4}{5}+\frac{b_1}{T}\\ \frac{S^0\left(T\right)}{R}=-a_1\frac{T^{-2}}{2}+a_2\frac{T^{-1}}{2}+a_3\ln \left(T\right)+a_{4}T+a_5\frac{T^2}{2}+a_6\frac{T^3}{3}+a_7\frac{T^4}{4}+b_2\end{array}$ (2)

where R and T represent the constant of perfect gases and the temperature in Kelvin. The coefficients a_i and b_i for each particle are given by [22] [23].

For air-aerosol mixtures, 34 monatomic species have been considered (C, O, N, Si, Al, Fe, Ca, C⁺, O⁺, N⁺, Si⁺, Al⁺, Fe⁺, Ca⁺, C⁻, O⁻, N⁻, Si⁻, Al⁻, Fe⁻, C⁺⁺, O⁺⁺, N⁺⁺, Si⁺⁺, Al⁺⁺, Fe⁺⁺, Ca⁺⁺, C⁺⁺⁺, O⁺⁺⁺, N⁺⁺⁺, Si⁺⁺⁺, Al⁺⁺⁺, Fe⁺⁺⁺, Ca⁺⁺⁺) and electrons; 31 diatomic species (C₂, O₂, N₂, Si₂, Al₂, Fe₂, Ca₂ CO, CN, SiC, AlC, NO, SiO, AlO, SiN, FeO, AlN, CaO, C₂⁺, O₂⁺, N₂⁺, CO⁺, CN⁺, NO⁺, AlO⁺, CaO⁺, N₂⁻, C₂⁻, O₂⁻, CN⁻, and AlO⁻); and 40 polyatomic species (CO₂, C₃, CCN, CNC, CNN, C₂O, O₃, N₃, NCO, NO₂, N₂O, NCN, SiC₂, SiO₂, Si₂C, Si₂N, Si₃, AlC₂, AlO₂, Al₂O, OCCN, C₂N₂, CNCOCN, C₃O₂, C₄, NO₃, N₂O₃, N₂O₄, N₂O₅, Al₂C₂, Al₂O₂, Al₂O₃, Fe(CO)₅, N₂O⁺, CO₂⁺, Al₂O⁺, Al₂O₂⁺, AlO₂⁻, NO₃⁻, and NO₂⁻).

In this study, the temperature range for the equilibrium composition was 2000 - 30000 K, assuming only the gaseous phase. Metals and their components are in solid form at low temperatures. At temperatures lower than approximately 2000 K, the plasma component can be established in air. The experiments are conducted at atmospheric pressure (1 bar), and therefore, all results of the thermodynamic properties are presented in this range.

2.1. Mass Density (kg/m³)

Mass density is the quantity involved in the fluid mechanics equation. The density measures the amount of material contained in a given volume of plasma.

The following formula in Equation (3) was used [24].

$\rho =\frac{P}{RT}{\displaystyle \sum _{i=1}^N{x}_i{M}_i}$ (3)

where $x_i$ , $M_i$ , P, R, T, and N represent the molar fraction, molar mass of species$i$ , pressure, molar gas constant, absolute temperature, and number of species in the plasma, respectively.

2.2. Mass Enthalpy (J/kg)

Mass enthalpy was calculated using the specific enthalpies of each particle and their molar fractions using $x_i$ presented in Equation (4) [24] as:

$h=\frac{1}{M}\left({\displaystyle \sum _{i=1}^N{x}_i\left(H_i^0+H_f\right)}\right)-\frac{k_{b}T}{6\pi {\lambda }_D^3}$ (4)

where $M$ represents the average molar mass, $M={\displaystyle \sum _{i=1}^N{x}_i{M}_i}$ $H_i^0$ represents the molar enthalpy, and $H_f$ represents the heat of formation at 298.15 K (J/mol) [23], and $k_{b}T/6\pi {\lambda }_D^3$ represents the Debye-Huckel term.

2.3. Specific Heat at Constant Pressure (J/kg/K)

The specific heat ($C_p$ ) is the amount of energy to be supplied by heat exchange to raise the temperature of a medium by 1˚. This indicated the ability of the system to store heat. If the thermodynamic transformation of the system is performed at constant pressure, the specific heat can be calculated and given by Equation (5) as [25].

