Multiscale Modeling and Simulation of a Microbead in an Optical Trapping Process

Abstract

The purpose of this work is to generate a theoretical model for the dynamics of a polystyrene microsphere under the influence of Gaussian beam optical tweezers (OTs) in the ray-optics regime. OTs use the radiation pressure from a focused laser beam to manipulate microscopic objects as small as atoms [1]. They have been used in the biological sciences to measure nanometer-range displacements, apply picoNewton-range forces, and determine the mechanical properties of DNA, cell membranes, whole cells, and microtubules. The proposed model takes into account the forces and moments imparted onto the microbead by the OTs beam, and uses a Newton-Euler Dynamics framework to generate the equations of motion. Although examination of dimensionless numbers and other indicators including, Reynolds number 10−9 ≤ Re ≤ 10−4, Knudsen number 0.0001875, and the disproportionality between the mass and the viscous drag co-efficients O(10−4), does not clearly indicate whether this is a multiscale problem or not; but, a numerical integration of the original model leads to a long simulation run-time, a few days. Moreover, investigation of the step size showed that the adaptive numerical integrator was proceeding with a picosecond step size in order to achieve the requested accuracy. This situation implies a multiscale feature involved in the dynamics of optical trapping process of the small bead. To address this issue, a multiscale model is developed that helps to significantly reduce the simulation run-time and reveals underdamped behavior of the bead. In order to verify the theoretical model, experiments were carried out on a microsphere bead with 1.6μm diameter. A comparison of experimental data and simulation data indicate that this approach closely models microparticle behavior to the accuracy of the experiment under Gaussian beam optical tweezers.