Flow Induced Instabilities, Shear-Thickening And Fluctuation Relations In Sheared Soft Matter
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In day to day life we encounter many different materials which are intermediate between crystalline solids and simple liquids that include paints , glues , suspensions, polymers, surfactants, food and cosmetic products and so on. ‘Soft condensed matter’ is an emerging field of science that aims to generalize the flow and various deformation mechanisms in this apparent diverse class of materials from a ‘mesoscopic’ point of view (important length scales for these systems is usually 10nm-1μm) where the actual atomic and molecular details governed by various quantum mechanical laws are not very important. These soft systems are held together by weaken tropic forces and therefore can be perturbed easily (the typical elastic modulus of these materials is many orders of magnitude lower compared to metallic solids). Moreover, very long relaxation times in these systems(∼10−3 to 1 s) have made them ideal candidates to study non-equilibrium physics. The present Thesis is an endeavor to understand linear and non-linear flow behavior and low Reynolds number instabilities in various soft matter systems like suspensions of flocculated carbon nanotubes and carbon black, surfactant gels, colloidal glasses, Langmuir monolayers etc probed mainly by bulk and interfacial rheology, in-situ light scattering, particle image velocimetry(PIV) techniques and Fourier transform rheology. We also use dynamic light scattering techniques for particle sizing and characterization of Brownian systems. Chapter 1 gives a general introduction to soft condensed matter, particularly, the important length and time scales, various interactions and the rich phase behavior emerged from the delicate balance between energy and entropy in these systems. In this context, We describe the detailed phase behavior of two such systems studied in this thesis. We next describe briefly a few important concepts which motivate the main problems studied in the present thesis like the shear-thickening in suspensions of Brownian and non-Brownian particles, non-equilibrium steady state fluctuation relations in driven systems, elasticity driven instabilities in complex fluids, jamming transitions and aging behavior. This is followed by a discussion of the experimental techniques like linear and nonlinear rheology, including the Fourier transform rheology. Chapter 2 discusses the experimental techniques used by us in detail. We first describe the different components and mode of operations of the MCR-300 stress-controlled rheometer (Paar Physica, Germany) and various experimental geometries. Next we discuss the set up for two dimensional rheological measurements. The homebuilt imaging set up for in-situ polarized light scattering and direct imaging studies is described along with the in-situ particle image velocimetry (PIV) to map out the exact spatially resolved velocity profiles in 2D systems. We give a brief account of the techniques of Fourier transform rheology. At the end of this chapter, we briefly describe the angle resolved dynamic light scattering (DLS) set up (Brookhaven Instruments, USA). In Chapter 3, we study colossal discontinuous shear-thickening transition in confined suspensions of fractal clusters formed by multi-wall carbon nanotubes (MWNT) by rheology and in-situ imaging experiments. Monotonic decrease in viscosity with increasing shear stress, known as shear thinning, is a known rheological response to shear flow in complex fluids in general and for flocculated suspensions in particular. In the present experiments we demonstrate a discontinuous shear thickening transition where the viscosity jumps sharply above a critical shear stress by four to six orders of magnitude in flocculated suspensions of MWNT even at very low weight fractions(∼0.5%). Rheo-optical observations reveal the shear-thickened state as a percolated structure of MWNT flocs spanning the system size. We present a dynamic phase diagram of the non-Brownian MWNT dispersions revealing a starting jammed state followed by shear-thinning and shear-thickened states. The present study further suggests that the shear-thickened state obtained as a function of shear stress is likely to be a generic feature of fractal clusters under flow, albeit under confinement. An understanding of the shear thickening phenomena in confined geometries is pertinent for flow controlled fabrication techniques in enhancing the mechanical strength and transport properties of thin films and wires of nanostructured composites as well as in lubrication issues. We try to understand the flow of jammed and shear-thickened states under constant applied strain rate by studying the building up and relaxation of individual stress fluctuation events similar to the flow in dense granular materials. We also characterize the metastable shear thickened states by superposing a small sinusoidal stress component on a steady applied stress as well as by studying the a thermal entropy consuming fluctuations which are also observed for other jammed systems under an applied steady shear stress as described in the next chapter. Chapter 4 reports the study of non-equilibrium