It has been observed that a nanoparticle can exhibit underdamped motion while moving toward the focal point of an optical trap. It is unclear whether this motion is caused by laser or fluid forces. Dielectrophoretic forces can trap nanoparticles as an alternate approach to optical trapping. The electrical trap uses no laser, so we can determine which force causes the underdamped motion. A microchannel with a quad-electrode arrangement on its ceiling and floor was designed to explore this question. Supplying an oscillating voltage to these electrodes generates an oscillating electric field resulting in the dielectrophoretic force that traps the particle. However, matching common characteristics, such as trap stiffness, is difficult between the two methods. This paper compares the two approaches for a 2 μm diameter particle. Instead of matching the trapping characteristics, the next step in this work is to use the dielectrophoretic device to explore the effect of the particle’s momentum on its motion, which can explain the underdamped motion. Combining optical and dielectrophoretic trapping will offer new insights into the dynamic behavior of small particles in a fluid medium.
The majority of microscale and nanoscale mechanical systems encountered in the world are stiff. One example of such a system is a microbead trapped in an optical tweezer. For this example, the ratio of a body’s mass to the viscous damping coefficient is negligible. Apart from being stiff, this system is also stochastic meaning that the differential equations representing the system include a random variable. This type of model can be solved with existing stochastic differential equation (SDE) solvers. Addressing the stochastic nature of the model usually requires averaging the results of multiple simulations. The computational time required to run the hundreds of simulations that may be necessary to obtain a useful average can be prohibitive. This paper presents a scaling approach that significantly reduces the computational time required to obtain these averages. However, this scaling changes the model and therefore the power spectral density (PSD) of the predicted motion. This work provides a general analysis of a mass-spring-damper model, such as an optical tweezer, that clearly shows the effect of scaling on the frequency content of the stochastic system. This analysis shows that the scaling technique can be used effectively without much loss of information. An experimental dataset of a 2 μm diameter microbead falling into an optical trap is compared with the simulation for validating the scaling method.
The stochastic differential equations (SDEs) representing a bead’s motion in an optical tweezer are stiff, meaning that the ratio of bead’s inertia to the viscous force from the surrounding fluid is extremely large. A scaling technique can be used to improve the computational time required to solve these SDEs numerically using adaptive SDE solvers. However, this scaling changes the SDEs as well as the power spectral density (PSD) of the bead’s position that the SDEs predict. This work shows that the scaling technique can be used effectively without too much loss of information but with significant reduction in computational time. The model uses Mie Scattering theory to compute the laser beam force, while Stokes’ law is used to calculate the drag force. Adaptive Stiff solvers, available in Julia programming language, are used to solve the SDEs. The PSD analysis is done in MATLAB. Experimental datasets for 2000nm, 1950nm, 990nm and 500nm diameter polystyrene beads are compared with the numerical results. We focus on the 2000nm bead because it is the only case where we can obtain PSD directly from the experimental data; in the other cases the PSD is indirectly obtained from experimental data. Interestingly, the 990nm and 500nm beads overshoot the focal point of the optical trap. This work presents the PSD analysis for these cases in addition to the reduction in computational time using the proposed scaling approach.
This paper investigates the underdamped motion of a bead as it moves toward the focal point of an optical trap. The model used herein represents a new approach toward addressing singular perturbation problems in dynamics. The experiments involve trapping microbeads at the focal point of an optical tweezer/trap. The optical trap can accurately measure the position of a microbead only in two directions. Given experimental data, the model can be used to estimate the bead’s position in the third direction. This estimate allows an examination of the full position, velocity and acceleration of the bead, which in turn allows and investigation of its particle Reynolds number (Rep). It is generally believed that a low Rep implies that a small bead will exhibit overdamped motion. The velocity estimates obtained herein for three bead diameters, 1950nm, 990nm and 500nm, provide new insights into the interpretation of a low Rep in light of the underdamped motion observed in experiments.
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