Fig. 1. A conceptual depiction of particle trapping in a dynamic potential well with the presence of fluid flow and laser-beam-induced thermal convection. The images above the flow channel represent the potential well and particle distributions with (left) and without (right) external flow.

Fig. 2. (a) The scheme of particle escape rates in a static symmetric potential well. (b) The distribution of 300-nm particles in a static symmetric potential well. Theoretical predictions are shown in solid curve and simulation results are shown in scattered points and histograms. Particle motion in a static potential well with different depths is also presented in Visualization 1. (c) Dependence of trapping time on the depth of potential well in the static symmetric potential well for different particle sizes and well widths. The y-axis intercepts represent the characteristic value τ0. (d) The potential wells calculated with focused Gaussian beam by simulation (purple dashed line) and theoretical (cerulean line) method. The intensity of Gaussian beam with waist radius of 1 μm is also presented in red line for comparison.

Fig. 3. (a) The calculated velocity field of a convective flow around the trapping point, with maximum vertical velocity of 12 μm/s, which can seriously disturb the trapping stability (COMSOL simulation with the power of the Gaussian beam of 55 mW). The scheme of (b) force and (c) potential wells in static and dynamic conditions. (d) The scheme of particle escape rates in a dynamic asymmetric potential well. (e) The biased distribution of 300-nm particles in a tilted dynamic potential well having a velocity of 200 μm/s. Theoretical predictions are shown in solid curve and simulation results are shown in scattered points or histograms. The red and blue dashed lines represent the bottom of origin static and tilting potential well. Particle motion in flow-skewed potential well with different flow velocities is presented in Visualization 2. (f) Dependence of the effective depth and trapping time on the relative velocity in the dynamic potential well. The dotted lines show the effective depth with respect to the left y-axis. The solid lines represent trapping time (MFTT) with respect to the right y-axis.

Fig. 4. The biasing of trapping force and the tilting of potential well along different directions for an ellipsoidal focus point on both axes: (a) the biasing of trapping force in transverse direction different flow velocity; (b) the biasing of trapping force in longitudinal direction different flow velocity; (c) the tilting of potential well in transverse direction; (d) the tilting of potential well in longitudinal direction. The dynamic motions of particles in ellipsoidal potential wells are also shown in Visualization 3.

Fig. 5. Experimental setup and a schematic of trapping time measurement. (a) Schematic of the experimental configuration. The source wavelength is 976 nm. (b) Particle trapping in the microfluidic channel. The red line indicates the static potential well, the blue line is the dynamic potential well, and the inset (right) shows the signal trace due to transmitted light signal detected by the QPD. (c) Photograph of the experimental system shown in (a). (d) Trapped data measured on the rear focal plane interferometer; the red part is the stable trapped part obtained by screening with 500-nm particles at 57 μm/s flow rate and 35 mW optical power. (e), (f) Locally enlarged figures of (d). The complete experimental signals and videos with and without directional flow are shown in Visualization 4 and Visualization 5.

Fig. 6. Comparison between experimental results and calculated data. (a) Theoretical and experimental distributions of trapping time in a Gaussian potential well with different relative velocities at 57 (red), 113 (blue), and 227 (green) μm/s; the particle diameter is 300 nm and the optical power is 15 mW. The distribution of trapping time in logarithmic scale by varying the (b) relative velocity, (c) beam power, and (d) particle diameter. In (c), the diameter of the particles is 300 nm and the relative velocity is 227 μm/s. In (c), the beam power is 15 mW and the relative velocity is 227 μm/s.