Studies of the dynamics of two viscously coupled particles in optical tweezers

Kumar, Randhir (2018) Studies of the dynamics of two viscously coupled particles in optical tweezers. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

Since, the invention of optical tweezers, it has been extensively used as a device for trapping and manipulation of micron-sized particles. Today, it is widely used to study the dynamic motion of dielectric particles or biological cells. In this report, we study the dynamics of two viscously coupled particles in an optical tweezer. In the first project, We modulated one of the trap externally and measured the response of the second trapped particle. The study of the response of the second particle shows a motional resonance. We demonstrated that the amplitude and phase characteristics of the motional resonance can be used as a sensitive tool for two-point active microrheology to measure the viscosity of a viscous fluid. Thus, we measure the viscosity of viscous liquids from both the amplitude and phase response of the resonance. We also, demonstrate that the zero-crossing of the phase response of the probe particle with respect to the external drive is superior compared to the amplitude response in measuring viscosity at large particle separations. In order to check the implications of our measurement method, we did some numerical simulations. It is found that measurement sensitivity is maximum for small stiffness ratio and low viscosity fluid. we also found that the value of the phase sensitivity is higher than the amplitude (tens of degrees, as compared to few nm), which makes the phase measurement less challenging for experiments. We then went out to compare our viscosity measurements with that using a commercial rheometer and obtain an agreement ≈1%. The method can be extended to viscoelastic material where the frequency dependence of the resonance may provide further accuracy for active microrheological measurements. In the second project, we study the dynamics of two viscously coupled particles in an optical tweezers by measuring the positions auto and cross correlation of Brownian fluctuations. The particles are trapped in very close proximity of each other and the resultant hydrodynamic interactions lead to a double exponential autocorrelation function for the Brownian motion of each particle which is in clear violation of Doob's theorem for Markovian processes where the autocorrelation should necessarily be exponential. We show that the fluctuations of the pair of particles in a viscous medium thus resemble that of a single particle in a linear viscoelastic medium where the correlation function is also a double exponential in time and the surrounding medium of a particle between the pair of particles can store energy and thus the probe particle access frequency dependent storage modulus. The emergence of memory in the viscous medium is thus a consequence of near-field hydrodynamic interactions and gradually dies out as the separation between the two particles is increased.

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