Electrodynamics

Thermophoretic Force

The presence of temperature gradient imposes thermophoretic force on the particle, which is given as

,      for     , .                 (34)

where  is the mean thermal speed of the gas and

,                                                       (35)

,                                                                           (36)

for monatomic gases. Here  and  are the momentum and thermal accommodation coefficients and   and  are the thermal conductivity of gas and the particle.

The accommodation coefficients vary between zero and infinity. For mono-atomic gases, . Typical values are listed in Table 3,

Table 3.  Variations of momentum and thermal accommodation factors.

For the continuum limit, the thermophoretic force is given as

,      (37)

where

,                                                           (38)

                    

A simpler expression for thermophoretic force given by

    for                                                  (39)

is more commonly used.

Photophoretic Force

The force generated by the electromagnetic radiation is referred to as the photophoretic force.  For large  (free molecular) flow regimes, the photophoretic force is given by

, ,                                              (40)

where  is the gas pressure,  is the radiation flux, and  is the gas constant.

Diffusiophoretic Force

Non-uniformity in the composition of a gas mixture results in a diffusion (diffusiophoretic) force acting on the suspended particle. This force is proportional to the negative of concentration gradient and has a similar form as the thermophoretic force described earlier.