Surface modification of polymeric materials by cold atmospheric plasma jet

In this work we report the surface modification of different engineering polymers, such as, polyethylene terephthalate (PET), polyethylene (PE) and polypropylene (PP) by an atmospheric pressure plasma jet (APPJ). It was operated with Ar gas using 10 kV, 37 kHz, sine wave as an excitation source. The aim of this study is to determine the optimal treatment conditions and also to compare the polymer surface modification induced by plasma jet with the one obtained by another atmospheric pressure plasma source the dielectric barrier discharge (DBD). The samples were exposed to the plasma jet effluent using a scanning procedure, which allowed achieving a uniform surface modification. The wettability assessments of all polymers reveal that the treatment leads to reduction of more than 40 degrees in the water contact angle (WCA). Changes in surface composition and chemical bonding were analyzed by x-ray photoelectron spectroscopy (XPS) and Fourier-Transformed Infrared spectroscopy (FTIR) that both detected incorporation of oxygen-related functional groups. Surface morphology of polymer samples was investigated by Atomic Force Microscopy (AFM) and an increase of polymer roughness after the APPJ treatment was found. The plasma-treated polymers exhibited hydrophobic recovery expressed in reduction of the O-content of the surface upon rinsing with water. This process was caused by the dissolution of low molecular weight oxidized materials (LMWOMs) formed on the surface as a result of the plasma exposure. (C) 2014 Elsevier B.V. All rights reserved.

Transfer of a cold atmospheric pressure plasma jet through a long flexible plastic tube

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Inactivation of candida albicans by cold atmospheric pressure plasma jet

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Studio dell'interazione tra un plasma jet nanopulsato con substrati metallici, dielettrici e liquidi

Il plasma è denominato quarto stato della materia ed è generalmente definito come un gas ionizzato costituito da elettroni e ioni. In ambito industriale i plasmi hanno trovato impiego per diversi tipi di applicazione quali il trattamento di superfici, la degradazione e lo smaltimento di rifiuti, il taglio di materiali, primi fra tutti i metalli. In particolare i plasmi atmosferici di non equilibrio, che possiedono la caratteristica di mantenere una temperatura macroscopica paragonabile a quella ambiente, sono studiati anche per applicazioni in campo biomedicale, oltre che in quello industriale. Da alcuni anni sono quindi oggetto di indagine per le caratteristiche di sterilizzazione di fluidi o solidi, per la coagulazione e il trattamento di lesioni e lacerazioni, per trattamenti su superfici quali la pelle, per il trattamento di cellule tumorali e staminali o per interfacce dispositivi biomedicali – corpo umano. Questo nuovo settore di ricerca, in grande sviluppo, viene comunemente definito Plasma & Medicine. Poiché in ambito biomedicale, un trattamento plasma può interessare diverse tipologie di substrati biologici e materiali, è stato scelto come obiettivo della tesi la caratterizzazione di una sorgente di plasma di non equilibrio a pressione atmosferica, denominata Plasma Jet, posta ad interagire con substrati di diversa natura (metallico, dielettrico, liquido). La sorgente utilizzata è in grado di produrre un plasma freddo e biocompatibile, generando diverse specie chimiche che garantiscono effetti molto interessanti (sterilizzazione, accelerazione della coagulazione sanguigna, cura di infezioni) per un utilizzo a contatto con il corpo umano o con componenti ingegneristiche che devono venire ad interagire con esso, quali stent, cateteri, bisturi. La caratterizzazione è stata effettuata mediante l’ausilio di due tecniche diagnostiche: la Schlieren Imaging, che permette di studiare la fluidodinamica del gas, OES (Optical Emission Spettroscopy), che permette di analizzare la composizione chimica della piuma di plasma e di determinare le specie chimiche che si producono. Questo elaborato si propone quindi di fornire una breve introduzione sul mondo dei plasmi e sulle loro caratteristiche, citando alcuni dei settori in cui viene utilizzato, industriali e biomedicali, con particolare attenzione per questi ultimi. Successivamente saranno riportati i setup utilizzati per le acquisizioni e una discussione sui risultati ottenuti dalle diverse tecniche diagnostiche utilizzate sul Jet durante i trattamenti. In ultimo sono poi riportate le conclusioni in modo da presentare le caratteristiche più importanti del comportamento della sorgente.

