Nature of trapping forces in optically induced electrothermal vortex based tweezers

Avanish Mishra, Kshitiz Gupta, and Steven T. Wereley

Phys. Rev. Fluids 6, 023701 – Published 17 February 2021

Abstract

Rapid electrokinetic patterning (REP) is an emerging microfluidic tweezer which can dynamically trap and manipulate micro- and nanoparticles via modulation of electrothermal vortices with optical patterns. By analyzing the trajectory of trapped particles with subpixel resolution, we show that the transverse trapping force in REP originates due to axisymmetric Stokes drag experienced by the particles in toroidal electrothermal vortices. The trapping force scales linearly with radial distance from the trap center and trap stiffness is on the order of femtonewtons/μm in the transverse plane. This low trap stiffness is a direct feature of the fluidic nature of the REP trapping and would be useful for measuring femtonewton-scale forces.

Received 19 August 2020
Accepted 26 January 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.023701

Physics Subject Headings (PhySH)

Electrokinetic flows Fluid-particle interactions Microfluidics

Fluid Dynamics

Authors & Affiliations

Avanish Mishra^1,*, Kshitiz Gupta ^2,*, and Steven T. Wereley^2,†

¹Center for Engineering in Medicine, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts 02129, USA
²Department of Mechanical Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA

^*A.M. and K.G. contributed equally to this work.
^†Corresponding author. wereley@purdue.edu

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Issue

Vol. 6, Iss. 2 — February 2021

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Images

Figure 1
Rapid electrokinetic patterning (REP). (a) Schematic diagram of the REP setup. (b) Forces acting on a particle in a REP trap. (c) A 2-μm trapped particle; plus mark identifies the particle center. (d) The intensity distribution of the particle image was approximated by a Gaussian function to locate the particle center with subpixel accuracy.
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Figure 2
A schematic illustration of the REP chip.
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Figure 3
(a), (b) Fluctuations in $x$ and $y$ positions of a trapped 1-μm particle over 5000 frames. (c) Trajectory of a particle in a 3.9-mW REP trap. (d) The experimentally determined trajectory of a freely diffusing 1-μm sphere by subpixel tracking. (e) MSD of a particle trapped in a REP trap. MSD increases linearly at short time scales and plateaus to an equilibrium value which is defined by spring constants of the trap. (f) The mean square displacement (MSD) of the 1-μm sphere over time in the $x − y$ plane. The MSD is directly proportional to the time and slope is equal to $4 D$ , where $D$ is the diffusion coefficient.
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Figure 4
Histograms and potential energy distributions of a 1-μm polystyrene particle in a REP trap. (a), (b) Histograms of particle positions in the $x$ and $y$ directions. (c) Red circles show the potential energy calculated using Eq. (7) corresponding to the particle motion in the $x$ direction. The solid blue line represents potential energy distribution calculated using $k_{x} x^{2} / 2$ . Results show that the potential energy distribution is parabolic in nature. (d) Potential energy distribution corresponding to the particle motion in the $y$ direction. The solid blue line represents potential energy distribution calculated using $k_{y} y^{2} / 2$ .
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Figure 5
(a) Velocity profile of a 1-μm particle in a REP trap as a function of radial position. (b) The drag force on a particle. (c) Effect of particle diameter on MSD. With an increase in particle size, MSD plateaus to a lower value due to greater trap stiffness. (d) Drag force as a function of radial position. With an increase in size, restoring drag force on the particles increases due to the larger size and the higher radial velocity experienced. The dotted lines represent the linear fit to the drag force data.
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Figure 6
Effect of laser beam power on trap stiffness for a 1-μm particle. (a) MSD variation with time for laser powers of 2.2 and 3.9 mW. (b) Drag force as a function of radial position. With the increase in laser power, radial velocity increases resulting in the higher drag force on the particles. The dotted lines represent the linear fit to the drag force data.
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