Universality and scaling behavior of injected power in elastic turbulence in wormlike micellar gel

Complex dynamics of a sheared nematic fluid

Nonlinearities in constitutive equations of extended objects in shear flow lead to novel phenomena, e.g. 'rheochaos' in solutions of wormlike micelles and 'elastic turbulence' in polymer solutions. Since both phenomena involve anisotropic objects, their contributions to the deviatoric stress are likely to be similar. However, these two fields have evolved rather independently and an attempt at connecting these fields is still lacking. We show that a minimal model in which the anisotropic nature of the constituting objects is taken into account by a nematic alignment tensor field reproduces several statistical features found in rheochaos and elastic turbulence. We numerically analyse the full non-linear hydrodynamic equations of a sheared nematic fluid under shear stress and strain rate controlled situations, incorporating spatial heterogeneity only in the gradient direction. For a certain range of imposed stress and strain rates, this extended dynamical system shows signatures of spatiotemporal chaos and transient shear banding. In the chaotic regime the power spectra of the order parameter stress, velocity fluctuations and the total injected power show power law behavior and the total injected power shows a non-gaussian, skewed probability distribution. These dynamical features bear resemblance to elastic turbulence phenomena observed in polymer solutions. The scaling behavior is independent of the choice of shear rate/stress controlled method.

Flow fluctuations in wormlike micelle fluids

We investigate the unstable flow of wormlike micelle solutions in pressure driven capillary flow, with a focus on the effect of entrance geometry on the fluid fluctuations. The flow is measured at different points in the capillary using particle image velocimetry while simultaneously measuring the pressure drop across the entire capillary. The fluctuations are characterized by rapid flow rate jumps that correspond with a decrease in the pressure drop followed by a longer recovery period. Velocimetry measurements in the entrance region show a transition to unstable flow above a critical flow rate, where large flow circulations are observed in the tapered geometry and localized jets are observed in an abrupt contraction. The transition to this unstable flow is shown to occur at a similar dimensionless extension rate normalized by the micelle relaxation time. A rapid breakdown in micelle alignment is observed in polarized light microscopy at the onset of the flow rate jump, indicating the importance of rapid micelle structural changes on the fluctuations. We characterize the system by analyzing the power spectral densities and develop a dynamical systems model to describe the relationship between pressure and flow rate. These developments provide understanding to control flow fluctuations and motivation for more detailed study of the coupling of fluid microstructure transitions and flow fluctuations.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry

The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.

Melting of a nonequilibrium vortex crystal in a fluid film with polymers: Elastic versus fluid turbulence

We perform a direct numerical simulation of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer-conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers Re, the film attains a steady state that is a square lattice of vortices and antivortices. We find that, as we increase the Weissenberg number Wi, a sequence of nonequilibrium phase transitions transforms this lattice, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low Wi, and quasiperiodically, for slightly larger Wi. Finally, the system becomes disordered and displays spatiotemporal chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the Wi-Ω plane, where Ω∝Re, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter Λ provides us with a natural measure for characterizing the phases and transitions in this diagram.

Flows of living polymer fluids

We report on the recent progress made on flows of living polymer fluids. Such fluids have been model systems for rheological research for more than twenty years and they continue to be fascinating. Like most if not all soft matter systems, living polymers under flow show a strong feedback between the structure of the fluid and that of the flow, the first influencing the second and vice versa. In our opinion, such interplay between microscopic kinetics and macroscopic kinematics has historically been mostly understood from a "structural perspective", in the tradition of physical chemistry. Nevertheless, in recent years, a more "hydrodynamical perspective" has emerged by making fruitful analogies with elastic and inertio-elastic instabilities known in solutions of regular polymers. We also underline how this new perspective constrains theoretical modelling and calls for the use of new tools of investigation.

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I_{3}/I_{1} shows a power-law behavior with strain amplitude. In addition, I_{3}/I_{1} and the elastic component of stress amplitude σ_{0}{E} show a very prominent maximum at the strain value where the number density (n_{v}) of the Taylor vortices is maximum. A subsequent increase in applied strain (γ) results in the distortions of the vortices and a concomitant decrease in n_{v}, accompanied by a sharp drop in I_{3} and σ_{0}{E}. The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of γ corresponding to the peak of I_{3}, similar to that observed for hard-sphere glasses.

Instabilities in wormlike micelle systems. From shear-banding to elastic turbulence

Shear-banding is ubiquitous in complex fluids. It is related to the organization of the flow into macroscopic bands bearing different viscosities and local shear rates and stacked along the velocity gradient direction. This flow-induced transition towards a heterogeneous flow state has been reported in a variety of systems, including wormlike micellar solutions, telechelic polymers, emulsions, clay suspensions, colloidal gels, star polymers, granular materials, or foams. In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In wormlike micelle solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Different candidates have been identified, the main ones being wall slip, interfacial instability between bands or bulk instability of one of the bands. In this review, we present experimental evidence for a purely elastic instability of the high shear rate band as the main origin for fluctuating shear-banding flows.