Thermophoretic Force

The Thermophoretic Force accounts for a force on a particle due to gradients in the temperature of the background fluid. The thermophoretic force is defined as:

•

k (SI unit: W/(m·K)) is the thermal conductivity of the fluid,

•

kp (SI unit: W/(m·K)) is the particle thermal conductivity,

•

μ (SI unit: Pa·s) is the fluid dynamic viscosity,

This expression for the thermophoretic force is valid for continuum flows, in which the particle Knudsen number is very small. The thermophoretic force makes particles move from hotter to cooler regions. This is why dust tends to settle in a corner of the kitchen, furthest away from the oven.

If the check box is selected in the physics interface section, other expressions for the thermophoretic force are available. The model is equivalent to the expression for continuum flow.

If the model is selected, the thermophoretic force is defined as:

•

kB = 1.380649 × 10-23 J/K is the Boltzmann constant, and

The model is appropriate for free molecular flows.

If the Talbot model is selected, the thermophoretic force is defined as:

If the Linearized BGK model is selected, the thermophoretic force is expressed using the analysis of the linearized Bhatnagar-Gross-Krook (BGK) and S model kinetic equations by Beresnev and Chernyak (Ref. 26). The thermophoretic force is defined in terms of the free-molecular limit,

where FW (SI unit: N) is the thermophoretic force as calculated in the Waldmann model, R is a dimensionless number defined as

where Pr (dimensionless) is the fluid Prandtl number,

and αE (dimensionless) is the energy accommodation coefficient, with αE = 1 and αE = 0 corresponding to diffuse and specular reflection of all gas molecules at the surface, respectively. The dimensionless coefficients φi are defined as

R	f11	f12	f21	f22
1000	-1.324 × 10-5	1.317 × 10-5	1.366 × 10-9	4.924 × 10-8
800	-2.067 × 10-5	2.055 × 10-5	2.677 × 10-9	9.601 × 10-8
600	-3.673 × 10-5	3.645 × 10-5	6.379 × 10-9	2.270 × 10-7
400	-8.256 × 10-5	8.159 × 10-5	2.175 × 10-8	7.619 × 10-7
200	-3.291 × 10-4	3.215 × 10-4	1.791 × 10-7	5.997 × 10-6
100	-1.307 × 10-3	1.248 × 10-3	1.502 × 10-6	4.643 × 10-5
80	-2.036 × 10-3	1.921 × 10-3	2.987 × 10-6	8.917 × 10-5
60	-3.598 × 10-3	3.331 × 10-3	7.225 × 10-6	2.055 × 10-4
40	-8.004 × 10-3	7.139 × 10-3	2.439 × 10-5	6.551 × 10-4
20	-3.115 × 10-2	2.505 × 10-2	1.066 × 10-4	4.417 × 10-3
10	–0.1109	7.525 × 10-2	-1.852 × 10-3	2.639 × 10-2
8	–0.1636	0.1039	-6.174 × 10-3	4.513 × 10-2
6	–0.2626	0.1524	-2.244 × 10-2	8.749 × 10-2
4	–0.4780	0.2443	–0.1013	0.2089
2	–1.058	0.4507	–0.7320	0.7674
1	–1.749	0.6623	–3.077	2.247
0.8	–1.952	0.7205	–4.501	3.051
0.6	–2.181	0.7851	–7.034	4.424
0.4	–2.439	0.8559	-1.237 × 101	7.214
0.2	–2.717	0.9310	-2.889 × 101	1.562 × 101
0.1	–2.857	0.9678	-6.220 × 101	3.238 × 101
0.08	–2.884	0.9748	-7.885 × 101	4.073 × 101
0.06	–2.910	0.9816	-1.066 × 102	5.463 × 101
0.04	–2.835	0.9881	-1.620 × 102	8.239 × 101

R	f31	f32	f41	f42
1000	1	–0.9947	–1.004	0.9991
800	1	–0.9934	–1.006	0.9989
600	1	–0.9912	–1.007	0.9985
400	1	–0.9868	–1.011	0.9978
200	1	–0.9739	–1.022	0.9955
100	1	–0.9489	–1.044	0.9909
80	1	–0.9367	–1.055	0.9885
60	1	–0.9169	–1.074	0.9846
40	1	–0.8794	–1.110	0.9765
20	1	–0.7812	–1.218	0.9512
10	1	–0.6360	–1.415	0.8994
8	1	–0.5819	–1.504	0.8737
6	1	–0.5101	–1.635	0.8319
4	1	–0.4098	–1.847	0.7535
2	1	–0.2570	–2.226	0.5676
1	1	–0.1421	–2.533	0.357
0.8	1	–0.1142	–2.609	0.2962
0.6	1	-8.453 × 10-2	–2.691	0.2265
0.4	1	-5.344 × 10-2	–2.781	0.1482
0.2	1	-2.237 × 10-2	–2.881	6.437 × 10-2
0.1	1	-8.413 × 10-3	–2.937	2.470 × 10-2
0.08	1	-5.993 × 10-3	–2.945	1.767 × 10-2
0.06	1	-3.793 × 10-3	–2.961	1.123 × 10-2
0.04	1	-1.900 × 10-3	–2.973	5.648 × 10-3