An analytical approach to sorting in periodic potentials

TL;DR

This paper develops an analytical framework to predict how particles are deflected by periodic and random surface features, aiding in particle sorting technologies, and validates these predictions with numerical simulations.

Contribution

It introduces an analytical method for predicting particle trajectories in periodic potentials, advancing beyond previous numerical models.

Findings

Analytical formulas match numerical simulations for particle deflection angles.

Surface patterning can be used to control particle sorting.

Predictions apply to both periodic and random surface configurations.

Abstract

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.