Hans Rohatschek

Semi-empirical model of photophoretic forces for the entire range of pressures

Abstract Photophoretic forces can be induced both by differences in the surface temperature T s and by differences in the thermal accommodation coefficient α. It is assumed that the particles are spheres, that either a difference ΔT s or Δα is present, and that the distribution of both quantities is rotationally symmetric ( T s about the direction of incident light, α about an axis fixed to the particle). Then, the photophoretic force F as a function of pressure p is described for both types by the expression F ( p ) = Φ ( p ) B 1 ( p ) which covers the entire range of p . A key to this is the introduction of the temperature T a in the gas next to the surface in place of the surface temperature T s . There, B 1 is the first-order coefficient of a Legendre expansion of T a . The derivation of the expression F = ΦB 1 and its pressure dependence are rigorous for the free molecule and continuum limits. For intermediate pressures, the function Φ ( p ) is constructed according to Hettners interpolation method which is found to be a good representation of available experimental data. Whereas Φ( p ) is common to both types of photophoretic forces, B 1 ( p ) is specific, leading to different force-pressure relationships for ΔT s - and Δα-forces. These results are discussed in the light of available experimental data.

Direction, magnitude and causes of photophoretic forces

Abstract The conventional theory which explains the photophoretic force as the result of a temperature difference on the surface of the body acted on is confronted with contradictory observations: in particular, motions of large powder particles against the direction of light and a magnitude of the force up to 10 4 times larger than calculated. In this paper, investigations aimed to solve these problems by relating photophoresis and physical properties of particles are presented. Particles of powders 10–100 μm in size are dropped into a horizontal beam of light, separated according to their deflection from the vertical by photophoretic forces, collected and examined by electron microscopy. Evidence is shown that with these particles the dominant type of photophoretic force is a force ( F α ) caused by differences of the thermal accommodation coefficient (α) over the particle surface. The well-known type of force ( F T ) induced by temperature differences nevertheless plays an essential, namely, directing role, as its torque can align a particle acted on by F α relative to the direction of light. In this way, motions of large, strongly absorbing particles towards the light source can be explained. A magnitude of F α up to 10 4 times larger than F T is deduced from differences of α of about 0.1. Surface details suitable to cause these differences of α (smooth and ragged parts of the surface, pockets formed by foliated structures, etc) are demonstrated by electron micrographs.

Levitation of stratospheric and mesospheric aerosols by gravito-photophoresis

Abstract It is shown theoretically that a certain type of photophoresis, called gravito-photophoresis can contribute to the levitation of sunlit, absorbing particles in the middle atmosphere. Reasons are discussed why gravito-photophoresis appears far more effective for levitation than conventional longitudinal photophoresis: This type of force (a) remains related to the vertical direction regardless of the elevation of the sun; (b) it can have a lifting component; and (c) the force as a function of pressure exhibits a very broad plateau extending over a pressure range of nearly three orders of magnitude. The effect requires a restoring torque related to the vertical direction, induced by different action points of gravity and drag force, and a body-fixed photophoretic force, induced by a difference Δα in accommodation coefficients α over the particle surface. Gravito-photophoretic levitation of a spherical model particle is investigated for the entire range of pressures. The model combines (1) the established mechanics of gravito-photophoresis, including perturbations of particle orientation by molecular collisions, with (2) the energy balance for a small light-absorbing particle irradiated by the sun, which exchanges heat with its surroundings by molecular transfer and thermal radiation, and (3) a recent formulation of the theory of Δα-forces by It is shown that at irradiances commensurate with the solar constant, levitation is restricted to a narrow particle radius range around 1 μm. For those particles however, levitation appears possible over a broad pressure range corresponding to stratospheric and mesospheric altitudes.

The photophoretic force on nonspherical particles

Abstract Previous calculations of the photophoretic force due to unequal heating of gas-suspended, illuminated particles have been restricted to spheres. An analytical formula for the photophoretic force acting on an arbitrary body in the free molecule regime is presented. Provided the source function is known, the force vector can be calculated by integration without solving the heat transfer equation. In general, the photophoretic force deviates from the direction of light. Three extreme, idealized cases are discussed: a particle with uniform source function, a perfectly opaque particle, and a perfectly transparent particle with an adsorbing core.

