# Difference between revisions of "Like-charged particles at a liquid liquid interface"

Original entry: Tom Kodger, APPHY 226, Spring 2009

## Reference

M.G. Nikolaides, A.R. Bausch, M.F. Hsu, A.D. Dinsmore, M.P. Brenner, C. Gay, D.A. Weitz and M. Megens, J. Aizenberg Nature Communications 424, August (2003);

## Keywords

Dipole, Electrostatics in oil, Interface distortion

## Abstract

This communication discusses a simple enigmatic attraction at an oil-water interface between like charged particles. The original paper (Nature 420, 299-310, 2002) claims that a distortion of the interface due to a diploar electric field induces a long range capillary attraction. Megens and Aizenberg claims= that this cannot be so due to a fundamental force balance. In this communcation, these authors claim that the range of the capillary distortion is only short ranged and insignifanct (10^-5 kT). The original authors then respond by acknowledging that their original response was not complete but defend their original approach of a capillary distortion. This is true when but only when the free charge density of the oil is accounted for, thus a large dipole imbalance can be created.

## Capillarity In Action

The original paper claims an attactive potential of,

U(r) = F2 / (2* π γ) * ln(r/r0)


Which due to the logarithmic behavior, a long range attraction is claimed. As a follow-up, Megens and Aizenberg claim that this equation is not applicable unless there is some unbalanced on the edges of the vessel. They conclude that the more applicable equation is the well known equation for calculating the attractive potential caused by the overlap of their dimples is,

U(r) = F2 / (π γ) * ln(rc/r)6


This is a much shorter range attraction and would not result in an attraction between micron sized particles (see Fig. 1)

The original authors reply by modifying their original explanation but not the governing equation. A capillary distortion can only form when a force imbalance occurs. In order to establish a stable attraction this imbalance must occur over a distance larger than the interparticle separation. These authors suggest that this distance imbalance could not be resolved by the water side, but by charges on the oil side. The screening length is much larger due to the density of free charges. The electrophoretic mobility of these particles was measured to be as high as 200e, which results in a screening length of 20μm, much farther than the interparticle distance, and thus stabilizing the particles at the interface.