Wall slip, shear banding, and instability in the flow of a triblock copolymer micellar solution

Temperature-dependent yield stress and wall slip behaviour of thermoresponsive Pluronic F127 hydrogels

This study explores the temperature-dependent dynamic yield stress of a triblock thermoresponsive polymer, Pluronic F127, with chemical structure (PEO)100(PPO)65(PEO)100, during the sol-gel transition. The yield stress can be defined as static, dynamic, or elastic, depending on the experimental protocol. We examine the dynamic yield stress estimation for this study, which usually entails utilizing non-Newtonian models like the Herschel-Bulkley (HB) or Bingham models to extrapolate the flow curve (shear rate against shear stress). Initially, we determine the yield stress using the HB model. However, apparent wall slip makes it difficult to calculate yield stress using conventional methods, which could lead to underestimates. To validate the existence of apparent wall slip in our trials, we carry out meticulous experiments in a range of rheometric geometries. To determine the true yield stress corrected for slip, we first use the traditional Mooney method, which requires labor-intensive steps and large sample sizes over various gaps in the parallel plate (PP) design. To overcome these drawbacks, we use a different strategy. We modify the Windhab model equation by adding slip boundary conditions to the HB equation, which allowed us to calculate the slip yield stress in addition to the true yield stress. In contrast to other typical thermoresponsive polymers like poly(N-isopropyl acrylamide) (PNIPAM), our findings demonstrate that PF127's yield stress obeys the Boltzmann equation and increases with temperature.

Heterogeneity-induced retraction in viscoelastic fluids following cessation of flow

Complex fluids including colloidal suspensions, microgels, and entangled wormlike micelles (WLMs) can develop heterogeneous flow regions under imposed steady shear. In some of these systems, the evolution to this flow state from rest is accompanied by flow reversal - when a portion of the fluid moves opposite to the imposed flow direction. Flow reversal was proposed to occur in shear startup when (1) the fluid has significant elasticity, and (2) the flow becomes heterogeneous immediately following the stress overshoot [McCauley et al., J. Rheol., 2023, 67, 661-681]. To verify this hypothesis, a new method is developed for measuring flow heterogeneity. Upon cessation of the imposed flow, elasticity and flow heterogeneity cause retraction of the fluid, which is quantified with particle tracking velocimetry. Flow is stopped at key times during shear startup in two systems: a gel-like WLM that exhibits flow reversal before heterogeneous flow and a viscoelastic, fluid-like WLM that does not. The degree of flow heterogeneity is inferred from the shape and magnitude of velocity profiles measured during retraction. Flow heterogeneity develops earlier in gel-like WLMs - supporting the proposed flow reversal criteria. For comparison, heterogeneous Couette flows described with the upper-convected Maxwell or Germann-Cook-Beris models are analyzed. These theoretical flow problems confirm that stark differences in rheological properties across the flow geometry can cause significant fluid retraction and reproduce key features of the experimentally observed retraction. This new method can be used to extract quantitative information about spatially heterogeneous flows in viscoelastic complex fluids, whether or not flow reversal occurs.

Role of confinement in the shear banding and shear jamming in noncolloidal fiber suspensions

The jamming effect is critical in processing short fiber-reinforced thermoplastics (FRTs). Fiber jamming can induce discontinuous shear thickening (DST) in simple shear and result in fiber-matrix separation in more complex flows such as injection molding and compression molding of FRTs. The confinement effect commonly induces local jams and strongly enhances fiber jamming. However, the transient evolution of local fiber jams under confinement and its correlation with the tumbling of fibers are still elusive. In this study, we adopted rheo-PIV (particle image velocity) techniques to study this effect for glass fiber-reinforced thermoplastics (FRTs). The translational and tumbling motion of fiber were determined during rheological measurements, and the distribution of fiber orientation was determined by X-ray CT. Three shear banding regions appeared after the viscosity overshoot under high shear stress in suspensions with high fiber content, which was associated with the three regions of fiber orientation across the gap due to confinement. Shear banding was ascribed to the different tumbling speeds across the gap because of the different initial orientations and different wall confinements near and far from the wall. The local shear thickening and jamming behavior became most significant under intermediate confinement, and were affected by shear strain, shear stress, and fiber contents. 3D state diagrams were constructed to show the confinement effect on the evolution of shear banding and jamming.