fluctuations in concentrated gels and glassy systems(in jammed state), the nature of fluctuations and their systemsize dependence in the framework of fluctuation relation and Generalized Gumbel distribution. In the first part, we show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions (PDFs) of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress and in all cases show similar symmetry properties as predicted by Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear rate fluctuations increase with the decrease of the systemsize. In the second part of this chapter, we report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the Generalized Gumbel (GG) distribution like many other equilibrium and non-equilibrium systems with high degree of correlations but do not obey Gallavotti-Cohen Steady State Fluctuation Relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution. We also establish the universality of the observations reported in this chapter in the light of other jammed systems under shear. We examine in the first part of Chapter 5, the shear-thinning behavior of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve (stress vs shear rate) consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs showing coexistence of fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile which is linear at low shear rates becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behavior like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation. In the second part of this chapter, we study in detail the non-linear viscoelastic behavior of Langmuir monolayers. Under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes(γ), the storage modulus (G”) decreases monotonically whereas the loss modulus (G”) exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G” and G” are in the ratio 2:1. The peak in G” is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence of the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is very general and exhibits many of the features observed in 3D complex fluids. We report in the first part of Chapter 6 scattering dichroism experiments to quantify the spatio-temporal nematodynamics of shear-thinning worm like micellar gels of surfactant Cetyltrimethylammonium Tosylate (CTAT) in the presence of salt sodium chloride (NaCl) enroute to rheochaos. For shear rates past the plateau onset, we observe a presence of alternating bright and dark‘ intertwined’ birefringent structures along the vorticity direction. The orientational order corresponding to these structures are predominantly oriented at +45deg and−45deg to the flow (v) in the (v,∇v) plane. The orientational dynamics of the nematics especially at the interface between the structures, has a one-to-one correspondence with the temporal behavior of the stress. Experiments show that the spatial motion of the vorticity structures depend on the gap thickness of the Couette cell. We next discuss the random temporal flow behavior of this system at high values of applied shear rate/stress in the framework of elastic turbulence in the second part of this chapter. Here, we study the statistical properties of spatially averaged global injected power fluctuations for the worm-like micellar system described above. At sufficiently high Weissenberg numbers (Wi) the shear rate and hence the injected power p(t) at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian pdf scan be well described by an universal large deviation functional form given by the Generalized Gumbel (GG) distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in-situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence. In Chapter 7, we study the vorticity banding under large amplitude oscillatory shear (LAOS) in a dilute worm-like micellar gel formed by surfactant CTAT by Fourier transform rheology and in-situ polarized light scattering. Under LAOS we found the signature of a non-trivial order-disorder transition of Taylor vortices. In the non-linear regime, higher harmonicde composition of the resulting stress signal reveals that the third harmonic I3 shows a very prominent maximum at the strain value where the number density (nv) of the Taylor vortices is maximum for a wide range of angular frequencies both above and below the linear crossover point. Subsequent increase in applied strain results in distortions of the vortices and a concomitant decrease in nv when I3 also drops very sharply and acts like an order parameter for this order-disorder transition. We further quantify the transition by defining an independent order parameter like quantity from the spatial correlation function of the scattered intensity and equivalently its Fourier transform which essentially captures the non monotonous third harmonic behavior. Lissajous plots indicate an intra-cycle strain hardening for the values of γ corresponding to the peak of I3 similar to that observed for hard-sphere glasses. Our study is an important step forward to correlating the structures developed in the system under LAOS to the appearances of the higher harmonics in the non-linear regime. The Thesis concludes with a summary of the main results and a brief account on the scope of future work as described in Chapter 8.
- Physics (PHY) 
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