Analytical Model of Particle Motion in Optical Interference Landscapes and Laminar Flow

Abstract

Optically defined one- and two-dimensional potential energy "landscapes" can create characteristic forces and torques on nano- and micro-scale spheroidal particles that may be specifically tailored to meet the manipulation and measurement needs within colloidal hydrodynamic systems. Similar to optical tweezers, optical landscapes are able to selectively sort, trap, mix, align, and order mesoscale particles, yet they hold the potential to perform these tasks on a massively parallel scope.

While recent publications have provided both experimental and theoretical support of optical landscapes' capabilities, none to date have derived an order-of-magnitude approximation of the response of spheroidal particles within them. While almost all analytical models of particle motion reported so far are limited to spheres, many particles of interest are in fact shaped like disks and rods (e.g. blood cells, nanowires). This work advances toward the goal of describing complete spheroidal particle response to laminar flow and general optical landscapes of one- and two-dimensions.

Here we derive the optically induced force and torque from first principles, resulting in a model capable of predicting results in agreement with previous experiments and theory. A key prediction of our model is that highly selective trapping within the landscapes can be achieved based on shape, in addition to size as described in the literature. In general, we find that as particles become more oblate or prolate, they become easier to trap as compared to spherical particles with an equivalent volume. Additionally, we find that a trapped elliptical particle will align in its lowest energy orientation as dictated by the shape of the optical landscape. Finally, we provide a brief comparison of one- and two-dimensional landscapes and their effects on spheroidal particles.