Criteria Governing Rod Formation and Growth in Nonionic Polymer Micelles

Self-assembled wormlike micelles (WLMs) are widely studied in small-molecule surfactants due to their unique ability to break and recombine; however, less is known about the structure and dynamics of nonionic polymer WLMs. Here, solutions of seven triblock poloxamers, composed of poly(propylene oxide) (PPO) midblocks and poly(ethylene oxide) (PEO) end blocks, are comprehensively examined to determine the role of poloxamer composition, temperature, and inorganic salt type and concentration on rod formation and subsequent elongation into WLMs. Phase separation and sphere-to-rod transition temperatures were quantified via cloud point measurements and shear rheology, respectively, and corroborated with small-angle neutron scattering (SANS). The local microstructure of resulting rodlike micelles is remarkably similar across poloxamer type and sodium fluoride (NaF) or sodium chloride (NaCl) content. Salt addition reduces transition temperatures, with the most pronounced effects for poloxamers with high PEO molecular weights and PEO fractions. Between these two temperatures, several poloxamers elongate into WLMs, where shear rheology detects increases in viscosity up to 6 orders of magnitude. Despite similar local microstructures, poloxamer identity and salt content impact micelle growth substantially, where large poloxamers with lower PEO fractions exhibit the highest viscosities and longest relaxation times. While sodium fluoride has little impact on micelle growth, increasing NaCl concentration dramatically increases the WLM viscosity and relaxation time. This result is explained by different interactions of each salt with the micelle: whereas NaF interacts primarily with PEO chains, NaCl may also partition to the PPO/PEO interface in low levels, increasing micelle surface tension, scission energy, and contour length.

Interparticle attraction controls flow heterogeneity in calcite gels

We couple rheometry and ultrasonic velocimetry to study experimentally the flow behavior of gels of colloidal calcite particles dispersed in water, while tuning the strength of the interparticle attraction through physico-chemistry. We unveil, for the first time in a colloidal gel, a direct connection between attractive interactions and the occurrence of shear bands, as well as stress fluctuations.

Microstructural Origins of Nonlinear Response in Associating Polymers under Oscillatory Shear

The response of associating polymers with oscillatory shear is studied through large-scale simulations. A hybrid molecular dynamics (MD), Monte Carlo (MC) algorithm is employed. Polymer chains are modeled as a coarse-grained bead-spring system. Functionalized end groups, at both ends of the polymer chains, can form reversible bonds according to MC rules. Stress-strain curves show nonlinearities indicated by a non-ellipsoidal shape. We consider two types of nonlinearities. Type I occurs at a strain amplitude much larger than one, type II at a frequency at which the elastic storage modulus dominates the viscous loss modulus. In this last case, the network topology resembles that of the system at rest. The reversible bonds are broken and chains stretch when the system moves away from the zero-strain position. For type I, the chains relax and the number of reversible bonds peaks when the system is near an extreme of the motion. During the movement to the other extreme of the cycle, first a stress overshoot occurs, then a yield accompanied by shear-banding. Finally, the network restructures. Interestingly, the system periodically restores bonds between the same associating groups. Even though major restructuring occurs, the system remembers previous network topologies.

Microscopic origin of wall slip during flow of an entangled DNA solution in microfluidics: Flow induced chain stretching versus chain desorption

Despite the relevance and importance of slip, a fundamental understanding of the underlying molecular mechanisms of wall slip in polymer flow is still missing. In this work, we investigate the slip behavior of an entangled DNA solution at a molecular scale using a confocal microscope coupled to a microfluidic device. From microscopic measurement, we obtain both the velocity profile and conformation of polymeric chains by visualizing DNA molecules during flow on various surfaces (ranging from weak to strong interactions with DNA molecules). In channel flow at a low Weissenberg number (Wi = 0.14), we observe a parabolic flow for an APTES-treated glass (with strong interaction with DNA) in the absence of slip, while a significant amount of slip has been observed for a regular glass (with a weak interaction with DNA). At higher flow rates (Wi > 1.0), strong slip appears during flow on APTES-treated surfaces. In this case, only immobile DNA molecules are stretched on the surface and other bulk chains remain coiled. This observation suggests that the flow induced chain stretching at the interface is the main mechanism of slip during flow on strong surfaces. Conversely, for slip flow on surfaces with weak interactions (such as unmodified or acrylate-modified glasses), polymeric chains are desorbed from the surface and a thin layer of water is present near the surface, which induces an effective slip during flow. By imaging DNA conformations during both channel and shear flows on different surfaces, we elucidate that either chain desorption or flow-induced stretching of adsorbed chains occurs depending on the surface condition. In general, we expect that these new insights into the slip phenomenon will be useful for studying the biological flow involving single DNA molecule experiments in micro/nanofluidic devices.

