# Brownian dynamics simulations to explore experimental microsphere diffusion with optical tweezers

## TL;DR

This paper presents two-dimensional Brownian dynamics simulations of microsphere motion under optical tweezers, providing a new method to estimate diffusion coefficients with high accuracy in experimental conditions.

## Contribution

The study introduces an experimental-like simulation framework and an alternative approach to calculate diffusion coefficients for microspheres under optical trapping.

## Key findings

- Simulations closely match theoretical diffusion coefficients within 1%
- Proposed methodology offers a reliable way to determine diffusion in optical tweezer experiments
- Simulation results validate the theoretical models of microsphere diffusion

## Abstract

We develop two-dimensional Brownian dynamics simulations to examine the motion of disks under thermal fluctuations and Hookean forces. Our simulations are designed to be experimental-like, since the experimental conditions define the available time-scales which characterize the solution of Langevin equations. To define the fluid model and methodology, we explain the basics of the theory of Brownian motion applicable to quasi-twodimensional diffusion of optically-trapped microspheres. Using the data produced by the simulations, we propose an alternative methodology to calculate diffusion coefficients. We obtain that, using typical input parameters in video-microscopy experiments, the averaged values of the diffusion coefficient differ from the theoretical one less than a 1\%.