Instrumentation studies for plasma jet and hypersonic wind tunnel,

"This research was supported by the McDonnell Aircraft Corporation under Contract no. 6140-20 P.O. 7S4899-R."

Deposition of thin films by a non-equilibrium atmospheric pressure Plasma Jet: a poly-diagnostic study

The use of atmospheric pressure plasmas for thin film deposition on thermo-sensitive materials is currently one of the main challenges of the plasma scientific community. Despite the growing interest in this field, the existing knowledge gap between gas-phase reaction mechanisms and thin film properties is still one of the most important barriers to overcome for a complete understanding of the process. In this work, thin films surface characterization techniques, combined with passive and active gas-phase diagnostic methods, were used to provide a comprehensive study of the Ar/TEOS deposition process assisted by an atmospheric pressure plasma jet. SiO2-based thin films exhibiting a well-defined chemistry, a good morphological structure and high uniformity were studied in detail by FTIR, XPS, AFM and SEM analysis. Furthermore, non-intrusive spectroscopy techniques (OES, filter imaging) and laser spectroscopic methods (Rayleigh scattering, LIF and TALIF) were employed to shed light on the complexity of gas-phase mechanisms involved in the deposition process and discuss the influence of TEOS admixture on gas temperature, electron density and spatial-temporal behaviours of active species. The poly-diagnostic approach proposed in this work opens interesting perspectives both in terms of process control and optimization of thin film performances.

Desenho e Construção de um protótipo gerador de jato de plasma frio a pressão atmosférica para aplicações biomédicas

Research for better performance materials in biomedical applications are constants. Thus recent studies aimed at the development of new techniques for modification of surfaces. The low pressure plasma has been highlighted for its versatility and for being environmentally friendly, achieving good results in the modification of physic chemical properties of materials. However, it is requires an expensive vacuum system and cannot able to generate superficial changes in specific regions. Furthermore, it is limits their use in polymeric materials and sensitive terms due to high process temperatures. Therefore, new techniques capable of generating cold plasma at atmospheric pressure (APPJ) were created. In order to perform surface treatments on biomaterials in specific regions was built a prototype capable of generating a cold plasma jet. The prototype plasma generator consists of a high voltage source, a support arm, sample port and a nozzle through which the ionized argon. The device was formed to a dielectric tube and two electrodes. This work was varied some parameters such as position between electrodes, voltage and electrical frequency to verify the behavior of glow discharges. The disc of titanium was polished and there was a surface modification. The power consumed, length, intensity and surface modifications of titanium were analyzed. The energy consumed during the discharges was observed by the Lissajous figure method. To check the length of the jets was realized with Image Pro Plus software. The modifications of the titanium surfaces were observed by optical microscopy (OM ) and atomic force microscopy (AFM ). The study showed that variations of the parameters such as voltage, frequency and geometric position between the electrodes influence the formation of the plasma jet. It was concluded that the plasma jet near room temperature and atmospheric pressure was able to cause modifications in titanium surface

Surface Modification of Polycarbonate by Atmospheric-Pressure Plasma Jets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Tratamento de polímeros com jato de plasma em pressão atmosférica

Pós-graduação em Física - FEG

Estudo das modificações na superfície do Ti cp titânio comercialmente puro e da liga Ti-6AI-4V usados como biomateriais utilizando-se deposição por plasma spray

Pós-graduação em Química - IQ

Jato de plasma frio em pressão atmosférica para tratamento de materiais e esterilização

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influência de tratamentos a plasma na resistência à corrosão e na propriedade de adesão de uma camada protetiva sobre a superfície de ligas de alumínio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Separation control by means of oriented DBD plasma actuators: an experimental analysis in a wind tunnel