$C_p=\left(\frac{dh}{dT}\right)=\frac{h\left(T+\Delta T\right)-h\left(T\right)}{\Delta T}$ (5)

where $\Delta T$ represents the variation in temperature ($\Delta T=100K$ ), and $T$ represents the temperature.

2.4. Velocity of Sound (m/s)

The velocity of sound was calculated using Equation (6) below [26]:

$V_S={\left(\frac{RT}{M}\right)}^{1/2}$ (6)

Table 1. Mass percentage of the mixtures considered in this study.

%Air	%aerosol	%C	%O	%N	%Si	%Al	%Fe	%Ca
100	0	0	22.2	77.8	0	0	0	0
99	1	0.021	22.423	77.022	0.234	0.053	0.140	0.107
90	10	0.214	24.428	70.02	2.337	0.53	1.399	1.072
80	20	0.429	26.657	62.240	4.674	1.058	2.798	2.144
50	50	1.072	33.341	38.900	11.686	2.647	6.994	5.360
20	80	1.715	40.026	15.560	18.698	4.234	11.191	8.576

Table 2. Comparative analysis of the thermodynamic properties.

Temperature (K)	Mass density (kg∙m−3)			Mass enthalpy (J∙kg−1)			Specific heat (Jkg−1∙K−1)
	Boulos	Result	Ecart (%)	Boulos	Result	Ecart (%)	Boulos	Result	Ecart (%)
7000	3.15E−2	3.22E−2	2.17	2.59E−7	2.60E−7	0.38	14,026	14,050.5	0.17
10000	1.72E−2	1.68E−2	2.38	4.84E−7	4.83E−7	0.21	4867.2	4761.62	2.22
15000	7.75E−3	7.78E−3	0.39	1.16E−8	1.11E−8	4.50	21,652	19,290.8	12.24
	D’Angola	Result	Ecart	D’Angola	Result	Ecart	D’Angola	Result	Ecart
7000	3.100E−2	3.223E−2	3.72	2.63E−7	2.60E−7	1.16	14,053.9	14,050.5	0.02
10000	1.69E−2	1.68E−2	0.59	4.87E−7	4.83E−7	0.83	4749.75	4761.62	0.25

3. Results and Discussions

3.1. Comparison

Figure 3. Comparison of mass density data of air plasma at atmospheric pressure.

Figure 4. Comparison of mass enthalpy data of air plasma at atmospheric pressure.

Figure 5. Comparison of specific heat data of air plasma at atmospheric pressure.

The thermodynamic of air-aerosol mixtures under the local thermodynamic equilibrium (L.T.E) assumption were evaluated across a temperature range of 2000 K - 30000 K at atmospheric pressure. These properties depend on the plasma composition, which is determined by minimising the Gibbs free energy. The local thermodynamic equilibrium is achieved when the rate of collisional processes is much higher than the rate of radiative processes (mainly radiative recombination and spontaneous emission).

No existing data were available for the exact mixture type studied here. However, previous research has examined various plasma models, including air, nitrogen, carbon dioxide (CO₂), CF₃I, argon-copper, argon-aluminium, C₄F₇N-CO₂-O₂, air-PA₆₆-copper, and C₄F₇N plasmas [27]-[38]. The MATLAB calculation method was validated by comparing its results with those from previous plasma studies. Thus, the properties of dry air plasma were compared with results from prior work to verify the data and equations used in these calculations [27]-[30]. The thermodynamic properties are presented in Table 2, where the mass density, mass enthalpy, and specific heat show satisfactory agreement with existing data, with an overall deviation of less than 7%. However, heat capacity showed a maximum deviation of 12.24% at 15,000 K compared to the data from Boulos et al. [27]. Figures 3-5 show comparisons of the results for mass density, mass enthalpy, and heat capacity with the data from Boulos et al. [27] and D’Angola et al. [28]. The discrepancies observed can be attributed to the specific data used in this calculation program. Specific enthalpies, entropies, and chemical potentials were also calculated.

