On the photophoretic force exerted on mm- and sub-mm-sized particles

Zwei durch direkte Beleuchtung hervorgerufene Kräfte wirken auf von Gas umgebenen Teilchen: Strahlungsdruck und Photophorese, Letzteres herrührend von Wechselwirkungen zwischen Gas und Partikeloberfläche. Photophorese führt zu Impulsübertrag zwischen Gas und Teilchen, da im Allgemeinen Gasteilchen, die von der Teilchenoberfläche kurzzeitig adsorbiert wurden, diese mit einer Geschwindigkeit verlassen, die mit der Oberflächentemperatur oder der Akkommodation korreliert. Sie ist auch ein Kandidat um Teilchentransport in optisch dünnen Bereichen protoplanetarer Scheiben, besonders am inneren Rand oder der optischen Obefläche zu erklären. Um jenen Transport zu modellieren und die sich daraus ergebenen Effekte detailliert zu verstehen, ist es notwendig, die photophoretische Kraft für verschiedene Partikelklassen zu quantifizieren. In der vorliegenden Arbeit wird die Photophorese auf Kugeln und realistische, näherungsweise sphärischen Objekte untersucht, insbesondere in Druckbereichen, in denen die mittlere freie Weglänge der Gasteilchen größer als die charakteristische Länge des Partikels ist. Dabei werden zwei neue und ziemlich genaue Näherungen für longitudinale Photophorese auf Kugeln gezeigt. Eine der Näherungen ist temperaturunterschiedsbasierend, die andere hängt von den Eingangsparametern Bestrahlungsintensität, Radius und Wärmeleitfähigkeit ab, wobei auch thermische Abstrahlung nach dem Stefan-Boltzmann-Gesetz berücksichtigt wird, um Oberflächentemperaturen, die die des Gases übersteigen, ebenso einfließen zu lassen. Für die nicht-sphärischen Teilchen homogener Zusammensetzung, die untersucht wurden, fand sich eine nahezu perfekte Übereinstimmung des mittleren Kraftbetrags|gemittelt über einhundert gleichmäßig verteilte Eintrahlungsrichtungen mit derjenigen Kraft, die auf eine Kugel gleichen Volumens wirken würde, blieben alle weiteren Parameter gleich. Eine auf die photophoretische Kraft bezogene effektive Wärmeleitfähigkeit wurde ebenso eingeführt. Beide Größen, das Volumen, ausgedrückt durch einen Radius, und die effektive Wärmeleitfähigkeit ermöglichen die Berechnung des Mittelwertes der photophoretischen Kraft auf ein Teilchen mit sternförmigem Gebiet mithilfe derselben Näherungen, die für Kugeln Gültigkeit besitzen. Alle neuen Erkenntnisse werden auf die Ergebnisse von Fallturmexperimenten bezogen und mögliche Transport- und Größensortierungsszenarios werde kurz erklärt anhand des minimum mass solar nebula.Two major forces caused by directed illumination act on a particle suspended in a gas: radiation pressure and photophoresis, the latter arising from interaction of gas atoms/molecules with the particle surface. Photophoresis leads to momentum transfer as for the general case the gas atoms/molecules leave the surface at a speed, that correlates with the temperature and gas accommodation differences across this surface. It is also a candidate to transport particles in basically optically thin parts of protoplanetary disks, especially at the inner edge and at the optical surface. To model the transport and resulting effects in detail it is necessary to quantify the photophoretic strength for different particle classes as a fundamental input. In this work photophoresis exerted on perfectly spherical particles and those with star-convex domain is investigated, essentially in pressure domains where the mean free path of the gas atoms/molecules is larger than the characteristic length of the suspended particle. Two new high-quality approximations with unprecedented accuracy, valid for longitudinal photophoresis on spheres resulting from directed illumination are introduced, one temperature-difference-based, the other based on the parameters light flux, radius, and thermal conductivity, as well as thermal radiation along the Stefan-Boltzmann law to account for the case that the sphere's temperature considerably exceeds the gas temperature. For the homogeneous non-spherical particles investigated, an almost perfect equality of the mean absolute force | averaged over 100 equally distributed directions of illumination | with the force acting on a sphere with the same volume but all other parameters kept constant is found and discussed. An effective thermal conductivity in terms of the phothophoretic strength is also introduced. Both variables, the radius of a volume-equivalent sphere and the effective thermal conductivity, enable to describe the mean value of the total photophoretic force exerted on star-convex particles with the same approximations derived for spheres. The new findings are compared and applied to the results of drop tower experiments and possible transport and size-sorting scenarios are briefly discussed for the minimum mass solar nebula