This thesis provides an experimental analysis of the effectiveness of oriented DBD plasma actuators over a NACA 0015 airfoil at low Reynolds numbers. Tests were performed in partnership with the Department of Electrical Engineering of Bologna University, in the wind tunnel of the Applied Aerodynamics Laboratory of Aerospace Engineering faculty. Lift coefficient measurements were carried out in order to verify how an oriented plasma jet succeeds in prevent boundary layer separation. Both actuators’ chord wise position and plasma jet orientation angle have been investigated to examine which configurations lead to the best results. A particular attention has been paid also to the analysis of results in steady and unsteady plasma actuation. Questa tesi offre un’analisi sperimentale sull’efficacia di attuatori al plasma orientabili, basati su una tecnologia DBD, installati su un profilo alare NACA 0015, a bassi numeri di Reynolds. Le prove sono state condotte in collaborazione con il Dipartimento di Ingegneria Elettrica dell’Università di Bologna, nella galleria del vento del Laboratorio di Aerodinamica Applicata della Facoltà di Ingegneria Aerospaziale di Forlì. Per verificare come un getto orientabile di plasma riesca a prevenire la separazione dello strato limite, sono state eseguite misure sul coefficiente di portanza. Sono state indagate sia la posizione degli attuatori lungo la corda che l’angolo con cui è orientato il getto di plasma, per vedere quali configurazioni conducono ai migliori risultati. Una particolare attenzione è stata riservata all’analisi dei risultati ottenuti con plasma continuo e pulsato.

