# Photophoresis

Photophoresis denotes the phenomenon that small particles suspended in gas (aerosols) or liquids (hydrocolloids) start to migrate when illuminated by a sufficiently intense beam of light. The existence of this phenomenon is owed to a non-uniform distribution of temperature of an illuminated particle in a fluid medium.[1] Separately from photophoresis, in a fluid mixture of different kinds of particles, the migration of some kinds of particles may be due to differences in their absorptions of thermal radiation and other thermal effects collectively known as thermophoresis. In laser photophoresis, particles migrate once they have a refractive index different from their surrounding medium. The migration of particles is usually possible when the laser is slightly or not focused. A particle with a higher refractive index compared to its surrounding molecule moves away from the light source due to momentum transfer from absorbed and scattered light photons. This is referred to as a radiation pressure force. This force depends on light intensity and particle size but has nothing to do with the surrounding medium. Just like in Crookes radiometer, light can heat up one side and gas molecules bounce from that surface with greater velocity, hence push the particle to the other side. Under certain conditions, with particles of diameter comparable to the wavelength of light, the phenomenon of a negative indirect photophoresis occurs, due to the unequal heat generation on the laser irradiation between the back and front sides of particles, this produces a temperature gradient in the medium around the particle such that molecules at the far side of the particle from the light source may get to heat up more, causing the particle to move towards the light source.[2]

If the suspended particle is rotating, it will also experience the Yarkovsky effect.

Discovery of photophoresis is usually attributed to Felix Ehrenhaft in the 1920s, though earlier observations were made by others including Augustin-Jean Fresnel.

## Applications of photophoresis

The applications of photophoresis expand into the various divisions of science, thus physics, chemistry as well as in biology. Photophoresis is applied in particle trapping and levitation,[3] in the field flow fractionation of particles,[4] in the determination of thermal conductivity and temperature of microscopic grains[5] and also in the transport of soot particles in the atmosphere.[6] The use of light in the separation of particles aerosols based on their optical properties, makes possible the separation of organic and inorganic particles of the same aerodynamic size.[7]

Recently, photophoresis has been suggested as a chiral sorting mechanism for single walled carbon nanotubes.[8] The proposed method would utilise differences in the absorption spectra of semiconducting carbon nanotubes arising from optically excited transitions in electronic structure. If developed the technique would be orders of magnitudes faster than currently established ultracentrifugation techniques.

## Theory of photophoresis

Direct photophoresis is caused by the transfer of photon momentum to a particle by refraction and reflection.[9] Movement of particles in the forward direction occurs when the particle is transparent and has an index of refraction larger compared to its surrounding medium.[10] Indirect photophoresis occurs as a result of an increase in the kinetic energy of molecules when particles absorb incident light only on the irradiated side, thus creating a temperature gradient within the particle. In this situation the surrounding gas layer reaches temperature equilibrium with the surface of the particle. Molecules with higher kinetic energy in the region of higher gas temperature impinge on the particle with greater momenta than molecules in the cold region; this causes a migration of particles in a direction opposite to the surface temperature gradient. The component of the photophoretic force responsible for this phenomenon is called the radiometric force.[11] This comes as a result of uneven distribution of radiant energy (source function within a particle). Indirect photophoretic force depends on the physical properties of the particle and the surrounding medium.

For pressures ${\displaystyle p}$, where the free mean path of the gas is much larger than the characteristic size ${\displaystyle r_{0}}$ of the suspended particle (direct photophoresis), the longitudinal force is [12]

${\displaystyle \mathbf {F} _{\text{phot}}=-{\frac {\pi }{3}}\,\alpha \,\alpha _{\text{m}}{\frac {p}{\sqrt {{\overline {T_{\text{gas}}^{\text{out}}}}\,T_{\text{gas}}^{\text{in}}}}}\,r_{0}^{2}\,{\frac {I\,J_{1}}{{\frac {k}{r_{0}}}+4\sigma _{\text{SB}}\varepsilon \,T_{\text{black body}}^{3}}}\,\mathbf {e} _{z}}$

where the mean temperature of the scattered gas is (thermal accommodation coefficient ${\displaystyle \alpha }$, momentum accommodation coefficient ${\displaystyle \alpha _{\text{m}}}$)

