10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
A Closed Form Expression for the Collision Kernel to Describe Attractive Coulombic Interactions and a Framework for Generalization to Arbitrary Attractive Potentials
Harjindar Singh Chahl, RANGANATHAN GOPALAKRISHNAN, The University of Memphis
Abstract Number: 845 Working Group: Aerosol Physics
Abstract Accurate collision rate kernel models for describing collision processes in aerosol and dusty plasmas are necessary for high-fidelity engineering of synthesis reactors and for analyzing experimental data from electrical mobility analysis and Languir Probes. While the effect of strong Coulombic interactions is described accurately at conditions of infinite collisionality (continuum limit) and zero collisionality (free-molecular limit), descriptive self-consistent models in the transitiion regime and more importantly in the near-free molecular regime remain elusive. The key challenge in modeling these regimes is modeling the loss of momentum and kinetic energy of charging ions due to collisions with neutral gas molecules in their approach towards an aerosol particle or a dust grain. In the absence of viable alternatives, the free-molecular expression for the collision kernel (also known as the Orbital-Motion Limited theory) is used in instances wherein the pressure is low but not exactly zero. While the collision kernel is higher by several orders of magnitude due to increased frequency of ion-gas molecule scattering (also referred to as three body trapping or charge exchange collisions), this effect is not captured by the collision-less free-molecular expression, leading to erroneous interpretation of aerosol and dusty plasma charge distributions as well as Langmuir Probe currents. It is known that the collision kernel asymptotically approaches the free molecular limit, but an accurate expression that captures the physics is unavailable at the moment. Following prior work, we use ab initio Brownian Dynamics to infer the non-dimensional collision kernel H as a function of the electrostatic potential energy to thermal energy ratio ψE and the diffusive Knudsen number KnD. By analyzing the underlying distribution of H, we have discovered that a 3-parameter generalized extreme value distribution accurately describes the same. By analyzing the dependence of the distribution parameters on ψE and KnD, we have derived a closed form expression for the H that is valid for any ψE and KnD. This expression is tested against H calculations at values of ψE and KnD that were chosen outside the range considered here to prove its applicability at any KnD all the way up to the free molecular limit as KnD → ∞. Beyond the specific Coulombic potential considered here, a generalization to accommodate any potential is shown. This has important consequences as the abstract model of collision between two entities through a long range Coulombic interaction acting along with short range image and van der Waals, and very short range repulsion interactions (part of Lennard-Jones type potentials) model phenomena that span several fields such as aerosol science, plasma science and gas-phase physical chemistry. Lastly, a pathway to generalizing this approach to accommodate the effect of high concentration is outlined for future work in this direction to move beyond the dilute-limit approximations for systems that necessitate the same.