Direct experimental measurement of many-body hydrodynamic interactions with optical tweezers

Abstract

Many-body hydrodynamic interactions (HIs) play an important role in the dynamics of fluid suspensions. While many-body HIs have been studied extensively using particle simulations, there is a dearth of experimental frameworks with which to quantify fluid-mediated multi-body interactions. To address this, we design an experimental method that utilizes optical laser tweezers for quantifying fluid-mediated colloidal interactions with exquisite precision and control. By inducing translation-rotation hydrodynamic coupling between trapped fluorescently-labeled colloids, we obtain a direct reporter of few- to many-body HIs experimentally. We leverage the torque-free nature of laser tweezers to enable sensitive measurements of signals between trapped colloids. First, we measure the pair HI between a stationary tracer probe and a translating particle as a function of their separation distance. We discover that our technique can precisely quantify distant fluid disturbances that are generated by ~2 pN of hydrodynamic force at 12 particle radii of separation. To study the effect of many-body HIs, we measure the rotational mobility of a probe in a three-particle setup and in a model material, a two-dimensional hexagonally-close-packed lattice, that undergoes oscillatory strain. Respectively, we discover that the probe's rotation can reverse in certain three-body configurations, and we find that rotational mobility in the crystalline array is strongly attenuated by particle rigidity. Experimental measurements are corroborated by microhydrodynamic theory and Stokesian Dynamics simulations with excellent agreement, highlighting our ability to measure accurately many-body HIs. Lastly, we extend our theoretical framework to manipulate colloidal-scale fluid flows. With experimental validation, we compute the required trajectory of a moving particle to induce a desired angular velocity of a probe.