# Difference between revisions of "Capillary attraction: Like-charged particles at liquid interfaces"

Original entry: Nan Niu, APPHY 226, Spring 2009

by M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz, Mischa Megens, and Joanna Aizenberg

## Abstract

This is a short but interesting article. In this article, the authors examined the attraction at an oil-water interface between like charged particles. They also confirmed that the particles do have a measurable charge, even when immersed in oil. Through doing experiment, the authors's finding shows that interface distortion due to diploar electric field can induce long range capillary attractions, and such phenomenon is not a result of fundamental force balance. Moreover, the authors states that the range of the capillary distortion is short. In the absence of solubilized charges which results in larger screening length than particle separation, the force imbalance between the particle and the interface will persist far enough for significant interfacial distortion to exist at scales comparable to the interparticle separation. As a result, the authors believe that electric-field-induced capillary distortion is the most likely cause for the attractive interactions between like-charged interfacial particles.

## Experiment

Pushing a sphere into water creates a dimple (left) in the surface, caused by the force on the particle being balanced by the surface tension. But if the electrostatic force pushing the sphere into the liquid is balanced by the electrostatic pressure on the liquid interface, there is no force on the rim and the surface is flattened again (right), inhibiting capillary attraction. R1, R2 are the radii of curvature of the surface.

The authors assume that the sum total of the electrostatic pressure acting on the liquid interface is equivalent to an external force, F, pushing the particle into the water. The long-range interparticle interaction energy is obtained:

• $U(r) = (\frac{F^2}{2\pi\gamma})ln(\frac{r}{r_{0}})$

Capillary attraction between spheres is caused by the overlap of their dimples, and for large r, the attraction energy is:

• $U(r) = -(\frac{F^2}{\pi\gamma})(\frac{r_{c}}{r})^6$

Professor Aizenberg believes the first equation can only be practical when there is unbalance on the edges of the vessel, therefore they introduced the second equation.

All in all, the authors insisted that capillary distortion can occur only if there is an imbalance between the force pulling the particle into the water and the force pushing the interface outwards towards the oil. The authors believe that to resolve the imbalance, they should not focus on the charges on the water side. The critical resolution is the charges on the oil side. Last but not least, the origin of the capillary distortion remains electrostatic in nature.