# Transport in weakly ionic liquids

## Images of particle motion in weakly ionic liquid

Material related to the investigaion of weakly ionic liquids is presented here. Measurements of ion currents and particle motion in isopar with some quantity of dissolved charge director are shown. This is part of an ongoing experimental and theoretical study of these systems. The goals are to better understand the charging of surfaces by such solutions, and the factors determining particle motion.

This movie is of +10v on ITO with 10 mil gap (3MB) in isopar with 500ppm NBP. It shows particle motion at 0.5sec into the run. Wavelengths of the instability are very short, so the amount of motion is small, but quite visible. Oscilloscope timebase is 200msec per division. Vertical scale is 50nA per division. The width of the field of view is approximately 400u.

# Boltzmann Equation

## Elliptic Representation of the Boltzmann equation

For use with the elliptic representation discussed in Phys. Rev. E. v. 59 no.4, the following utility functions have been implemented in C and are distributed in the files elliptic_utils.c and elliptic_utils.h:

• get_X_gamma(Xs) returns X/gamma
• get_Pterm(Xs) returns .5(1-X/gamma)
• get_Vterm(Xs)returns (3X/gamma-1)/(2X*X)
as functions of the quantity: Xs = X*X . These functions cache arrays of values the first time they are called, and then perform a cubic interpolation of those values on subsequent calls. These should be used instead of the formulas given in the article, as they are more accurate. Please report problems or comments to me at richley@mailaps.org

## Unbounded Anisotropy Formulation of the Elliptic Representation

Some computational advantages result from a change of variables. This little article describes how the new equations are derived, and here are some slides presented at the 2003 Gaseous Electronics Conference which show some nice results.

# Convective form of Gauss' Law

Many plasma simulations require the inclusion of Gauss' law, which causes no end of numerical trouble due to the infinite propagation speed of truncation error. It is possible to implement a time-dependent form, which allows for all the nice features of shock-capturing reactive flow techniques to be applied to the electric and magnetic fields, along with the other simulation quantities. A brief descrition can be found here. This idea was originally published in simpler form in Phys Rev E v66 026402.

# pbd

## C function for solving sets of ODEs

pbd is an ODE solution package, written in C, and based on the PBD method of van Bokhoven (IEEE Trans. on Circuits and Systems, v CAS-22, no 2, Feb. 1975, pp109-115). pbd provides a callable function, pbd(), which is intended to be called from user supplied code as part of a larger simulation or computation. It consists of fairly simple code, and is released under the GNU General Public License: pbd page.

# MD_FCT

## Multi-dimensional Flux Corrected Transport algorithm

This code is a very general implementation of the Multidimensional FCT algorithm described by Zalesak (JCP v31, pp335-362 (1979)).

# poscol

## An analysis of the DC positive column in neon

This code was used for the analysis of the DC positive column in neon using the elliptic representation as discussed in Phys. Rev. E, v66, n2, Aug. 2002.