Thermophoresis in gases at small Knudsen numbers

ABSTRACT. An analytical study is presented for the thermophoresis of a sphere in a constant applied temperature gradient perpendicular to a plane surface. The Knudsen number is assumed to be small so that the uid ow is described by a continuum model with a thermal creep and a hydrodynamic slip at the particle surface. The asymptotic formulas for the temperature and velocity elds in the quasisteady situation are obtained by using a method of re ections. The plane surface may be a solid wall or a free surface. The boundary effect on the thermophoretic motion is found to be weaker than that on the motion driven by a gravitational force. Even so, the interaction between the plane and the particle can be very strong when the gap thickness approaches zero. For the motion of a particle normal to a solid plane, the effect of the plane surface is to reduce the thermophoretic velocity of the particle. For the case of particle migration toward a free surface owing to thermophoresis, the particle velocity can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity and the surface properties of the particle and its relative distance from the plane. Also, the deposition time for a particle translating perpendicularly through the thermophoretic boundary layer is integrated by considering its thermophoretic mobility. Generally speaking, a free surface exerts less in uence on particle movement than a solid surface does.

Section: Introductionmentioning

confidence: 90%

Thermophoretic Deposition of a Sphere Normal to a Plane Surface

Chen¹

1999

“…0, while the particle Knudsen number may lie anywhere in the range 0 < Kn R < 1. Important reviews of this case include those by Loyalka (1992), Bakanov (1991), Fuchs (1982), Talbot et al (1980), and Waldmann and Schmitt (1966). Of particular importance here is Waldmann's expression (Waldmann 1959;Waldmann and Schmitt 1966) for the thermophoretic force on a free-molecular particle (Kn R !…”

Section: Introductionmentioning

confidence: 99%

Thermophoresis in Rarefied Gas Flows

Gallis¹,

Rader²,

Torczynski³

2002

Numerical calculations are presented for the thermophoretic force acting on a free-molecular, motionless, spherical particle suspended in a rare ed gas ow between parallel plates of unequal temperature. The rare ed gas ow is calculated with the direct simulation Monte Carlo (DSMC) method, which provides a timeaveraged approximation to the local molecular velocity distribution at discrete locations between the plates. A force Green's function is used to calculate the thermophoretic force directly from the DSMC simulations for the molecular velocity distribution, with the underlying assumption that the particle does not in uence the molecular velocity distribution. Perfect accommodation of energy and momentum is assumed at all solid/gas boundaries. Earlier work for monatomic gases (helium and argon) is reviewed, and new calculations for a diatomic gas (nitrogen) are presented. Gas heat ux and particle thermophoretic forces for argon, helium, and nitrogen are given for a 0.01 m spacing between plates held at 263 and 283 K over a pressure range from 0.1 to 1000 mTorr (0.01333 -133.3 Pa). A simple, approximate expression is introduced that can be used to correlate the thermophoretic force calculations accurately over a wide range of pressures, corresponding to a wide range of Knudsen numbers (ratio of the gas mean free path to the interplate separation).

“…An extensive review and historical development of thermophoresis was provided by Bakanov (1991). A more recent theoretical study on thermophoresis was reported by Brock (1962), who derived the expression for the thermal force.…”

Section: Introductionmentioning

confidence: 99%

“…Montassier et al (1991) measured particle collection efficiency in laminar tube flows. Bakanov (1991) reviewed the earlier experimental data and theoretical development, and concluded that most available models are suitable only for small Knudsen numbers. Tsai and Lu (1995) used a plate-to-plate thermal precipitator to test the thermophoretic particle collection efficiency.…”

Section: Introductionmentioning

confidence: 99%

Particle Deposition with Thermophoresis in Laminar and Turbulent Duct Flows

Ahmadi

1998

136

ABSTRACT. A numerical simulation procedure for studying deposition of aerosol particles in duct flows including the effect of thermal force under laminar and turbulent flow conditions is developed. An improved model for thermophoretic force acting on small particles is presented. Perturbation based analytical expressions for velocity and temperature profiles are used in the analysis for the laminar duct flow. The Reynolds stress transport model (RSM) of the FLUENT code is used to evaluate the mean flow and temperature fields for the turbulent duct flow case. The instantaneous fluctuation velocity field is generated by the continuous filtered white noise model. Effects of Brownian diffusion, thermophoresis, lift force, and gravity are included in the computation. Ensembles of particle trajectories are generated and statistically analyzed. Particle dispersion from a point source in the presence of a temperature gradient field in laminar and turbulent duct flows is studied. For an initially uniform concentration, several simulations for transport of aerosol particles of various sizes in different temperature gradient fields are performed, and the corresponding collection efficiencies and deposition velocities are evaluated. The results are compared with the existing experimental data and discussed. AEROSOL