Jetting of a shear banding fluid in rectangular ducts

Non-Newtonian fluids are susceptible to flow instabilities such as shear banding, in which the fluid may exhibit a markedly discontinuous viscosity at a critical stress. Here we report the characteristics and causes of a jetting flow instability of shear banding wormlike micelle solutions in microfluidic channels with rectangular cross sections over an intermediate volumetric flow regime. Particle-tracking methods are used to measure the three-dimensional flow field in channels of differing aspect ratios, sizes, and wall materials. When jetting occurs, it is self-contained within a portion of the channel where the flow velocity is greater than the surroundings. We observe that the instability forms in channels with aspect ratio greater than 5, and that the location of the high-velocity jet appears to be sensitive to stress localizations. Jetting is not observed in a lower concentration solution without shear banding. Simulations using the Johnson-Segalman viscoelastic model show a qualitatively similar behavior to the experimental observations and indicate that compressive normal stresses in the cross-stream directions support the development of the jetting flow. Our results show that nonuniform flow of shear thinning fluids can develop across the wide dimension in rectangular microfluidic channels, with implications for microfluidic rheometry.

Shear banding in entangled polymers in the micron scale gap: a confocal-rheoscopic study

Recent shear experiments in well-entangled polymer solutions demonstrated that interfacial wall slip is the only source of shear rate loss and there is no evidence of shear banding in the micron scale gap. In this work, we experimentally elucidate how molecular parameters such as slip length, b, influence shear inhomogeneity of entangled polybutadiene (PBD) solutions during shear in a small gap H ∼ 50 μm. Simultaneous rheometric and velocimetric measurements are performed on two PBD solutions with the same level of entanglements (Z = 54) in two PBD solvents with molecular weights of 1.5 kg mol(-1) and 10 kg mol(-1) that possess different levels of shear inhomogeneity (2bmax/H = 17 and 240). For the PBD solution made with a low molecular weight PBD solvent of 1.5 kg mol(-1), wall slip is the dominant response within the accessible range of the shear rate, i.e., up to the nominal Weissenberg number (Wi) as high as 290. On the other hand, wall slip is minimized using a high molecular-weight PBD solvent of 10 kg mol(-1) so that bulk shear banding is observed to take place in the steady state for Wi > 100. Finally, these findings and previous results are in good agreement with our recently proposed phase diagram in the parameter space of apparent Wi versus 2bmax/H suggesting that shear banding develops across the micron scale gap when the imposed Wi exceeds 2bmax/H [Wang et al., Macromolecules, 2011, 44, 183].

Heterogeneous flow kinematics of cellulose nanofibril suspensions under shear

The rheology of NFC suspensions that exhibited different microstructures and colloidal stability, namely TEMPO and enzymatic NFC suspensions, was investigated at the macro and mesoscales using a transparent Couette rheometer combined with optical observations and ultrasonic speckle velocimetry (USV). Both NFC suspensions showed a complex rheology, which was typical of yield stress, non-linear and thixotropic fluids. Hysteresis loops and erratic evolutions of the macroscale shear stress were also observed, thereby suggesting important mesostructural changes and/or inhomogeneous flow conditions. The in situ optical observations revealed drastic mesostructural changes for the enzymatic NFC suspensions, whereas the TEMPO NFC suspensions did not exhibit mesoscale heterogeneities. However, for both suspensions, USV measurements showed that the flow was heterogeneous and exhibited complex situations with the coexistence of multiple flow bands, wall slippage and possibly multidimensional effects. Using USV measurements, we also showed that the fluidization of these suspensions could presumably be attributed to a progressive and spatially heterogeneous transition from a solid-like to a liquid-like behavior. As the shear rate was increased, the multiple coexisting shear bands progressively enlarged and nearly completely spanned over the rheometer gap, whereas the plug-like flow bands were eroded.

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.

Surfactant micelles: model systems for flow instabilities of complex fluids

Complex fluids such as emulsions, colloidal gels, polymer or surfactant solutions are all characterized by the existence of a "microstructure" which may couple to an external flow on time scales that are easily probed in experiments. Such a coupling between flow and microstructure usually leads to instabilities under relatively weak shear flows that correspond to vanishingly small Reynolds numbers. Wormlike micellar surfactant solutions appear as model systems to study two examples of such instabilities, namely shear banding and elastic instabilities. Focusing on a semidilute sample we show that two-dimensional ultrafast ultrasonic imaging allows for a thorough investigation of unstable shear-banded micellar flows. In steady state, radial and azimuthal velocity components are recovered and unveil the original structure of the vortical flow within an elastically unstable high shear rate band. Furthermore thanks to an unprecedented frame rate of up to 20,000 fps, transients and fast dynamics can be resolved, which paves the way for a better understanding of elastic turbulence.

