Pattern formation and self-organization in plasmas interacting with surfaces

Abstract

Pattern formation and self-organization are fascinating phenomena commonly observed in diverse types of biological, chemical and physical systems, including plasmas. These phenomena are often responsible for the occurrence of coherent structures found in nature, such as recirculation cells and spot arrangements; and their understanding and control can have important implications in technology, e.g. from determining the uniformity of plasma surface treatments to electrode erosion rates. This review comprises theoretical, computational and experimental investigations of the formation of spatiotemporal patterns that result from self-organization events due to the interaction of low-temperature plasmas in contact with confining or intervening surfaces, particularly electrodes. The basic definitions associated to pattern formation and self-organization are provided, as well as some of the characteristics of these phenomena within natural and technological contexts, especially those specific to plasmas. Phenomenological aspects of pattern formation include the competition between production/forcing and dissipation/transport processes, as well as nonequilibrium, stability, bifurcation and nonlinear interactions. The mathematical modeling of pattern formation in plasmas has encompassed from theoretical approaches and canonical models, such as reaction-diffusion systems, to drift-diffusion and nonequilibrium fluid flow models. The computational simulation of pattern formation phenomena imposes distinct challenges to numerical methods, such as high sensitivity to numerical approximations and the occurrence of multiple solutions. Representative experimental and numerical investigations of pattern formation and self-organization in diverse types of low-temperature electrical discharges (low and high pressure glow, dielectric barrier and arc discharges, etc) in contact with solid and liquid electrodes are reviewed. Notably, plasmas in contact with liquids, found in diverse emerging applications ranging from nanomaterial synthesis to medicine, show marked sensitivity to pattern formation and a broadened range of controlling parameters. The results related to the characteristics of the patterns, such as their geometric configuration and static or dynamic nature; as well as their controlling factors, including gas composition, driving voltage and current, electrode cooling, and imposed gas flow, are summarized and discussed. The article finalizes with an outlook of the research area, including theoretical, computational, and experimental needs to advance the field.

The 2017 Plasma Roadmap: Low temperature plasma science and technology

“…Plasmas on liquids can generate coherent structures that have not been modelled from first principles. In fact, modelling coherent structures is generally a challenge [169]. The large dynamic range of time/ spatial scales and physical phenomena continues to challenge the field.…”

Spatial‐temporal evolutions of surface discharge patterns generated on dielectric target interacted with a plasma jet

“…As a result, there are complex interactions among plasma jet, dielectric, and surface discharges. These interactions can lead to pattern formation . A crescent pattern appears on a dielectric colliding obliquely with a helium plasma plume, which transits to a solid‐disk pattern for vertical incidence of the plume .…”

“…These interactions can lead to pattern formation. [26,27] A crescent pattern appears on a dielectric colliding obliquely with a helium plasma plume, [28] which transits to a solid-disk pattern for vertical incidence of the plume. [29,30] Moreover, the solid disk can transit to a single ring by varying the gas flow rate, [29,30] changing the gap distance, [31] or adding trace of nitrogen into helium.…”

Finite Element Methods for Arc Discharge Simulation

“…The results show that patterns appear at a critical value of h w ∼ 10 3 –10 4 Wm −2 K −1 , almost independently of the value of I tot ; the patterns become more accentuated with increasing cooling; and for very high cooling, the patterns become dynamic (which explains the asymmetric distribution of spots in Figure ). Two‐dimensional, steady‐state, and/or LTE models cannot adequately capture the occurrence of pattern formation in arc discharges − a fact that highlights the need for time‐dependent, three‐dimensional NLTE models for accurate arc discharge simulations …”

“…Two-dimensional, steady-state, and/or LTE models cannot adequately capture the occurrence of pattern formation in arc discharges À a fact that highlights the need for time-dependent, three-dimensional NLTE models for accurate arc discharge simulations. [83]…”