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The present study is concerned with a theoretical analysis of the photophoresis of a microsized long cylinder in a perpendicular optical field. Different from previous studies of photophoresis, thermal stress slip usually neglected is taken into account in the analysis. The gaseous fluid relative to the microparticle in photophoretic motion falls into slip-flow regime. Asymmetric distribution of the absorbed heat energy within the particle becomes the driving force for photophoretic motion of the cylinder-shaped particle. By evaluating heat source function distributions at various conditions, the study focuses on the effects of particle size and optical properties on the energy distribution and the resultant influences on the photophoresis. The photophoretic mobility is developed by the slip flow model with consideration of thermal stress slip. The results reveal that the photophoretic mobility decreases with the increase of particle thermal conductivity (k*) and increases with Knudsen number (Kn). The thermal stress slip effect on photophoretic velocity is more noticeable at high Kn, but disappears at the continuum limit. A long cylinder-shaped particle has higher photophoretic velocity than a spherical particle at low k*, while the situation reverses at high k*. With thermal stress slip considered, the critical condition for crossing of the photophoretic velocity curves of cylindrical and spherical particles is mildly influenced by Kn.

The present article pertains to a theoretical analysis for thermophoresis of a micro-particle in rarefied gas environment. Different from the conventional analyses, thermal stress effect in velocity slip boundary condition is taken into account. This interfacial thermal characteristic is always ignored in previous theoretical studies. The present theory with consideration of the thermal stress slip provides an appropriate modification and thus agrees well with the measured data of thermophoretic mobility of various particles. Order-of-magnitude analysis also qualitatively demonstrates enhancement of the thermal stress slip with reducing particle size or increasing characteristic temperature gradient. Finally, a parametric analysis shows that the thermal stress slip effect becomes more pronounced at conditions of high particle thermal conductivity and high Knudsen number as well.

The objective of the present study is to investigate photophoretic motion of a spherical microparticle in slip-flow regime of gaseous medium. Energy from incident light absorbed by the particle is calculated by employing Mie scattering theory. Temperature and relative velocity distributions of the gaseous flow around the microparticle are developed using a slip-flow model with consideration of thermal stress slip effect. It is demonstrated that the present results agree well with previous measurements and theoretical predictions. Heat source function and asymmetry factor indicating, respectively, the level and the uneven characteristics of the energy distribution within the particle are evaluated. At low, intermediate, and high absorptivities, three different patterns of asymmetry factor versus size parameter are found and named negative photophoresis prevailing, normal switching of photophoresis, and positive photophoresis dominant. Influences of particle optical properties on the critical size for transition of negative–positive photophoresis are analyzed. The results demonstrate that increasing absorptivity or refractivity of the particle leads to a reduction in critical size for photophoresis transition. Both increase in Knudsen number and reduction in particle-to-gas thermal conductivity ratio enhance the photophoretic mobility.

The study deals with photophoresis of a spherical micro-particle suspended in absorbing gaseous media. Photophoretic motion of the particle stems from the asymmetric distribution of absorbed energy within the particle. By evaluating the so-called heat source function at various conditions, the study focuses on the effects of governing parameters on the energy distribution within the particle and their potential influences to the photophoresis. The results reveal that the increase in either particle size or absorptivity enhances the energy intensity on the illuminated (leading) side and tends to generate positive photophoresis. For a particle of low absorptivity, the energy distribution is dominated by particle refraction. Enhancing particle refractivity, the energy tends to be focused onto a certain spot area on the shaded (trailing) side and leads to a tendency of negative photophoresis. Increasing medium absorptivity significantly degrades the level of energy absorbed by the particle and in turn weakens the driving force of the particle photophoresis. Defence Science Journal, 2010, 60(3), pp.233-237 , DOI:http://dx.doi.org/10.14429/dsj.60.347

The present study is concerned with photophoresis of a microsized long cylinder-shaped particle suspended in an absorbing gas medium. To facilitate the analysis, an infinite cylinder subjected to an intensive light beam is considered as the physical model. The electromagnetic energy can be absorbed by the particle and turned into thermal energy heating surface unevenly, which results in a net momentum transfer between gas molecules and the particle to drive particle in photophoretic motion. Effects of the governing parameters on the absorbed energy distribution in the cylindrical particle are investigated. The results demonstrate that increasing either the radius or absorptivity of the cylinder enhances the energy absorbed on the illuminated side and tends to generate positive photophoresis; while an increase in the refractivity of the particle tends to enhance the internal electric field intensity and shift the absorption peak on the shaded side toward the particle center. Increase in medium absorptivity reduces the energy reaching at the particle, which significantly degrades the level of energy absorption and therefore weakens the photophoretic mobility of the particle. It is also found that, at the same conditions, the source function peaks in long cylinder-shaped particles are generally lower than those in spheres due to the weaker light refraction of the cylindrical shape.

