AAAR 36th Annual Conference October 16 - October 20, 2017 Raleigh Convention Center Raleigh, North Carolina, USA
Abstract View
True vs. Average Electrical Mobility. Happel And Brenner’s Settling Velocity vs. Mason and McDaniel’s First Collision Integral
CARLOS LARRIBA-ANDALUZ, Tianyang Wu, IUPUI
Abstract Number: 381 Working Group: Aerosol Physics
Abstract Arguably, the most accepted simplifications when acquiring the average Collision Cross Section (CCS) for an ion are 1) the consideration that all directions are equally probable and 2) that non-inertial effects can be ignored. The first of such simplifications has had the most controversy in the last few years.
Two distinct approaches to calculating CCS are compared: A) the averaged first collision integral calculated by Mason and McDaniel (M&M) which assumes that all directions are equally probable, and B) the tensorial Drag Force calculation from Happel and Brenner which, for every orientation, provides a drift velocity that does not necessarily have to be in the direction of the field. The problem arises when comparing both approaches. The averaged CCS calculated from Happel and Brenner disagrees with that of the averaged first collision integral. The explanation of this difference was not well understood.
Preliminary Data shows that the CCS calculated using the Happel and Brenner (H&B) method is always equal or smaller than that calculated by the first collision integral. This is particularly obvious for planar and 1D structures (long cylindrical ions) where the difference can be more than triple. We show that this difference occurs due to a misinterpretation of the H&B method. Given an ion in an electric field, such as that in a drift tube, one is generally only interested in the time an ion takes to cover a desired length while assuming that the ion travels a straight path. This straight path consideration is however not true for all but spherical ions, i.e. the resultant velocity of drift is not in the direction of the field. In general, therefore, we have to talk about two displacements; the average displacement in the direction of the field and the true displacement of the ion which considers movements off axis. We show that the collision integral method(M&M) results in a CCS that provides an “average” Mobility for an average drift velocity assuming a straight path. It is the correct CCS to compare to experimental measurements. The H&B method on the contrary calculates the true displacement of the ion, including off axis, and therefore gives the true mobility of the ion. No instrument at the moment is capable of providing true mobility and therefore, its calculation should be used with care. However, this result is of extreme importance in developing new instruments. The mobility of ions with a preferential direction, such as those with a permanent dipole, can be easily calculated using the H&B method, whereas the first collision integral would lead to wrong conclusions. Moreover, this knowledge could lead to enhanced-separation instruments, due to the fact that the true displacement of each ion is unique.