Dust agglomeration

Abstract

Dust agglomeration plays an important role in astrophysics and atmospheric sciences as well as in industrial processes. This article reviews the current knowledge of the physical interactions that lead to particle sticking in gaseous environments as well as the morphologies of the resulting dust aggregates. With this basic knowledge of dust–dust interactions, the development of ensembles of interacting dust particles can be treated using Smoluchowski's equation. Considering analytical solutions and simplified physical conditions, the temporal evolution and the mass distribution functions of dust aggregates are discussed. Based on this, general dust aggregation phenomena can be modelled and introduced into more complex scenarios.

Acknowledgements

This article was initiated during a stay at Hokkaido University for which the support of Prof. Dr. Takashi Kozasa and the Japanese Society for the Promotion of Science (JSPS) is warmly acknowledged. I also thank Prof. Kozasa for his hospitality during my stay and some simulations of random ballistic deposition. I am indebted to Maya Krause who provided figures 2–4 and to Dr Lars Heim who provided the basis for figure 12.

Notes

†Examples for small solid grains (frequently termed monomers) are soot, aerosols and interstellar dust.

†In the following, the expression ‘dust particle’, ‘dust aggregate’ and ‘dust agglomerate’ will be used synonymously and it will not be distinguished between single solid grains and aggregates thereof.

‡For the validity of equation 4, it is required that the number densities are not too high so that only binary collisions are important. Equation 4 is also termed growth equation, coagulation equation or rate equation.

†In many practical cases, the radius of gyration (see equation 72) is used as the radius of the aggregate.

†M ₁ in equation 33 is unity due to the normalisation in equation 28.

†The difference between τ_c = 1/2 (equation 40) and τ_c = 1 (equation 35) depends on the use of the kernel i + j = 2i for i = j. The factor 2 directly enters into the denominator of the timescale (see equation 20).

†For spherical particles, s(i) and s(j) are the particle radii in equation (73).

†The error for the exponent is a formal result of an unconstrained three-parameter fit of the data points in figure 8 to a function given in equation 22. Constraining τ_c and c in equation 22 would result in a smaller error for the exponent.

†This is the same number of aggregates that was used for the generation of the experimental mass spectrum in figure 9.

†For further reading on equilibrium particle contacts, see 90.

†The pre-factor 1/4 results from the fact that the kinetic energy in a collision between two equal-mass grains with relative velocity v _s is E _kin = μ/2, where m ₀ · m ₀/(m ₀ + m ₀) = m ₀/2 denotes the reduced mass.

†In all the presented cases in Refs. 97, 107, 118, one of the particle samples consisted of spherical SiO₂ grains with 1–2 µm diameter.

‡Perfect plasticity is not exactly fulfilled in the experiments as can be seen by a non-negligible rebound energy of the aggregates after a non-sticking collision (see right-hand side of figure 14).

†The constant c in 120 has a typing error and must be replaced by

†Exceptions are nanometer-sized dust grains for which sticking at ∼ km s⁻¹ collision velocity might still be possible 2 and planetary ring particles whose individual orbits only marginally deviate from a perfect circle so that their relative velocities are very small 134.

‡Due to the differential rotation of the Galaxy, any extended part of it will have a non-zero angular momentum.

†If that assumption is true, comets are the largest dust aggregates known. That comets indeed contain vast amounts of dust particles can be seen by the huge cometary comae and dust tails that form when comets approach the sun. In addition to that, the recent Deep Impact mission impressively confirmed the dusty nature of comets when it launched a 362 kg projectile into the nucleus of comet 9P/Tempel 1 and released several thousand tonnes of dust 153.

‡The perhaps most accurate estimate of a cometary bulk density to date was obtained recently for Comet 9P/Tempel 1, as a result of the NASA Deep Impact mission, ρ_bulk = 400 ± 300 kg m⁻³ 154 which shows clear evidence of a very porous body.

†Chondrules are mm-sized melt droplets frequently found in primitive meteorites.