Optically-Trapped Particle Tracking Velocimetry

TL;DR

Ot-PTV introduces a two-phase trap-release velocimetry strategy that fixes tracer positions before allowing advection by the flow, enabling rapid, at-point sampling of slow microflows with explicit handling of Brownian noise. The method yields Gaussian velocity PDFs at fixed locations, with mean flow velocities fitting analytical profiles and diffusion-dominated variability quantified by $D$ and $ au$, supporting accurate near-wall flow measurements. Validation in a pressure-driven straight microchannel demonstrates agreement with Poiseuille-like flow, while application to optothermal microflows shows ot-PTV can overcome diffusion-limited sampling when tracers are scarce. The approach offers a practical, calibration-free alternative to traditional PIV/PTV methods for slow, localized microflows, with potential extensions via multi-trap configurations to accelerate full-field profiling.

Abstract

In this paper, we propose a microflow velocimetry based on particle tracking with the aid of the optical trapping of tracers, namely, optically-trapped particle tracking velocimetry (ot-PTV). The ot-PTV has two phases: a trap phase, in which individual tracers are trapped by an optical force and held at a measurement position; a release phase, in which the tracer is released and advected by the fluid flow, without interference from the optical force. The released tracer is subsequently trapped again by the optical force. By repeating the set of trap and release phases, we can accumulate the sequential images of the tracer that have the same initial position. The advantages of ot-PTV are that (i) the measurement positions can be chosen by experimenters and (ii) the effect of statistical noise inherent in the Brownian motion of small tracers can be evaluated quantitatively. These features are useful for the analysis of extremely slow microflows, such as near-wall creeping flows, and the flows under some external effects acting on tracers, such as thermally-induced microflows. The concept of ot-PTV is validated using a benchmark experiment, i.e., a pressure-driven flow in a straight microchannel with a square cross-section. An application to thermally-induced microflows is also demonstrated.

Figures (14)

• Figure 1: Schematic description of the present paper. (a) Concept of optically-trapped particle-tracking velocimetry (ot-PTV). In the trap phase, a tracer is captured at a measurement position using the optical force. In the release phase, the tracer follows the fluid flow in the absence of the optical force. These two phases are instantaneously switched and repeated. (b) Cross-sectional view of the microchannel. The laser focus, i.e., the trap position of a tracer in the $y$ direction plane, can be controlled by AOD.
• Figure 2: Schematic illustration of the experimental protocol. (a) AOD alternates between the trap and release phases. The time duration for the trap and release phases is $T_{\mathrm{trap}}=40$ ms and $T_{\mathrm{release}}=60$ ms, respectively. Trigger signals are sent to the camera to acquire images during the release phase. A time jitter between the start of the release phase and the first acquisition is $T_{\mathrm{jitter}}\approx 6$ ms. The released tracer is advected in the flow direction on average. Note that the tracer position curve is hand-drawn for schematic description. (b) Snapshots during a release phase ([i]--[iii]); A snapshot in the subsequent release phase [iv].
• Figure 3: (a) Probability density of tracer velocity $v_x$ at $y=5.5$ µ m and $z=5$ µ m for sample sizes $N=80$ (red-triangle), $640$ (green-square), and $5120$ (blue-circle), where the bold-solid curve (magenta) is the Gaussian fit to the case of $N=5120$. In the panel, "$V$" and "SD" indicate the mean and the standard deviation, respectively. (b) Coefficient of determination $R^2$ for $y=3.4$ µ m (red), $4.5$ µ m (green), $5.5$ µ m (blue), $6.6$ µ m (magenta), and $7.6$ µ m (cyan), with $z=1$, $2$, $3$, $5$, and $6$ µ m. The inset shows $1-R^2$ in a double-logarithmic scale.
• Figure 4: Probability density of tracer velocity $v_x$ at (a) $z=2$ µ m and (b) $5$ µ m for $y=7.6$ µ m (red-circle), $6.6$ µ m (green-square), $5.5$ µ m (blue-triangle), $4.5$ µ m (magenta-lower-triangle), and $3.4$ µ m (cyan-diamond). The curves show the corresponding Gaussian fits. The sample size is $N>6600$ for all cases. Results for other values of $z$ are presented in Supplemental Material \ref{['sec:SI-probability-density']}Supp-THT2024.
• Figure 5: Average tracer velocity $\bar{v}_x$ as a function of (a) $y$ and (b) $z$, where symbols show the experimental data, curves indicate the results of fitting using Eq. \ref{['eq:flow']}, and shaded regions indicate the 95% confidence interval. Note that experimental data (symbols) are shifted by (a) $\delta y=-1.01$ µ m in the $y$ direction and (b) $\delta z=0.61$ µ m in the $z$ direction to consider sub-micron scale errors due to the difficulty of microscopic observation. (a) $z=1$ µ m (red-circle), $2$ µ m (green-square), $3$ µ m (blue-triangle), $5$ µ m (magenta-lower-triangle), and $6$ µ m (cyan-diamond), and (b) $y=3.4$ µ m (red-circle), $4.4$ µ m (green-square), $5.5$ µ m (blue-triangle), $6.5$ µ m (magenta-lower-triangle), and $7.6$ µ m (cyan-diamond).