Optical tweezers-based velocimetry: a method to measure microscale unsteady flows

Abstract: In the study of micro-scale biological flows, velocimetry methods based on passive tracers, such as micro-PIV and micro-PTV, are well established to characterize steady flows. However, these methods become inappropriate for measuring unsteady flows of small amplitude, because, on these scales, the motion of passive tracers cannot be distinguished from Brownian motion. In this study, we use optical tweezers (OTs) in combination with Kalman filtering, to measure unsteady microscopic flows with high temporal accuracy. This method is referred to as optical tweezers-based velocimetry (OTV). The OTV method measures the nanometric displacements of a trapped bead, and predicts the instantaneous velocity of the flow by employing a Kalman filter. We discuss the accuracy of OTV in measuring unsteady flows with 1.5–70 μ m s^{- 1} amplitudes and 10–90 Hz frequencies. We quantify how the bead size and the laser power affect the velocimetry accuracy, and specify the optimal choices for the bead size and laser power to measure different unsteady flows. OTV accurately measures unsteady flows with amplitudes as small as 3–6 μ m s^{- 1}. We compare the accuracy of OTV and micro-PTV, and characterize the flow regime for which OTV outperforms micro-PTV. We also demonstrate the robustness of OTV by measuring the unsteady flow created by the cilia of green alga Chlamydomonas reinhardtii, and comparing with numerical predictions based on Stokes equations. An open-source implementation of the OTV software in Matlab is available through the 4TU.Centre for Research Data. Graphic abstract: [Figure not available: see fulltext.].