Atmospheric pressure arcs have recently found application in the production of nanoparticles. Distinguishing features of such arcs are small length and hot ablating anode characterized by intensive electron emission and radiation from its surface. We performed one-dimensional modeling of argon arc, which shows that near-electrode effects of thermal and ionization non-equilibrium play important role in operation of a short arc, because the non-equilibrium regions are up to several millimeters long and are comparable with the arc length. The near-anode region is typically longer than the near-cathode region and its length depends more strongly on the current density. The model was extensively verified and validated against previous simulation results and experimental data. Volt-Ampere characteristic (VAC) of the near-anode region depends on the anode cooling mechanism. The anode voltage is negative. In case of strong anode cooling (water-cooled anode) when anode is cold, temperature and plasma density gradients increase with current density resulting in decrease of the anode voltage (absolute value increases). Falling VAC of the near-anode region suggests the arc constriction near the anode. Without anode cooling, the anode temperature increases significantly with current density, leading to drastic increase in the thermionic emission current from the anode. Correspondingly, the anode voltage increases to suppress the emission -and the opposite trend in the VAC is observed. The results of simulations were found to be independent of sheath model used: collisional (fluid) or collisionless model gave the same plasma profiles for both near-anode and near-cathode regions.Parametric studies of short atmospheric pressure argon arc with tungsten electrodes were performed for various current densities and inter-electrode gap sizes. Non-equilibrium effects in the near-electrode regions were studied. Anodes with and without water cooling were considered. Effect of electron emission on current-voltage characteristic of the near-anode layer was investigated. Analytical formulas for scaling of non-equilibrium regions widths and Volt-Ampere's characteristics of these regions and the whole arc are given in the accompanying paper 44 .The organization of the paper is as follows. In Section II governing equations and boundary conditions for plasma and electrodes are presented. Section III describes numerical procedure of solving the governing equations. Results of simulations including validation of the model and parametric studies of the arc are presented and discussed in Section IV. Conclusions of this work are summarized in Section V.

Short atmospheric pressure argon arc is studied numerically and analytically. In a short arc with interelectrode gap of several millimeters non-equilibrium effects in plasma play important role in operation of the arc. High anode temperature leads to electron emission and intensive radiation from its surface. Complete self-consistent analytical model of the whole arc comprising of models for near-electrode regions, arc column and a model of heat transfer in cylindrical electrodes was developed. The model predicts width of non-equilibrium layers and arc column, voltages and plasma profiles in these regions, heat and ion fluxes to the electrodes. Parametric studies of the arc have been performed for a range of the arc current densities, inter-electrode gap widths and gas pressures. The model was validated against experimental data and verified by comparison with numerical solution. Good agreement between the analytical model and simulations and reasonable agreement with experimental data were obtained.

In order to study the properties of short carbon arcs, a self-consistent model was implemented into a CFD code ANSYS-CFX. The model treats the transport of heat and electric current in the plasma and electrodes in a coupled manner and accounts for gas convection in the chamber. Multiple surface processes at the electrodes are modeled, including the formation of space-charge limited sheaths, ablation and deposition of carbon, and emission and absorption of radiation and electrons. The simulations show that the arc is constricted near the cathode and anode front surfaces, leading to the formation of electrode spots. The cathode spot is a well-known phenomenon, and mechanisms of its formation were reported elsewhere. However, the anode spot formation mechanism discovered in this work was not previously reported. We conclude that the spot formation is not related to plasma instability, as commonly believed in the case of constricted discharge columns, but rather occurs due to the highly nonlinear nature of heat balance in the anode. We additionally demonstrate this property with a reduced anode heat transfer model. We also show that the spot size increases with the arc current. This anode spot behavior was also confirmed in our experiments. Due to the anode spot formation, a large gradient of carbon gas density occurs near the anode, which drives a portion of the ablated carbon back to the anode at its periphery. This can consequently reduce the total ablation rate. Simulation results also show that the arc can reach the local chemical equilibrium state in the column region, while the local thermal equilibrium state is not typically achieved for experimental conditions. It shows that it is important to account for different electron and gas temperatures in the modeling of short carbon arcs.

This work studies the region of nanoparticle growth in atmospheric pressure carbon arc.Detection of the nanoparticles is realized via the planar laser induced incandescence (PLII) approach.Measurements revealed large clouds of nanoparticles in the arc periphery, bordering the region with high density of diatomic carbon molecules. Two-dimensional computational fluid dynamic simulations of the arc combined with thermodynamic modeling explain these results due to interplay of the condensation of carbon molecular species and the convection flow pattern. The results have shown that the nanoparticles are formed in the colder, outside regions of the arc and described the parameters necessary for coagulation.