Interface instabilities and chaotic rheological responses in binary polymer mixtures under shear flow

The numerical results of RP–FH model reveal another possible cause of the rheochaos: a vortex structure emerges within the central band.

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.

Shear banding from lattice kinetic models with competing interactions

We present numerical simulations based on a Boltzmann kinetic model with competing interactions, aimed at characterizing the rheological properties of soft-glassy materials. The lattice kinetic model is shown to reproduce typical signatures of driven soft-glassy flows in confined geometries, such as Herschel-Bulkley rheology, shear banding and hysteresis. This lends further credit to the present lattice kinetic model as a valuable tool for the theoretical/computational investigation of the rheology of driven soft-glassy materials under confinement.

Self-organization in the flow of complex fluids (colloid and polymer systems). Part 2: Theoretical models

Flow induced transitions in complex fluids are usually accompanied by changes in the internal media structure and the flow symmetry. In this review paper, we discuss the theoretical models and approaches that have been used for the analysis of different types of flow instabilities and flow patterns. The main attention is focused on the basic fluid models which reveal vortex and banding flow structures at high shear rates. The Oldroyd-B fluid is one of such models. The Reynolds and the Weissenberg (or Deborah) numbers are the parameters governing its flow behavior. For this model, the secondary flow patterns arising in viscometric flows of different geometries at the bifurcation point are described. Complex fluids which are able to exist in multiple states can form coexisting bands of different structures with different rheological properties and flowing with different shear rates at the same shear stress. Shear banding is typical for fluids demonstrating non-monotonous flow curves described by such models as the diffusive Johnson-Segalman fluid model, for example. Recent progress in exploring this phenomenon is discussed.

Local velocity measurements in the shear-thickening transition of dilute micellar solutions of surfactants

Local velocimetry and rheometric measurements are performed on three dilute micellar solutions which undergo the shear-thickening transition. The three surfactants, namely, alkyltrimethyl ammonium bromide (C(n)TAB), all belong to the same family and only differ by the length of the aliphatic chain. Simultaneous ultrasonic velocimetry and rheometry recordings provide convincing evidence for a heterogeneous flow in the shear-thickening domain. A detailed analysis allows us to demonstrate surprisingly similar evolutions of the wall slip magnitude and of the apparent viscosity as well as subtle differences between the three systems. Together with the velocimetry results, the direct observation of the flow in the vorticity-velocity plane reveals that the shear-thickening transition is associated with the emergence of a three-dimensional unstable flow.

Molecular imaging of slip in entangled DNA solution

This work obtains the first molecular imaging of wall slip in entangled solutions. Using a combination of confocal fluorescence microscopy and rheometry, molecular images were captured in the nonlinear response regime of entangled DNA solutions. Conformations of DNA molecules were imaged during shear to correlate with the magnitude of wall slip. Interfacial chain disentanglement results in wall slip beyond the stress overshoot. Sufficient disentanglement can produce tumbling of individual DNA in the entangled solutions.

Taylor-like vortices in shear-banding flow of giant micelles

Using flow visualizations in Couette geometry, we demonstrate the existence of Taylor-like vortices in the shear-banding flow of a giant micelles system. We show that vortices stacked along the vorticity direction develop concomitantly with interfacial undulations. These cellular structures are mainly localized in the induced band and their dynamics is fully correlated with that of the interface. As the control parameter increases, we observe a transition from a steady vortex flow to a state where pairs of vortices are continuously created and destroyed. Normal stress effects are discussed as potential mechanisms driving the three-dimensional flow.

Shear banding and rheochaos in associative polymer networks

We present experimental evidence of an instability in the shear flow of transient networks formed by telechelic associative polymers. Velocimetry experiments show the formation of shear bands, following a complex pattern upon increasing the overall shear rate. The chaotic nature of the stress response in transient flow is indicative of spatiotemporal fluctuations of the banded structure. This is supported by time-resolved velocimetry measurements.

Shear banding and yield stress in soft glassy materials

Shear localization is a generic feature of flows in yield stress fluids and soft glassy materials but is incompletely understood. In the classical picture of yield stress fluids, shear banding happens because of a stress heterogeneity. Using recent developments in magnetic resonance imaging velocimetry, we show here for a colloidal gel that even in a homogeneous stress situation shear banding occurs, and that the width of the flowing band is uniquely determined by the macroscopically imposed shear rate rather than the stress. We present a simple physical model for flow of the gel showing that shear banding (localization) is a flow instability that is intrinsic to the material, and confirm the model predictions for our system using rheology and light scattering.