Photophoretic levitation of carbonaceous aerosols

Abstract Laboratory experiments have shown that photophoretic forces [2] could be able to levitate various aerosol particles irradiated by the sun in the stratosphere and even the mesosphere [5]. Optimum lifting effects are obtained for gravitophotophoresis [1] of carbonaceous, in particular, graphite powder particles. Up to now, however, it has remained unknown how far the domain of potential levitation would extend towards the earths surface. The present paper describes experiments on gravitophotophoresis at ground level atmospheric pressure with varied irradiance including the solar constant.

The role of gravitophotophoresis for stratospheric and mesospheric particulates

Gravitophotophoresis, a type of photophoresis related to the direction of gravity, is examined in view of its possible importance to some aerosols in stratosphere and mesosphere. particles of various materials from about 1 to 100 μm in size show levitation by photophoretic forces under laboratory simulation of irradiation by the sun at air densities of the middle atmosphere. Minimum air densities for levitation are about 2–3 g m−3 with mineral and metallic powders, about 0.08 g m−3 with carbonaceous powders. The fraction of rising particles can be about 0.01 to 1%. Velocities of ascent are in the range of 0.001 to 0.01 m s−1 at a pressure of several mbar. The magnitude and the mechanical character of the force of gravitophotophoresis can be explained if it is identified with a radiometer force caused by a difference of the accommodation coefficient on the surface. It is suggested that gravitophotophoresis can be important to the residence time and the maximum altitude of carbonaceous and mineral particles, such as volcanic ash or products of meteorite impact, and to the presence of microorgnisms in the middle atmosphere.

Representation and calculation of photophoretic forces and torques

Abstract For the free molecule regime analytical expressions for the photophoretic force and torque can be derived which do not explicitly involve the surface temperature but directly contain the heat sources. This makes it possible to easily calculate photophoretic forces and torques, even for non-spherical particles. For the expressions certain weight functions are required, which are either explicitly known or can be computed numerically. It is shown how the approach carries over to the continuum limit, where the medium surrounding the particle is assumed to satisfy the Stokes equations of fluid mechanics.

Photophoresis of nonspherical bodies in the free molecule regime

Abstract The photophoretic force and torque acting on a nonspherical (convex) body irradiated by light are calculated for the free molecule regime. The force is expressed in terms of vector asymmetries (total, figure, and source asymmetry), where the figure asymmetry is derived from the geometry and the source asymmetry from the source function. For the torque an analogous representation is found. Equations of photophoretic motion are given. A special example of a nonspherical opaque body of revolution is discussed. Results are applied to strongly absorbing, large particles. Conclusions concern the occurrence of a directional torque, the direction, and the magnitude of the force.

The resistance force on nonspherical bodies in the free molecule regime

Abstract Analytical formulas for the resistance force and torque acting on a convex body due to its translation and rotation through a gas in the free molecule regime are derived. Three tensors (translation, rotation, and coupling tensor) appear which are determined by the outer geometry and the momentum accommodation coefficient of the body. The tensors are expressed in terms of surface integrals. Analogy to the continuum regime is stressed. In particular, the existence of a distinguished “center of reaction” is shown.

Zur praktischen durchführung der wärmeleitfähigkeitsmessung mit der kugelsonde

Zusammenfassung Die Auswertung von Messungen der Warmeleitfahigkeit korniger Medien mittels einer kugelformigen Sonde wird auf die Bestimmung der Parameter linearer Funktionen zuruckgefuhrt. Diese graphisch oder numerisch auszufuhrende Methode hat gegenuber den bisherigen komplizierten Verfahren die Vorteile leichterer Handhabung und erhohter Genauigkeit, sie ermoglicht eine bessere Beurteilung von Meβfehlern und Abweichungen von theoretischen Annahmen und ihre Grundlagen sind leichter mitzuteilen. Eine realisierte Kugelsonde wird beschrieben und es werden Meβbeispiele diskutiert.