Código híbrido avanzado de motores de plasma de efecto Hall

La propulsión eléctrica constituye hoy una tecnología muy competitiva y de gran proyección de futuro. Dentro de los diversos motores de plasma existentes, el motor de efecto Hall ha adquirido una gran madurez y constituye un medio de propulsión idóneo para un rango amplio de misiones. En la presente Tesis se estudian los motores Hall con geometría convencional y paredes dieléctricas. La compleja interacción entre los múltiples fenómenos físicos presentes hace que sea difícil la simulación del plasma en estos motores. Los modelos híbridos son los que representan un mejor compromiso entre precisión y tiempo de cálculo. Se basan en utilizar un modelo fluido para los electrones y algoritmos de dinámica de partículas PIC (Particle-In- Cell) para los iones y los neutros. Permiten hacer uso de la hipótesis de cuasineutralidad del plasma, a cambio de resolver separadamente las capas límite (o vainas) que se forman en torno a las paredes de la cámara. Partiendo de un código híbrido existente, llamado HPHall-2, el objetivo de la Tesis doctoral ha sido el desarrollo de un código híbrido avanzado que mejorara la simulación de la descarga de plasma en un motor de efecto Hall. Las actualizaciones y mejoras realizadas en las diferentes partes que componen el código comprenden tanto aspectos teóricos como numéricos. Fruto de la extensa revisión de la algoritmia del código HPHall-2 se han conseguido reducir los errores de precisión un orden de magnitud, y se ha incrementado notablemente su consistencia y robustez, permitiendo la simulación del motor en un amplio rango de condiciones. Algunos aspectos relevantes a destacar en el subcódigo de partículas son: la implementación de un nuevo algoritmo de pesado que permite determinar de forma más precisa el flujo de las magnitudes del plasma; la implementación de un nuevo algoritmo de control de población, que permite tener suficiente número de partículas cerca de las paredes de la cámara, donde los gradientes son mayores y las condiciones de cálculo son más críticas; las mejoras en los balances de masa y energía; y un mejor cálculo del campo eléctrico en una malla no uniforme. Merece especial atención el cumplimiento de la condición de Bohm en el borde de vaina, que en los códigos híbridos representa una condición de contorno necesaria para obtener una solución consistente con el modelo de interacción plasma-pared, y que en HPHall-2 aún no se había resuelto satisfactoriamente. En esta Tesis se ha implementado el criterio cinético de Bohm para una población de iones con diferentes cargas eléctricas y una gran dispersión de velocidades. En el código, el cumplimiento de la condición cinética de Bohm se consigue por medio de un algoritmo que introduce una fina capa de aceleración nocolisional adyacente a la vaina y mide adecuadamente el flujo de partículas en el espacio y en el tiempo. Las mejoras realizadas en el subcódigo de electrones incrementan la capacidad de simulación del código, especialmente en la región aguas abajo del motor, donde se simula la neutralización del chorro del plasma por medio de un modelo de cátodo volumétrico. Sin abordar el estudio detallado de la turbulencia del plasma, se implementan modelos sencillos de ajuste de la difusión anómala de Bohm, que permiten reproducir los valores experimentales del potencial y la temperatura del plasma, así como la corriente de descarga del motor. En cuanto a los aspectos teóricos, se hace especial énfasis en la interacción plasma-pared y en la dinámica de los electrones secundarios libres en el interior del plasma, cuestiones que representan hoy en día problemas abiertos en la simulación de los motores Hall. Los nuevos modelos desarrollados buscan una imagen más fiel a la realidad. Así, se implementa el modelo de vaina de termalización parcial, que considera una función de distribución no-Maxwelliana para los electrones primarios y contabiliza unas pérdidas energéticas más cercanas a la realidad. Respecto a los electrones secundarios, se realiza un estudio cinético simplificado para evaluar su grado de confinamiento en el plasma, y mediante un modelo fluido en el límite no-colisional, se determinan las densidades y energías de los electrones secundarios libres, así como su posible efecto en la ionización. El resultado obtenido muestra que los electrones secundarios se pierden en las paredes rápidamente, por lo que su efecto en el plasma es despreciable, no así en las vainas, donde determinan el salto de potencial. Por último, el trabajo teórico y de simulación numérica se complementa con el trabajo experimental realizado en el Pnnceton Plasma Physics Laboratory, en el que se analiza el interesante transitorio inicial que experimenta el motor en el proceso de arranque. Del estudio se extrae que la presencia de gases residuales adheridos a las paredes juegan un papel relevante, y se recomienda, en general, la purga completa del motor antes del modo normal de operación. El resultado final de la investigación muestra que el código híbrido desarrollado representa una buena herramienta de simulación de un motor