3.2. Effect of Aerosol Concentration on Thermodynamic Properties

Determining the chemical composition of plasma is essential for calculating thermodynamic properties. Previous studies have analysed the thermodynamic properties of various gas mixtures, including air [31] [32], CO₂ [33], SF₆ [34], and N₂ [35], and CF3I [33].

Figure 6 shows the mass densities of the air plasmas contaminated by aerosols. The evolution is identical for the different plasmas. The mass density decreases with increasing temperature; this decrease is greater at low temperatures (<8000 K). This is reflected by the decrease in the total density of species (rarefaction of the environment) imposed by the ideal gas law and by the presence of less massive species (atoms, ions and especially electrons) at high temperatures. These are direct consequences of the dissociation and ionisation of molecular and atomic species, which lead to the gradual disappearance of molecules and atoms with an increase in temperature [39]. The mass density of pure air coincided with the mass density of plasma containing 1% aerosols. Beyond 1%, the values of contaminated air plasmas are higher than those of pure air plasma; the more the plasma is contaminated, the higher is the increase in its mass density because they contain heavier particles than air. Table 3 lists the molar masses of the neutral species in the plasma.

Table 3. Molecular weight of neutral species [23].

Species	Molecular	Species	Molecular	Species	Molecular	Species	Molecular
	weight (g/mol)		weight (g/mol)		weight (g/mol)		weight (g/mol)
C	12.01070	CO	28.01010	O2	31.99880	SiN	42.09220
N	14.00670	CN	26.01740	N2	28.01340	FeO	71.84440
O	15.99940	SiC	40.09620	Si2	56.17100	AlN	40.98828
Si	28.08550	AlC	38.99224	Al2	53.96308	CO2	44.00950
Al	26.98154	NO	30.00610	Fe2	111.6900	C3	36.03210
Fe	55.84500	SiO	44.08490	C2	24.02140	AlO	42.98094

Figure 6. Evolution of the mass density of the plasma according to the percentage of aerosols, units: kg/m³.

The enthalpy curves (Figure 7) show rapid phases of evolution that correspond to the reactivity of the medium and to the dissociation and ionisation phenomena. Enthalpy varies inversely with mass density, and therefore, the enthalpy of the air plasma is greater than that of the polluted air plasma. In other words, the more polluted the air, the greater is the decrease in enthalpy.

Figure 7. Evolution of the mass enthalpy of the plasma according to the percentage of aerosols, units: J/kg.

Figure 8 shows that specific heat strongly depends on the nature of the mixture and temperature, with the appearance of peaks in the regions where the enthalpy varies rapidly. The curves show the same pattern with the first peak at ~3500 K and the second at ~7000 K for up to 50% aerosols. Beyond this proportion, the peak gradually shifted towards lower temperatures (e.g. the peak was ~5500 K between 80% and 100% aerosols). The third peak occurs at ~15,000 K, where the peak moved slightly with an increase in the aerosol rate. These peaks represent the dissociation (of molecules) and ionisation (of atoms). The first peak (at ~3500 K) corresponds to the dissociation of CO₂, FeO, AlC, CN, SiC, AlC, SiN, NO, O₂, Al₂O, and SiO₃ molecules. For example, O₂, CO₂, and Al₂O dissociate at ~3500, 3400, and 4000 K [40]. Al₂ and Fe₂ dissociate below 3000 K [40], and C₃ and C₂ dissociate at ~5000 K [40]. The peak at ~5500 K for aerosols with mass percentages between 80% and 100% can be attributed to the dissociation of AlO and SiO. The dissociation peak of SiO appeared at ~5700 K at 1 atm [41].

The second peak corresponds to the dissociation of the CO and N₂ molecules. CO and N₂ dissociate at ~7000 K [40]. The first ionisation of the Al atom occurs at 9000 K [42] [43], whereas that of the Fe atom occurs between 8500 K and 9000 K [44]. Si and Ca ionise at the same temperature. The Al, Fe, Si, and Ca atoms ionise rapidly before the C, O, and N atoms because of their low ionisation energies (Ei0_Al = 5.986 eV, Ei0_Ca = 6.113 eV, Ei0_Fe = 7.902 eV, Ei0_Si = 8.151 eV, Ei0_C = 11.26 eV, Ei0_O = 13.628 eV, and Ei0_N = 14.55 eV). The third peak corresponds to the ionisation of C, O, and N atoms. The first ionisation of O and N is ~15,000 K [44].