Two-dimensional micro-scale Rayleigh–Benard flows are investigated numerically using direct simulation Monte Carlo method. An enclosure of length-to-height aspect ratio of AS = 4 is taken to explore the influence of initial setting of simulated molecules. The simulation domain is divided into 81 × 21 sampling cells and the range of Rayleigh number from 3000 to 10 000 corresponds to the convection state. Cases of 8, 10, 12, 14, 16 and 24 simulated particles in each collision cell are examined. It is shown that flow patterns with three-, four- or five-roll modes may appear depending on the number of simulated particles.

This study investigates numerically the convective instabilities of rarefied gas in two-dimensional enclosures by the direct-simulation Monte Carlo (DSMC) method. A simulation using an enclosure with length-to-height aspect ratio AS = 2.016 is conducted to validate the value of the critical Rayleigh number on the onset of convection. Enclosures of AS = 2 and 4 are chosen to explore the influences of the Knudsen number Kn and initial wall temperatures on the flow. The results indicate that the different initial conditions may cause multiple solutions for the convection rolls and the Boussinesq approximation is no longer valid for rarefied gases of high Kn.

A numerical calculation has been carried out to investigate the mixed convection heat transfer in inclined rectangular ducts with wall transpiration. The vorticity-velocity method is employed to solve the governing equations. The present paper particularly addresses the effects of the independent parameters, namely, mixed convection parameter Δ, modified Rayleigh number Ra*, wall Reynolds number Rew and aspect ratio γ. The predicted results show that either wall injection or wall suction has a considerable impact on the flow structure and heat transfer performance. Additionally, it was found that for injection case Rew0.

where the fourth-order dissipation term is added to prevent instability and it is recalculated in every stage while marching. This model equation is chosen to fit with the use of the effective third-order dissipative term that is implemented throughout smooth region. The multistage schemes designed are considered the artificial viscosity coefficient IJL of ^, -^, and ^. By using the van Leer optimization, the parameters of the optimal schemes for given central differencing, without use of residual smoothing, are shown in Table 1. In the table, v denotes the CourantFriedrichs-Lewy (CFL) number, otk is the Ath multistage coefficient, and |P|max is the equalized minimal maximum of the amplification factor of ^-stage scheme in the range [n/2, n]. The contours of the amplification factor of the optimal four-stage scheme for the central spatial differencing with IJL = -^, together with the locus of the Fourier transform z(p) of the spatial operator (dashed line) are shown in Fig. la. The contour levels for the magnitude of the amplification factor are |P| = 1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05, and 0.01. Note that the CFL number achieved in an £-stage scheme is considerably lower than the maximum stable CFL number for that £-stage scheme, which makes the optimal multistage

This Letter presents a study on photophoresis of a microparticle in gaseous media with focus on the effect of thermal stress slip, which is deemed as one of factors causing deviations of previous theoretical predictions from measurements. The present modified theory agrees well with the measurements and, combining with 1 order-of-magnitude analysis, demonstrates the significance of the thermal stress slip in photophoresis of a particle, especially, of small radius. With the physical mechanisms addressed, the parametric analysis reveals that this interfacial thermal effect becomes more pronounced with reducing thermal conductivity of the particle and increasing Knudsen number as well.

In the present study, combining the conventional photothermal analysis and the concept of interaction of solvent molecules in interfacial layer used for thermophoresis in liquid, a theory for photophoresis of a hydrophobic particle suspended in liquids is developed. To characterize hydrophobicity of the micro-particle, slip length in Navier's formula is used as an index. Analytical expressions are derived and a parametric analysis for photophoretic velocity is performed with emphasis on the influences of particle characteristics such as size, optical properties, hydrophobicity, and thermal conductivity. Heat source function and the corresponding asymmetry factor at various conditions are evaluated to interpret the mechanisms of negative and positive photophoresis and the conditions for transition between them. The present theory discloses that the particle surface hydrophobicity or fluid slippage at particle-liquid interface may lead to a remarkable enhancement in the particle photophoretic velocity in liquids. Higher particle thermal conductivity and larger size of liquid molecules both result in weaker photophoretic motion.