Hall. Reproduce adecuadamente la física del motor, proporcionando resultados similares a los experimentales, y demuestra ser un buen laboratorio numérico para estudiar el plasma en el interior del motor. Abstract Electric propulsion is today a very competitive technology and has a great projection into the future. Among the various existing plasma thrusters, the Hall effect thruster has acquired a considerable maturity and constitutes an ideal means of propulsion for a wide range of missions. In the present Thesis only Hall thrusters with conventional geometry and dielectric walls are studied. The complex interaction between multiple physical phenomena makes difficult the plasma simulation in these engines. Hybrid models are those representing a better compromise between precision and computational cost. They use a fluid model for electrons and Particle-In-Cell (PIC) algorithms for ions and neutrals. The hypothesis of plasma quasineutrality is invoked, which requires to solve separately the sheaths formed around the chamber walls. On the basis of an existing hybrid code, called HPHall-2, the aim of this doctoral Thesis is to develop an advanced hybrid code that better simulates the plasma discharge in a Hall effect thruster. Updates and improvements of the code include both theoretical and numerical issues. The extensive revision of the algorithms has succeeded in reducing the accuracy errors in one order of magnitude, and the consistency and robustness of the code have been notably increased, allowing the simulation of the thruster in a wide range of conditions. The most relevant achievements related to the particle subcode are: the implementation of a new weighing algorithm that determines more accurately the plasma flux magnitudes; the implementation of a new algorithm to control the particle population, assuring enough number of particles near the chamber walls, where there are strong gradients and the conditions to perform good computations are more critical; improvements in the mass and energy balances; and a new algorithm to compute the electric field in a non-uniform mesh. It deserves special attention the fulfilment of the Bohm condition at the edge of the sheath, which represents a boundary condition necessary to match consistently the hybrid code solution with the plasma-wall interaction, and remained as a question unsatisfactory solved in the HPHall-2 code. In this Thesis, the kinetic Bohm criterion has been implemented for an ion particle population with different electric charges and a large dispersion in their velocities. In the code, the fulfilment of the kinetic Bohm condition is accomplished by an algorithm that introduces a thin non-collisional layer next to the sheaths, producing the ion acceleration, and measures properly the flux of particles in time and space. The improvements made in the electron subcode increase the code simulation capabilities, specially in the region downstream of the thruster, where the neutralization of the plasma jet is simulated using a volumetric cathode model. Without addressing the detailed study of the plasma turbulence, simple models for a parametric adjustment of the anomalous Bohm difussion are implemented in the code. They allow to reproduce the experimental values of the plasma potential and the electron temperature, as well as the discharge current of the thruster. Regarding the theoretical issues, special emphasis has been made in the plasma-wall interaction of the thruster and in the dynamics of free secondary electrons within the plasma, questions that still remain unsolved in the simulation of Hall thrusters. The new developed models look for results closer to reality, such as the partial thermalization sheath model, that assumes a non-Maxwellian distribution functions for primary electrons, and better computes the energy losses at the walls. The evaluation of secondary electrons confinement within the chamber is addressed by a simplified kinetic study; and using a collisionless fluid model, the densities and energies of free secondary electrons are computed, as well as their effect on the plasma ionization. Simulations show that secondary electrons are quickly lost at walls, with a negligible effect in the bulk of the plasma, but they determine the potential fall at sheaths. Finally, numerical simulation and theoretical work is complemented by the experimental work carried out at the Princeton Plasma Physics Laboratory, devoted to analyze the interesting transitional regime experienced by the thruster in the startup process. It is concluded that the gas impurities adhered to the thruster walls play a relevant role in the transitional regime and, as a general recomendation, a complete purge of the thruster before starting its normal mode of operation it is suggested. The final result of the research conducted in this Thesis shows that the developed code represents a good tool for the simulation of Hall thrusters. The code reproduces properly the physics of the thruster, with results similar to the experimental ones, and represents a good numerical laboratory to study the plasma inside the thruster.

