In aerosol and dusty plasma systems, the behavior of suspended particles (grains) is often strongly influenced by collisions occurring between ions and particles, as well as between particles themselves. In determining the collision kernel or collision rate coefficient for such charged entities, complications arise in that the collision process can be completely described neither by continuum transport mechanics nor by free molecular (ballistic) mechanics; that is, collisions are transition regime processes. Further, both the thermal energy and the potential energy between colliding entities can strongly influence the collision rate and must be considered. Flux-matching theory, originally developed by Fuchs, is frequently applied for calculation of collision rate coefficients under these circumstances. However, recent work suggests that crucial assumptions in flux-matching theory are not appropriate to describe transition regime collisions in the presence of potential interactions. Here, we combine dimensional analysis and mean first passage time calculations to infer the collision kernel between dilute charged entities suspended in a light background gas at thermal equilibrium. The motion of colliding entities is described by a Langevin equation, and Coulombic interactions are considered. It is found that the dimensionless collision kernel for these conditions, H, is a function of the diffusive Knudsen number, Kn D (in contrast to the traditional Knudsen number), and the potential energy to thermal energy ratio, Ψ E. For small and large Kn D, it is found that the dimensionless collision kernels inferred from mean first passage time calculations collapse to the appropriate continuum and free molecular limiting forms, respectively. Further, for repulsive collisions (Ψ E negative) or attractive collisions with Ψ E<0.5, calculated results are in excellent agreement with flux-matching theory predictions, and the dimensionless collision kernel can be determined conveniently via use of the H(Kn D) relationship found for hard-sphere collisions with modified definitions of H and Kn D to account for potential energy. However, for Ψ E>0.5, it is found that flux-matching theory predictions substantially underestimate the collision kernel. We find that the collision process in this regime is governed by the minimum of Kn D and Kn Ψ (Kn Ψ=3Kn D/2Ψ E), and based on calculations, propose a function H(Kn D, Kn Ψ) for collision kernel evaluation. The situations for which Ψ E> 0.5 apply to singly charged nanoparticles and multiply charged submicrometer and supermicrometer particles, and are thus prevalent in both aerosol and dusty plasma environments.
|Original language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - Feb 27 2012|