Vapour condensation in boundary layer flows

This thesis has two purposes. Metaphorically we can say that it works in two different scales -which, makes sense, nevertheless-. First, it deals with homogeneous vapour condensation in boundary layer flows. Boundary layer flows, as it is very well known, has the property of ubiquity. Every flow in contact with solid surfaces or even flows in mutual contact become boundary layer flows at some scale. The vapour condensation, and many other phase transition phenomena, develops intensively in that boundary layers. However, the description and modeling of homogeneous condensation has been less treated in the literature if compared with the case of heterogeneous condensation (that is, the condensation in presence of particles). A model of homogeneous vapour condensation in a boundary layer flow has been developed for the special case of stagnation-point incompressible flow near a cold wall with self-similar solution and a monodisperse distribution of resulting droplets. Complete model has been solved numerically and in addition a very good approximation to the model has been obtained by applying perturbative methods. We have extended this model in several directions: other flows admitting self-similar solutions, polydisperse distribution of droplets, mixed homogeneous and heterogeneous condensation and homogeneous condensation in counter ow boundary layers in compressible ows. In the case of mixed condensation we have showed that it is possible to tackle homogeneous and heterogenous condensation independently, in an iterative scheme. Of course, all these new directions have been treated in a less detailed form and keep open to future work. Second, the thesis has intended to bring together closely related themes that has been, however, studied separately. Then, we have widened the initial scope to other aspects a, for instance, coagulation and agglomeration of nanometric particles, thermophoresis and ice formation. Specifically, agglomeration and thermophoresis become essential in the understanding of condensation processes in combustion chambers where a very rich chemical activity is taking place, and ice formation is important if we want to extend the condensation process to atmospheric environments. The essential theme of this thesis is important in many aspects: 1. It deals with phenomena present in a wide variety of natural and industrial situations whose understanding may result in improvements of known processes or in the better forecast of some desirable or not desirable behaviors. 2. We have been forced to gather a lot of normally disperse or not directly connected information and methods that have an e ect in the comprehension and description of those phenomena. The mathematical treatment of some aspects of the problem has been undertaken in parallel with numerical simulation of some others. Therefore, a lot of work is waiting for completion or full develop. This is mainly the case of the stochastic-thermophoretic simulation of the agglomeration process of nanometric particles, that is described in appendix A, or the proposed model for the description of wedge ows near the leading edge, that ends the chapter 2. We have adopted the terms 'boundary layer flow' and 'counter flow boundary layers' for denoting the boundary layers when ocurring close to solid walls and those ocurring at the interface of two flows away from any solid surfaces, respectively. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Este trabajo de tesis tiene dos propósitos. Metáfóricamente podemos decir que funciona en dos escalas diferentes -lo cual no deja de tener sentido-. En primer lugar, trata sobre la condensación de vapores en flujos de capa límite. Los flujos de capa límite, como es bien conocido, tienen el don de la ubicuidad. Cualquier flujo en contacto con superficies sólidas o, incluso en contacto mutuo, deviene un flujo de capa límite en alguna escala. La condensación de vapores, y muchos otros fenómenos de transición de fase, se desarrollan intensamente en esas capas límite. Sin embargo, la descripción y modelización de la condensación homogénea ha sido menos tratada en la literatura si la comparamos con la condensación heterogénea (aquella que ocurre sobre partículas presentes en el flujo). Hemos desarrollado un modelo para la condensación homogénea de vapor en un flujo de capa límite particular, el llamado flujo de remanso, cerca de una pared fría, para un fluido incompresible y asumiendo una distribución monodispersa de gotas resultantes. Este problema admite una solución de semejanza. El modelo completo ha sido resuelto numéricamente y además se ha obtenido una buena aproximación del mismo mediante la aplicación de métodos perturbativos. Ese modelo se ha extendido en varias direcciones: Otros tipos de flujo que admitan también soluciones auto-semejantes, la condensación mixta u homogénea y heterogénea simultáneas, y la condensación homogénea en el caso de capas límite en contra flujos con fluidos compresibles. En el caso de la condensación mixta hemos demostrado que es posible abordar las condensaciones homogénea y heterogénea independientemente, con un esquema iterativo. Por supuesto, todas estas nuevas direcciones han sido tratadas de forma menos detallada y está pendientes de trabajo futuro. En segundo lugar, el trabajo ha intentado acercarse a otros temas muy relacionados con él pero que han sido normalmente estudiados de forma separada. Así, hemos ampliado el objetivo inicial para abarcar otros aspectos como pueden ser la coagulación y la aglomeración de partículas nanométricas, la termoforesis o la formación de hielo. Específicamente, la aglomeración y la termoforesis son esenciales para entender los procesos de condensación en cámaras de combustión donde se está produciendo una muy rica actividad química. La formación de hielo es importante si queremos extender los procesos de condensación al ámbito atmosférico. El tema esencial de este trabajo de tesis es importante en varios aspectos: 1. Se ocupa de fenómenos presentes en una amplia variedad de situaciones tanto naturales como de los procesos industriales, cuya comprensión puede resultar en el perfeccionamiento de procesos conocidos o en un mejor pronóstico de algunas conductas tanto deseables como indeseables. 2. Nos hemos visto obligados a recopilar mucha información normalmente dispersa o no directamente conectada con el tema esencial, sobre métodos que tienen un gran efecto en la comprensión y descripción de los fenómenos más arriba señalados. El tratamiento matemático de algunos aspectos del problema ha sido llevado a cabo en paralelo con simulaciones numéricas de algunos otros. Por lo tanto, una gran cantidad de trabajo queda todavía por hacer o por completar. Este es principalmente el caso de la simulación estocástico-termoforética de la aglomeración de partículas nanométricas, que es descrita en el apéndice A, o el modelo propuesto para la descripción de flujos de cu'na muy cerca del vórtice, que cierra el capítulo 2. Hemos adoptado los términos 'boundary layer flow' y 'conter flow boundary layers' para referirnos a las capas límite que ocurren cerca de una pared sólida y las que ocurren en la interfaz de dos flujos, lejos de cualquier superficie sólida, respectivamente