${\displaystyle {\overline {T_{\text{gas}}^{\text{out}}}}=T_{\text{gas}}^{\text{in}}+\alpha \left(T_{\text{black body}}-T_{\text{gas}}^{\text{in}}\right)}$

and the black body temperature of the particle (net light flux ${\displaystyle I=\varepsilon \,I_{0}}$, Stefan Boltzmann constant ${\displaystyle \sigma _{\text{SB}}}$, temperature of the radiation field ${\displaystyle T_{\text{opt}}}$)

${\displaystyle T_{\text{black body}}={\sqrt[{4}]{{\frac {I_{0}}{4\sigma _{\text{SB}}}}+T_{\text{opt}}^{4}}}}$.

${\displaystyle k}$ is the thermal conductivity of the particle. The asymmetry factor for spheres ${\displaystyle J_{1}}$ is usually ${\displaystyle 1/2}$ (positive longitudinal photophoresis). For non-spherical particles, the average force exerted on the particle is given by the same equation where the radius ${\displaystyle r_{0}}$ is now the radius of the respective volume-equivalent sphere.[13]

## References

1. ^ Shahram Tehranian et al. 2001. Photophoresis of micrometer-sized particles in the free-molecular regime. International Journal of Heat and Mass Transfer, 44, 1649.
2. ^ Hitoshi WATARAI et al. 2004.Migration Analysis of Micro-Particles in Liquids Using Microscopically Designed External Fields. Analytical Sciences, Vol 20, p 423.re
3. ^ M. Rosenberg, D.A. Mendis, D.P. Sheehan.1999. Positively charged dust crystals induced by radiative heating, IEEE Trans. Plasma Sci.27, 239-242
4. ^ V.L. Kononenko, J.K. Shimkus, J.C. Giddings, M.N. Myers. (1997). Feasibility studies on photophoretic effect in field flow fractionation of particles, J. Liquid Chromatogr. Related Technol. 20, 2907-2929
5. ^ X.F. Zhang, E. Bar-Ziv. (1997). A novel approach to determine thermal conductivity of micrometre-sized fuel particles, Combust. Sci.Technol.130, 79-95.
6. ^ H. Rohatschek. (1997). Levitation of stratospheric and mesospheric aerosols by gravito-photophoresis, J. Aerosol Sci. 27,467-475.
7. ^ C. Helmbrecht, C. Kykal, C. Haisch. Photophoretic Particle Separation in Institute of Hydrochemistry, Annual report, 2006. p11
8. ^ D. Smith. (2014). Photophoretic separation of single-walled carbon nanotubes: a novel approach to selective chiral sorting, Phys. Chem. Chem. Phys., 2014,16, 5221-5228.
9. ^ Ashkin, A. 2000 IEEE Journal of Selected Topics in Quantum Electronics, 6,841-856.
10. ^ C. Helmbrecht, C. Kykal, C. Haisch. Photophoretic Particle Separation in Institute of Hydrochemistry, Annual report, 2006. p11.
11. ^ YU. I. Yalamov, V. B. Kutukov, and E. R. Shchukin, "Theory of the Photophoretic Motion of the Large-Size Volatile Aerosol Particle," Journal of Colloid and Interface Science, vol. 57, pp. 564-571, 1976
12. ^ Loesche, C. and Husmann, T. (2016). Photophoresis on particles hotter/colder than the ambient gas for the entire range of pressures, Journal of Aerosol Science, 102:55, 10.1016/j.jaerosci.2016.08.013
13. ^ Loesche, C., Wurm, G., Teiser, J., Friedrich, J. M., and Bischoff, A. (2013). Photophoretic Strength on Chondrules. 1. Modeling. Astrophysical Journal, 778(2):101, 10.1088/0004-637X/778/2/101