# Week 2 : Hydrodynamic Coupling of Two Brownian Spheres to a Planar Surface, E. R. Dufresne, T. M. Squires, M. P. Brenner and D. G. Grier, Phys. Rev. Lett,85, 3317 (2000).

INPROGRESS!!! INPROGRESS!!! INPROGRESS!!! INPROGRESS!!! INPROGRESS!!! INPROGRESS!!!

## Introduction

## Methodology

The authors used a single laser to position two colloidal spheres in a plane perpendicular to the optical axis simulatnesouly at a set horizontal distance with respect to one antoher. Two spheres with simultaneously trappes by oscialltion the x-y position of the beam using a mirror, and the particules were allowed to freely diffuse after setting the initial positions by diverting the beam. A salt solution was used to reduce the debye length to 7 nm, ensuring minimization of surface forces interfering with measurements. The authors did not report the mean fluctuation from the focal plane, but commented that it did not interefere with measurements. They made measurements for several disfferent distances from the surface between 1 micron and 30 microns (using 0.5 micron particles) and particle-particle distances of 2 and 10 microns. It would be interesting to see near field interactions on the order of nm. It is unclea rto the reader what the distance threshold is for their theory to hold (though we do know how the error scales).

The authors computed cooperative motion <math>{\vec{p}}</math>, and relative motion <math>{\vec{r}}</math>, for particle positions of <math>{\vec{r1}}</math> and <math>{\vec{r2}}</math>.

<math>{\vec{p} = \vec{r_1} + \vec{r_2}}</math>

<math>{\vec{r} = \vec{r_1} - \vec{r_2}}</math>

For different time steps, the authors computed the variance in the cooperative motion and fit the data to a linear

## Theory

## Results

## Commentary

It is unclear to the reader why the authors did not need to account for possible drift, or atleast confirm that there is no drift, as they did not appear to match the viscosity of the solution with the viscosity of the particle (so there should be a finite gravitational force). It may be negligible for thier particles, or for the timescales used, but this was not addressed.