Analysis of Magnetic Nozzles For Space Plasma Thrusters = Análisis de Toberas Magnéticas para Motores Espaciales de Plasma

Esta tesis presenta un análisis teórico del funcionamiento de toberas magnéticas para la propulsión espacial por plasmas. El estudio está basado en un modelo tridimensional y bi-fluido de la expansión supersónica de un plasma caliente en un campo magnético divergente. El modelo básico es ampliado progresivamente con la inclusión de términos convectivos dominantes de electrones, el campo magnético inducido por el plasma, poblaciones electrónicas múltiples a distintas temperaturas, y la capacidad de integrar el flujo en la región de expansión lejana. La respuesta hiperbólica del plasma es integrada con alta precisión y eficiencia haciendo uso del método de las líneas características. Se realiza una caracterización paramétrica de la expansión 2D del plasma en términos del grado de magnetización de iones, la geometría del campo magnético, y el perfil inicial del plasma. Se investigan los mecanismos de aceleración, mostrando que el campo ambipolar convierte la energía interna de electrones en energía dirigida de iones. Las corrientes diamagnéticas de Hall, que pueden hallarse distribuidas en el volumen del plasma o localizadas en una delgada capa de corriente en el borde del chorro, son esenciales para la operación de la tobera, ya que la fuerza magnética repulsiva sobre ellas es la encargada de confinar radialmente y acelerar axialmente el plasma. El empuje magnético es la reacción a esta fuerza sobre el motor. La respuesta del plasma muestra la separación gradual hacia adentro de los tubos de iones respecto de los magnéticos, lo cual produce la formación de corrientes eléctricas longitudinales y pone el plasma en rotación. La ganancia de empuje obtenida y las pérdidas radiales de la pluma de plasma se evalúan en función de los parámetros de diseño. Se analiza en detalle la separación magnética del plasma aguas abajo respecto a las líneas magnéticas (cerradas sobre sí mismas), necesaria para la aplicación de la tobera magnética a fines propulsivos. Se demuestra que tres teorías existentes sobre separación, que se fundamentan en la resistividad del plasma, la inercia de electrones, y el campo magnético que induce el plasma, son inadecuadas para la tobera magnética propulsiva, ya que producen separación hacia afuera en lugar de hacia adentro, aumentando la divergencia de la pluma. En su lugar, se muestra que la separación del plasma tiene lugar gracias a la inercia de iones y la desmagnetización gradual del plasma que tiene lugar aguas abajo, que permiten la separación ilimitada del flujo de iones respecto a las líneas de campo en condiciones muy generales. Se evalúa la cantidad de plasma que permanece unida al campo magnético y retorna hacia el motor a lo largo de las líneas cerradas de campo, mostrando que es marginal. Se muestra cómo el campo magnético inducido por el plasma incrementa la divergencia de la tobera magnética y por ende de la pluma de plasma en el caso propulsivo, contrariamente a las predicciones existentes. Se muestra también cómo el inducido favorece la desmagnetización del núcleo del chorro, acelerando la separación magnética. La hipótesis de ambipolaridad de corriente local, común a varios modelos de tobera magnética existentes, es discutida críticamente, mostrando que es inadecuada para el estudio de la separación de plasma. Una inconsistencia grave en la derivación matemática de uno de los modelos más aceptados es señalada y comentada. Incluyendo una especie adicional de electrones supratérmicos en el modelo, se estudia la formación y geometría de dobles capas eléctricas en el interior del plasma. Cuando dicha capa se forma, su curvatura aumenta cuanto más periféricamente se inyecten los electrones supratérmicos, cuanto menor sea el campo magnético, y cuanto más divergente sea la tobera magnética. El plasma con dos temperaturas electrónicas posee un mayor ratio de empuje magnético frente a total. A pesar de ello, no se encuentra ninguna ventaja propulsiva de las dobles capas, reforzando las críticas existentes frente a las propuestas de estas formaciones como un mecanismo de empuje. Por último, se presenta una formulación general de modelos autosemejantes de la expansión 2D de una pluma no magnetizada en el vacío. El error asociado a la hipótesis de autosemejanza es calculado, mostrando que es pequeño para plumas hipersónicas. Tres modelos de la literatura son particularizados a partir de la formulación general y comparados. Abstract This Thesis presents a theoretical analysis of the operation of magnetic nozzles for plasma space propulsion. The study is based on a two-dimensional, two-fluid model of the supersonic expansion of a hot plasma in a divergent magnetic field. The basic model is extended progressively to include the dominant electron convective terms, the plasma-induced magnetic field, multi-temperature electron populations, and the capability to integrate the plasma flow in the far expansion region. The hyperbolic plasma response is integrated accurately and efficiently with the method of the characteristic lines. The 2D plasma expansion is characterized parametrically in terms of the ion magnetization strength, the magnetic field geometry, and the initial plasma profile. Acceleration mechanisms are investigated, showing that the ambipolar electric field converts the internal electron energy into directed ion energy. The diamagnetic electron Hall current, which can be distributed in the plasma volume or localized in a thin current sheet at the jet edge, is shown to be central for the operation of the magnetic nozzle. The repelling magnetic force on this current is responsible for the radial confinement and axial acceleration of the plasma, and magnetic thrust is the reaction to this force on the magnetic coils of the thruster. The plasma response exhibits a gradual inward separation of the ion streamtubes from the magnetic streamtubes, which focuses the jet about the nozzle axis, gives rise to the formation of longitudinal currents and sets the plasma into rotation. The obtained thrust gain in the magnetic nozzle and radial plasma losses are evaluated as a function of the design parameters. The downstream plasma detachment from the closed magnetic field lines, required for the propulsive application of the magnetic nozzle, is investigated in detail. Three prevailing detachment theories for magnetic nozzles, relying on plasma resistivity, electron inertia, and the plasma-induced magnetic field, are shown to be inadequate for the propulsive magnetic nozzle, as these mechanisms detach the plume outward, increasing its divergence, rather than focusing it as desired. Instead, plasma detachment is shown to occur essentially due to ion inertia and the gradual demagnetization that takes place downstream, which enable the unbounded inward ion separation from the magnetic lines beyond the turning point of the outermost plasma streamline under rather general conditions. The plasma fraction that remains attached to the field and turns around along the magnetic field back to the thruster is evaluated and shown to be marginal. The plasmainduced magnetic field is shown to increase the divergence of the nozzle and the resulting plasma plume in the propulsive case, and to enhance the demagnetization of the central part of the plasma jet, contrary to existing predictions. The increased demagnetization favors the earlier ion inward separation from the magnetic field. The local current ambipolarity assumption, common to many existing magnetic nozzle models, is critically discussed, showing that it is unsuitable for the study of plasma detachment. A grave mathematical inconsistency in a well-accepted model, related to the acceptance of this assumption, is found out and commented on. The formation and 2D shape of electric double layers in the plasma expansion is studied with the inclusion of an additional suprathermal electron population in the model. When a double layer forms, its curvature is shown to increase the more peripherally suprathermal electrons are injected, the lower the magnetic field strength, and the more divergent the magnetic nozzle is. The twoelectron- temperature plasma is seen to have a greater magnetic-to-total thrust ratio. Notwithstanding, no propulsive advantage of the double layer is found, supporting and reinforcing previous critiques to their proposal as a thrust mechanism. Finally, a general framework of self-similar models of a 2D unmagnetized plasma plume expansion into vacuum is presented and discussed. The error associated with the self-similarity assumption is calculated and shown to be small for hypersonic plasma plumes. Three models of the literature are recovered as particularizations from the general framework and compared.