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Estimating orientation of optically trapped, near vertical, microsphere dimers using central moments and off-focus imaging

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Abstract

Near vertical optically trapped dimers, composed of pairs of microspheres, and constructed in situ, were imaged in bright-field in flow and at rest, and with displacement $\Delta z$ from the transverse $xy$ imaging plane of an inverted microscope. Image first central moments ${\mu _{01}}$ were measured, and their dependence on the imposed flow velocity of the surrounding fluid was calculated. This dependence was related to the at-rest restricted diffusion statistics. It was assumed that, for small perturbations, the torque $T$ on the dimer was proportional to the velocity of flow $v$ and resulting angular deflection $\Delta \theta$ so that $T \propto v \propto \Delta \theta$. Displacements $\Delta z$ at which $v \propto \Delta {\mu _{01}} \propto \Delta \theta$, which are typically off focus, were examined in more detail; in this range, $\Delta \theta = h\Delta {\mu _{01}}$. The hydrodynamics of the dimer were modeled as that of a prolate ellipsoid, and the constant of proportionality $h$ was determined by comparing the short-time mean-squared variation measured during diffusion to that predicted by the model calculation: ${h^2}\langle \Delta\mu_{01}^2(t)\rangle = \langle \Delta {\theta ^2}(t)\rangle$. With $h$ determined, the optical trap stiffness ${k_\theta}$ was determined from the long-time restricted diffusion of the dimer. The measured ${k_\theta}$ and $\Delta \theta$ can then be used compute torque: $T = {k_\theta}\Delta \theta$, potentially enabling the near vertical optically trapped dimer to be used as a torque probe.

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References

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Supplementary Material (7)

NameDescription
Data File 1       Optically trapped dimer image analysis.
Data File 2       Typical COMs and central moments of an optically trapped dimer and microsphere in oscillating translational flow.
Data File 3       Comparison of active and passive measurements for an optically trapped dimer.
Data File 4       Comparison of active and passive measurements for an optically trapped dimer to model calculations.
Data File 5       Computation of the translational and rotational MSD of an optically trapped dimer and microsphere.
Data File 6       Behavior of an optically trapped dimer near a surface.
Data File 7       Comparison of active measurement for optically trapped dimers composed of microsphere with different diameters.

Data availability

Data underlying the results presented in this paper are available in Data Files 1–7, Refs. [25,26,27,28,29,30,31].

25. A. Raudsepp, G. B. Jameson, and M. A. K. Williams, “Optically trapped dimer image analysis,” figshare (2021), https://doi.org/10.6084/m9.figshare.16850923.

26. A. Raudsepp, G. B. Jameson, and M. A. K. Williams, “Typical COMs and central moments of an optically trapped dimer and microsphere in oscillating translational flow,” figshare (2021), https://doi.org/10.6084/m9.figshare.16850929.

27. A. Raudsepp, G. B. Jameson, and M. A. K. Williams, “Comparing active and passive measurements for an optically trapped dimer,” figshare (2021), https://doi.org/10.6084/m9.figshare.16850932.

28. A. Raudsepp, G. B. Jameson, and M. A. K. Williams, “Comparing active and passive measurements for an optically trapped dimer to model calculations,” figshare (2021), https://doi.org/10.6084/m9.figshare.16850935.

29. A. Raudsepp, G. B. Jameson, and M. A. K. Williams, “Computing the translational and rotational MSD of an optically trapped dimer and microsphere,” figshare (2021), https://doi.org/10.6084/m9.figshare.16850944.

30. A. Raudsepp, G. B. Jameson, and M. A. K. Williams, “Behavior of an optically trapped dimer near a surface,” figshare (2021), https://doi.org/10.6084/m9.figshare.16850953.

31. A. Raudsepp, G. B. Jameson, and M. A. K. Williams, “Comparing active measurement for optically trapped dimers composed of microsphere with different diameters,” figshare (2021), https://doi.org/10.6084/m9.figshare.16850956.

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Figures (8)

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Equations (27)

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