NASA Tech Briefs, June 1990

Topics: New Product Ideas; NASA TU Services; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences

Symbolic computation of the phoretic acceleration of convex particles suspended in a non-uniform gas

A package has been developed for calculating analytic expressions for forces and torques onto an arbitrarily shaped convex tracer (aerosol) particle small compared to the mean free path of the surrounding nonequilibrium gas. The package Phoretic allows to compute analytical (and also numerical) expressions for forces and torques stemming from elastic and diffusive scattering processes parameterized by an accommodation coefficient. The method is based on calculating half-sphere integral tensors of arbitrary rank and on integrating forces and torques acting on surface elements. The surrounding gas is completely specified by an arbitrarily shaped velocity distribution function. Accordingly, Phoretic requires two inputs: A particle (surface) geometry and a velocity distribution function. For example, the particle may be a cylinder with flat end caps, and the distribution function the one of Maxwell (isotropic) or Grad (13th moment approximation). The package reproduces analytic results for spheres which were available in the literature, and the ones for other geometries (cylinders, cuboids, ellipsoids) which were, however, only partially available (some works considered only elastic collisions, others temperature, or pressure, or only velocity gradients, etc.). In addition, Phoretic takes into account angular velocities which have been usually neglected and become relevant for non-spherical particles. The package is geared towards the implementation of dynamical equations for aerosol particles suspended in dilute or semidilute gases and as such helps to obtain concentration profiles and mobilities of aerosol particles depending on their shape (distribution) and environmental conditions

Symbolic computation of the phoretic acceleration of convex particles suspended in a non-uniform gas

A package has been developed for calculating analytic expressions for forces and torques onto an arbitrarily shaped convex tracer (aerosol) particle small compared to the mean free path of the surrounding nonequilibrium gas. The package Phoretic allows to compute analytical (and also numerical) expressions for forces and torques stemming from elastic and diffusive scattering processes parameterized by an accommodation coefficient. The method is based on calculating half-sphere integral tensors of arbitrary rank and on integrating forces and torques acting on surface elements. The surrounding gas is completely specified by an arbitrarily shaped velocity distribution function. Accordingly, Phoretic requires two inputs: A particle (surface) geometry and a velocity distribution function. For example, the particle may be a cylinder with flat end caps, and the distribution function the one of Maxwell (isotropic) or Grad (13th moment approximation). The package reproduces analytic results for spheres which were available in the literature, and the ones for other geometries (cylinders, cuboids, ellipsoids) which were, however, only partially available (some works considered only elastic collisions, others temperature, or pressure, or only velocity gradients, etc.). In addition, Phoretic takes into account angular velocities which have been usually neglected and become relevant for non-spherical particles. The package is geared towards the implementation of dynamical equations for aerosol particles suspended in dilute or semidilute gases and as such helps to obtain concentration profiles and mobilities of aerosol particles depending on their shape (distribution) and environmental conditions

Clemson Newsletter, 1989-1991

Information for the faculty and staff of Clemson Universityhttps://tigerprints.clemson.edu/clemson_newsletter/1021/thumbnail.jp

Catalog for 1986-1987, University of Maine

The University of Maine catalog for the 1986-87 academic year includes calendars, general information, academic and financial information, the various colleges, University College (Bangor campus), Canadian Studies, Honors Program, and lists of administration, faculty, and staff members. An index appears on page 473