Hydrodynamic forces in optical tweezers

Abstract

Optical tweezers uses light to control and trap microscopic entities including spherical particles, cells or even three dimensionally (3D) printed structures. In most cases the trapped microscopic object is surrounded by a fluid, such as water, and the effects of hydrodynamic forces are significant. This dissertation investigates three aspects of these hydrodynamic forces relevant to optical tweezers systems. The first aspect is about how hydrodynamic forces in optical tweezers could be used to measure the medium's viscosity and elasticity (viscoelasticity). Previous methods of measuring viscoelasticity using optical tweezers have been limited by their several-minute measurement duration, making them unreliable in biological systems that are slowly changing. To solve this problem new theory and analysis is introduced, experimentally verified by Shu Zhang et al. [1, 2] , that enables optical tweezers to perform highly localised measurements of viscoelasticity in sub-minute times. The second part of the project investigates the hydrodynamic interactions between trapped particles and nearby boundaries. Both numerical and analytical techniques, including novel solutions to the Stokes equations, are presented and used to model the fluid dynamics. The effects of spherical and cylindrical boundaries on an internal sphere are quantified theoretically and compared to experimentally measured (by Shu Zhang et al. [3, 4]) wall effects of a 3D printed cylinder based on 2 photon photopolymerisation and round artificial liposomes on the rotation of an optically trapped sphere. An artificial feed-forward neural network is also trained to efficiently reproduce some of these results. The third part of the project relates to hydrodynamic forces acting on non-spherical star-shaped particles. Calculating drag tensors describing this geometry using existing methods is relatively slow (∼ 10 0 s). Using these slower numerical methods, the drag tensors of many randomly generated particles are computed and then train an artificial feed-forward neural network to improve the speed (∼ 10 −4 s) at which these drag tensors could be evaluated, making them practical for simulations or real time calculations. By improving existing techniques and quantifying these kinds of hydrodynamic forces, this work allows optical tweezers to be better applied in microfluidic or biological systems, such as inside a cell, and allows more accurate or more efficient optical tweezers simulations.