Direct verification of the fluctuation-dissipation relation in viscously coupled oscillators

Role of interactions in nonequilibrium transformations

For arbitrary nonequilibrium transformations in complex systems, we show that the distance between the current state and a target state can be decomposed into two terms: one corresponding to an independent estimate of the distance, and another corresponding to interactions, quantified using the relative mutual information between the variables. This decomposition is a special case of a more general decomposition involving successive orders of correlation or interactions among the degrees of freedom of the system. To illustrate its practical significance, we study the thermal relaxation of two interacting, optically trapped colloidal particles, where increasing pairwise interaction strength is shown to prolong the longevity of the time-dependent nonequilibrium state. Additionally, we study a system with both pairwise and triplet interactions, where our approach identifies their distinct contributions to the transformation. In more general setups where it is possible to control the strength of different orders of interactions, our findings provide a way to disentangle their effects and identify interactions that facilitate the transformation.

Bayesian inference of the viscoelastic properties of a Jeffrey's fluid using optical tweezers

Bayesian inference is a conscientious statistical method which is successfully used in many branches of physics and engineering. Compared to conventional approaches, it makes highly efficient use of information hidden in a measured quantity by predicting the distribution of future data points based on posterior information. Here we apply this method to determine the stress-relaxation time and the solvent and polymer contributions to the frequency dependent viscosity of a viscoelastic Jeffrey's fluid by the analysis of the measured trajectory of an optically trapped Brownian particle. When comparing the results to those obtained from the auto-correlation function, mean-squared displacement or the power spectrum, we find Bayesian inference to be much more accurate and less affected by systematic errors.

Single-shot phase-sensitive wideband active microrheology of viscoelastic fluids using pulse-scanned optical tweezers

We present a fast phase sensitive active microrheology technique exploring the phase response of a microscopic probe particle trapped in a linear viscoelastic fluid using optical tweezers under an external perturbation. Thus, we experimentally determine the cumulative response of the probe to an entire repertoire of sinusoidal excitations simultaneously by applying a spatial square pulse as an excitation to the trapped probe. The square pulse naturally contains the fundamental sinusoidal frequency component and higher odd harmonics, so that we measure the phase response of the probe over a wide frequency band in a single shot, with the band being tunable over the spectrum by choosing suitable experimental parameters. We then determine the responses to individual harmonics using a lock-in algorithm, and compare the phase shifts to those obtained theoretically by solving the equation of motion of the probe particle confined in a harmonic potential in the fluid in the presence of a sinusoidal perturbation. We go on to relate the phase response of the probe to the complex shear modulus [Formula: see text], and proceed to verify our technique in a mixture of polyacrylamide and water, which we compare with known values in literature and obtain very good agreement. Our method increases the robustness of active microrheology in general and ensures that any drifts in time are almost entirely ruled out from the data, with the added advantage of high speed and ease of use.

A quantitative analysis of memory effects in the viscously coupled dynamics of optically trapped Brownian particles

We provide a quantitative description of the memory effects existing in the apparently random Markovian dynamics of a pair of optically trapped colloidal microparticles in water. The particles are trapped in very close proximity to each other such that the resultant hydrodynamic interactions lead to non-Markovian signatures manifested by the double exponential auto-correlation function for the Brownian motion of each particle. In connection with the memory effects, we quantify the storage of energy in terms of various system parameters and demonstrate that a pair of Markovian particles - confined in individual optical traps in a viscous fluid - can be described in the framework of a single Brownian particle in a viscoelastic medium. We define and quantify the equivalent storage and loss moduli of the two-particle system, and show experimentally that the memory effects are maximized at a certain trap stiffness ratio, and reduce with increasing particle separation. The technique can be generally used to determine the effective viscoelastic parameters of any such fluid-particle systems, and can thus help understand the interactions between active particles mediated by simple or complex fluids.

Dynamics of hydrodynamically coupled Brownian harmonic oscillators in a Maxwell fluid

It has been shown recently that the coupled dynamics of micro-particles in a viscous fluid has many interesting aspects including motional resonance which can be used to perform two-point micro-rheology. However, it is expected that this phenomenon in a viscoelastic fluid is much more interesting due to the presence of the additional frequency-dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive characteristics. Initially, the response functions have been calculated and then the fluctuation-dissipation theorem has been used to calculate the correlation functions between the coloured noises present on the concerned particles placed in a Maxwell fluid due to the thermal motions of the fluid molecules. These correlation functions appear to be in a linear relationship with the delta-correlated noises in a viscous fluid. Consequently, this reduces the statistical description of a simple viscoelastic fluid to the statistical representation for an extended dynamical system subjected to delta-correlated random forces. Thereupon, the auto and cross-correlation functions in the time domain and frequency domain and the mean-square displacement functions of the particles have been calculated which are perfectly consistent with their corresponding established forms in a viscous fluid and emerge with exceptional features.

Optical Tweezers Microrheology: From the Basics to Advanced Techniques and Applications

Over the past few decades, microrheology has emerged as a widely used technique to measure the mechanical properties of soft viscoelastic materials. Optical tweezers offer a powerful platform for performing microrheology measurements and can measure rheological properties at the level of single molecules out to near macroscopic scales. Unlike passive microrheology methods, which use diffusing microspheres to extract rheological properties, optical tweezers can probe the nonlinear viscoelastic response, and measure the space- and time-dependent rheological properties of heterogeneous, nonequilibrium materials. In this Viewpoint, I describe the basic principles underlying optical tweezers microrheology, the instrumentation and material requirements, and key applications to widely studied soft biological materials. I also describe several sophisticated approaches that include coupling optical tweezers to fluorescence microscopy and microfluidics. The described techniques can robustly characterize noncontinuum mechanics, nonlinear mechanical responses, strain-field heterogeneities, stress propagation, force relaxation dynamics, and time-dependent mechanics of active materials.

Two-point active microrheology in a viscous medium exploiting a motional resonance excited in dual-trap optical tweezers

Two-point microrheology measurements from widely separated colloidal particles approach the bulk viscosity of the host medium more reliably than corresponding single-point measurements. In addition, active microrheology offers the advantage of enhanced signal to noise over passive techniques. Recently, we reported the observation of a motional resonance induced in a probe particle in dual-trap optical tweezers when the control particle was driven externally [Paul et al., Phys. Rev. E 96, 050102(R) (2017)2470-004510.1103/PhysRevE.96.050102]. We now demonstrate that the amplitude and phase characteristics of the motional resonance can be used as a sensitive tool for active two-point 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, and 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. We compare our viscosity measurements with those 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.