Non-equilibrium Dynamics and Memory Effects in Viscoelastic Media

Abstract

When observing a glass of water, it may appear stationary, but at the microscopic scale, the molecules are in constant random motion known as Brownian motion. This stochastic motion is fundamental in giving liquids their unique properties, such as viscosity. Now imagine deforming such a fluid by dragging a particle through it. In simple fluids, deformation displaces the molecules, but they quickly resume their Brownian motion in new positions without retaining any memory of the past. However, this is not the case with all kinds of fluids that we encounter in everyday life, such as viscoelastic fluids, which exhibit solid-like properties that resist deformation and attempt to recover their original configuration. When a particle is dragged through such a medium, the fluid “remembers” the disturbance, giving rise to non-Markovian effects that play important roles in both technological and biological systems.

This thesis investigates such non-Markovian responses of a model viscoelastic fluid to external perturbation using optical tweezers microrheology. By manipulating the position of micron-sized particles suspended in the fluid, optical tweezers enable both the application and measurement of well-defined forces on the order of picoNewtons in the fluid. This method offers clear advantages over conventional techniques like rheometry, as the response measured is in the microscale and not in the bulk. The recoil experiment is one such method, where a particle dragged through the fluid briefly retraces its path upon release. The experiments revealed two relaxation timescales, in contrast to the single timescale predicted by bulk rheological experiments and the classical Maxwell model. A microscopic two-bath particle model successfully reproduces the observed behavior as well as the equilibrium behavior of freely diffusing particles. This experiment is extended to anisotropic tracer particles by using a rigid colloidal particle pair resembling a dumbbell, instead of the spherical colloid. A memory-induced alignment (MIA) of the colloidal dumbbell along the recoil direction is observed during recoil, which was hidden in previous experiments due to the particle isotropy. These orientational effects originate from nonlinear tracer-bath interactions, which require going beyond linear models such as the 2-BP model. Moreover, the MIA exhibits an enhancement in fluctuation, revealing a highly nonlinear regime even in the shear regime where the translational response is linear. Finally, this thesis ends with testing a generalized extension of the fluctuation-dissipation theorem (FDT) under non-equilibrium conditions. The experiments include applying oscillatory shear using an optically trapped colloidal particle in water and a viscoelastic fluid as the bath. By quantifying the first three force cumulants, with the third measuring deviations from FDT, we validate the extended relation in both Newtonian and viscoelastic fluids. While broadly applicable, FDT violations are more pronounced in viscoelastic media, exhibiting strong signal-to-noise signatures.

Overall, this thesis deepens our understanding of viscoelasticity and non-Markovian relaxation at the microscale, where molecular interactions and thermal fluctuations govern the dynamics in both natural and engineered systems. Using a custom-designed optical tweezer setup, adapted for specific functionalities, this work not only captures complex relaxation dynamics and non-Markovian effects but also highlights the role of anisotropy and nonlinear responses, which are often overlooked in bulk rheological techniques.