Driven Granular and Soft-matter : Fluctuation Relations, Flocking and Oscillatory Sedimentation

Abstract

Active matter refers to systems driven out of thermal equilibrium by the uptake and dissipation of energy directly at the level of the individual constituents, which then undergo systematic movement in a direction decided by their own internal state. This category of nonequilibrium systems was defined as the physical model of motile, metabolizing matter, but the definition has a wider application. In this thesis we work with monolayer of macro-scopic granular particles lying on a vibrated surface and show that it provides a faithful realisation of active matter. The vibration feeds energy into the tilting vertical motion of the particles, which transduces it into a horizontal movement via frictional contact with the base in a direction determined by its orientation in the plane. We show that the dynamics of the particles can be easily controlled by manipulating their geometrical shapes. In the second part of the thesis, not addressing active matter, we do experiments on a soft condensed mat-ter system of viscoelastic surfactant gel formed of an entangled network of wormlike micelles and shows shear-thinning and is therefore non-Newtonian. These systems have relaxation times of the order of seconds and we have studied their non-equilibrium response properties when driven out of equilibrium externally by the gravitational sedimentation of objects and rising air-bubbles.

Chapter 1 gives a general introduction to the term active matter and emphasize particularly on how these systems are internally driven and work far away from the equilibrium. We then explain in detail how a system of granular particles lying on a vibrating surface acts as active matter. We later give a brief introduction to the field of soft condensed matter

and discuss the viscoelastic properties of surfactant solutions and their phase behaviour. We end this chapter by giving a brief introduction to flocking and non-equilibrium fluctuation relations which act as prerequisite to the following chapters.

In Chapter 2 we discuss the experimental techniques used by us. We will first describe the shapes and dimensions of the granular particles used in the experiments. Next we introduce the shaker set-up and describe the experimental cell in which the particles are confined and variation in cell’s boundary. We show the dynamics of the particles in a quasi one-dimensional channel and then in two-dimensions. We give a brief account of image analysis and tracking algorithms employed and other data analyses techniques.

In Chapter 3, we study the non-equilibrium fluctuations of a self-propelled polar particle moving through a background of non-motile spherical beads in the context of the Gallavotti-Cohen Fluctuation Relation (GCFR), which generalizes the second law of thermodynamics by quantifying the relative probabilities of the instantaneous events of entropy consumption and production. We find a fluctuation relation for a non-thermodynamic quantity, the velocity component along the long axis of the particle. We calculate the Large Deviation Function (LDF) of the velocity fluctuations and find the first experimental evidence for its theoretically predicted slope singularity at zero. We also propose an independent way to estimate the mean phase-space contraction rate.

In Chapter 4 we expand the analysis done in Chapter 3 and study the two-dimensional velocity vector of the particle in the context of Isometric Fluctuation Relation (IFR) which measures the relative probability of current fluctuations in different directions in space of dimension >1. We first show that the dynamics of the particle is not isotropic and present a minimal model for its dynamics as a biased random walker, driven by a noise with anisotropic strength and construct an Anisotropic IFR (AIFR). We then show that the velocity statistics of the polar particle agree with the AIFR. We also confirm that the GCFR can be obtained as a special case of AIFR when the velocity vectors point in opposite directions. We calculate the LDF of particle’s velocity vector and find an extended kink in the velocity plane.

In Chapter 5 we study the flocking phenomenon of a collection of polar particles when moving through a background of non-motile beads. We show that in the presence of bead

medium, polar particles can flock at much lower concentrations, in contrast to the Vicsek model which predicts flocking at high concentrations. We show that the moving rods lead to a bead flow which in turn helps them to communicate their orientations and velocities at much greater distances. We provide a phase diagram in the parameter space of concentrations of beads and polar particles and show power-law spatial correlations as we approach the phase boundary. We also discuss the numerical simulations and theoretical model presented which support the experiments results.

In Chapter 6 we experimentally study the angle dependence of the trapping of collection of active granular rods in a chevron shaped geometry. We show the particles undergo a trapping-detrapping transition at θ = 1150. On the contrary, this angle value is θ = 700 for a single rod. We find a substantial decrease in rotational noise for a collection of particles inside a trap as compared to a single rod which explains the increased value of θ for the trapping-detrapping transition. We also show that polar active particles which tend to change their direction of motion do not show the trapping phenomenon.

In Chapter 7 we conduct experiments on falling balls and rising air bubbles through a non-Newtonian solution of surfactant CTAT in water, which forms a viscoelastic wormlike micellar gel. We show that the motion of the ball undergoes a transition from a steady state to oscillatory as the diameter of the ball is increased. The oscillations in velocity of the ball are non-sinusoidal, consisting of high-frequency bursts occurring periodically at intervals long compared to the period within the bursts. We present a theoretical model based on a slow relaxation mechanism owing to structural instabilities in the constituent micelles of the viscoelastic gel. For the case of air bubbles, we show that an air bubble rising in the viscoelastic gel shows a discontinuous jump in the velocity beyond a critical volume followed by a drastic change in its shape from a teardrop to almost spherical. We also observe shape oscillations for bigger bubbles with the tail swapping in and out periodically.