A Generalized Approximation for the Thermophoretic Force on a Free-Molecular Particle

Figures & data

TABLE 1 Molecular model properties under standard conditions (P _ref = 101,325 Pa and T _ref = 273.15 K)

Gas	ζ int	Z int	Ω	α	Viscosity coefficient μ ref × 10^5 Nsm^−2	Molecular mass m× 10^27 kg	Diameter d× 10^10 m
He	0	—	0.66	1.26	1.865	6.65	2.30
N2	2	5	0.74	1.36	1.656	46.5	4.11
Ar	0	—	0.81	1.40	2.117	66.3	4.11
CO2	3.7	5	0.94	1.61	1.380	73.1	5.54
He/Ar	—	—	0.725	1.64	—	—	—
From Appendix A in Bird 1994.

FIG. 1 Schematic diagram of a particle (with size greatly exaggerated) suspended between parallel walls at unequal temperatures.

TABLE 2 Calculation parameters

Gas	Pressure (Torr)	Time step (ns)
100% He	5.56	3
75% He, 25% Ar	5.00	3
50% He, 50% Ar	4.00	3
25% He, 75% Ar	3.00	3
100% Ar	2.00	8
100% N2	1.87	8
100% N2	0.187	8
100% N2	0.0187	8
100% CO2	1.24	8

TABLE 3 Thermophoresis parameters for pure gases from CE analysis of equivalent IPL molecules

Gas	Ω	ξ1	ξ2	ξinfin;
Hard sphere	0.5	0.679 061	0.694 151	0.697 618
—	0.6	0.679 061	0.691 341	0.693 698
—	0.7	0.679 061	0.688 415	0.689 896
—	0.8	0.679 061	0.685 384	0.686 196
—	0.9	0.679 061	0.682 261	0.682 588
Maxwell	1.0	0.679 061	0.679 061	0.679 061
He	0.66	0.679 061	0.689 598	0.691 404
N2	0.74	0.679 061	0.687 214	0.688 404
Ar	0.81	0.679 061	0.685 075	0.685 832
CO2	0.94	0.679 061	0.680 990	0.681 168

FIG. 2 Profiles of (a) temperature and (b) thermophoresis parameter for monatomic gases: helium and argon.

FIG. 3 Profiles of (a) temperature and (b) thermophoresis parameter for polyatomic gases: nitrogen and carbon dioxide.

FIG. 4 DSMC results for helium–argon mixtures. Thermophoresis-parameter profiles for (a) 25% helium, 75% argon; (b) 50% helium, 50% argon; and (c) 75% helium, 25% argon. (d) Mole-fraction profiles for a nominally 50%–50% mixture.

FIG. 5 Thermophoresis-parameter profiles for nitrogen for varying degrees of rarefaction at two temperature gradients, (a) 20 K/mm and (b) 200 K/mm. Dotted line is IPL–CE value for nitrogen.

Bird , G. A. 1994 . Molecular Gas Dynamics and the Direct Simulation of Gas Flows , Oxford : Clarendon Press .

 Google Scholar