The second ionisation of Al and Fe occurs around 19,000 K [42] [44]. The temperature corresponding to the second ionisation of C, O, and N was ~30,000 K [40] [44]. The first and second ionisations of Si and Ca were observed in the same temperature zones as iron and aluminium because of their similar ionisation energies. The effect of the aerosols was clear over the entire temperature range. Modifications to the locations of the main dissociation peaks are clearly observed. The movement of the peaks at low temperatures can be attributed to the chemistry. For example, for a 20% air-80% aerosol mixture, a peak was detected at ~5500 K, which can be attributed to the dissociation of AlO and SiO. Therefore, aerosols cause a decrease in specific heat because of the small energy ionisation of metals, except at temperatures below 7000 K. A high heat capacity means that the plasma can absorb more thermal energy for a given increase in temperature. This is beneficial for arc cooling, as a large portion of the arc’s energy can be “stored” in the processes of dissociation and ionization rather than directly resulting in a temperature increase that would maintain the conductive plasma. These results show that the presence of aerosols leads to a slight increase in heat capacity. So a slight cooling of the plasma. The carbon released by the decomposition of CO can deposit as soot on insulating surfaces or contacts. These soot deposits can create undesirable conduction paths, leading to flashovers or a reduction in the dielectric strength of the insulators. In the presence of metallic vapors from the contacts, metallic carbides can form, also affecting the surfaces.

The presence of CO and its decomposition products can reduce the insulating capacity of the gaseous medium. Carbon particles can act as sites of electric field concentration, facilitating new discharges.

Figure 8. Evolution of the specific heat of the plasma according to the percentage of aerosols, units: J/kg/K.

Figure 9 shows the evolution of the sound velocity spread in air-aerosol plasmas, which decreases with the percentage of aerosols in the mixture. This decrease in sound propagation can be explained by heavy particles present in the polluted plasma. The higher the rate of contamination, the heavier is the plasma. This decreases the velocity.

Figure 9. Evolution of the sound velocity of the plasma according to the percentage of aerosols, units: m/s.

4. Conclusions

This study examined the effect of aerosols on the thermodynamic properties of air plasma in a state of local thermodynamic equilibrium. Findings indicate that plasma density increases, whereas enthalpy, specific heat, and sound velocity all decrease, as the aerosol concentration in the mixture rises. Specific heat increased at temperatures below 7000 K and decreased at higher temperatures, with notable peaks at approximately 3500 K, 7000 K, and 15,000 K. Mass specific enthalpy is a key indicator of the arc plasma’s energy state. Rapid reduction of this value is the fundamental goal of all arc extinction mechanisms in a circuit breaker to ensure reliable and safe current interruption. However, the presence of metal oxides can reduce the mass enthalpy and heat capacity at a given temperature. A potentially lower specific enthalpy and heat capacity would make arc quenching more difficult. The plasma remains conductive for longer, which extends the duration of the electric arc. A longer arc duration and sustained high temperatures increase the erosion of the circuit breaker’s contacts, reducing their lifespan and potentially their reliability. In extreme cases, excessive oxide accumulation and unfavorable changes in plasma properties can lead to a failure to interrupt the circuit, with serious consequences for the electrical grid and equipment.

This theoretical analysis demonstrates that aerosols significantly impact plasma characteristics, including density, mass enthalpy, heat capacity, and sound velocity. Moreover, the plasma must be a good electrical insulator at low temperatures to facilitate the transient recovery voltage and to avoid restrikes.

While thermodynamic properties alone are insufficient to determine a circuit breaker’s interruption capacity, they provide insight into the impact of aerosols on such capacity. Future studies should investigate the transport proprieties the dielectric strength properties, density variations, energy fluxes, and radiation effects, conducting experiments to comprehensively characterise plasma properties, including the influence of solid-phase aerosols.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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