Shear-thinning Response Research Articles

Strain rate effects on symmetric diblock copolymer liquid bridges: order-induced stability of polymer fibres.

Optical microscopy is used to study the effect of lamellar order on the evolution of polymer-melt bridges. Measurements are performed on symmetric diblock copolymers and linear homopolymers in the melt state. Diblock copolymer bridges measured in the disordered phase are shown to exhibit the same strain rate response as their homopolymer counterparts: shear thinning at low strain rates and shear thickening at high strain rates. However, when measured in the ordered phase, copolymer-melt bridges demonstrate an increased effective viscosity due to the lamellar order and a shear thinning response over the entire range of strain rates probed. The increased viscosity demonstrates an enhanced stability in lamellae forming diblock liquid bridges, presumed to be caused by the isotropic orientational order of lamellar domains that provide energy barriers to flow within the bridge. The shear thinning can be understood as an alignment of lamellae along the axis of the bridge due to flow, facilitating unimpeded diffusion of polymer out of the liquid bridge along lamellar boundaries.

Amyloids: Connecting from Single Fibril Mechanics to Macroscopic Rheology

Nearly all proteins and peptides have the ability to self-assemble into amyloids when they are denatured. These highly ordered nanofibrils exhibit superior mechanical properties, which are relatively insensitive to their protein amino acid sequence. This makes them attractive candidates for applications in materials science and food industry. However, their remarkable stability constitutes a problem in the context of amyloid-related diseases, where amyloids accumulate in tissues. Despite the wide interest in amyloids, the understanding and description of their mechanical properties is still limited. Our goal was to investigate both the micromechanics of individual fibrils and the emergent mechanics of networks on the mesoscopic scale.We will show macroscopic rheology and laser tweezer microrheology of the viscoelastic properties of amyloids formed from hen egg white lysozyme (HEWL). The macroscopic rheology of the networks will depend both on the stiffness of the fibrils and the energetics of their interactions. Therefore we show for the first time for the same system also measurements of the high bending rigidity based on fluorescence microscopy of single, fluctuating fibrils in solution. The high persistence length was further confirmed using atomic force microscopy (AFM) imaging. With laser tweezer microrheology we show the local properties of fibrils in networks. By using rheology in combination with small-angle neutron scattering (rheo-SANS), we show that the shear-thinning response results from fibril alignment. In conclusion, our results give a comprehensive description of the mechanical properties of single amyloid fibrils as well as networks of fibrils.

Edge contact effect on thermal elastohydrodynamic lubrication of finite contact lines

Minimum lubricant film thickness and maximum pressure every so often appear close to roller ends. This study combines the Boussinesq–Cerruti half-space equations with a free boundary correction procedure for precise modeling of edge contact conditions. The thermal EHL model developed associates this representation to a standard finite difference of the energy equation, and to a modified finite difference expansion of the Couette term of the Reynolds equation. To complete the model, the Carreau expression describes the shear-thinning response of the lubricant. The investigation includes different roller profile corrections. The results show that a large radius crowning modification combined with a rounding of the corners constitutes the most effective profile adjustment.

Nonlinear signatures of entangled polymer solutions in active microbead rheology.

We present experimental data and numerical modeling of a nonlinear phenomenon in active magnetic microbead rheology that appears to be common to entangled polymer solutions (EPS). Dynamic experiments in a modest range of magnetic forces show: 1. a short-lived high viscosity plateau, followed by 2. a bead acceleration phase with a sharp drop in apparent viscosity, and 3. a terminal steady state that we show resides on the shear-thinning slope of the steady-state flow curve from cone and plate data. This latter feature implies a new protocol to access the nonlinear steady-state flow curve for many biological EPS only available in microliter-scale volumes. We solve the moment-closure form of the Rolie-Poly kinetic model for EPS hydrodynamics, together with a decoupling approximation that obviates the need for a full 3D flow solver, and show that the model qualitatively reproduces the dynamic experimental sequence above. In this way, we explain the phenomenon in terms of entangled polymer physics, and show how the nonlinear event (acceleration and termination on the shear-thinning response curve) is tunable by the interplay between molecular-scale mechanisms (relaxation via reptation and chain retraction) and magnetic force controls. The experimental conditions mimic movement of cilia tips, bacteria, and sperm in mucus barriers, implying a physiological relevance of the phenomenon, and compelling further development of the fully coupled, 3D flow-microstructure model to achieve quantitative accuracy.

The structure and rheology of sheared model swimmer suspensions

We analyze the rheological response of a suspension of simple model swimmers subject to a steady Couette flow. We consider the squirmer model as a means to control systematically the interplay between self-propulsion and active stress generation and analyze their relative impact both on the effective viscosity of a suspension and the microstructure the squirmers develop. We show how self-propulsion introduces an intrinsic contribution to the effective viscosity of the active suspension. Accordingly, apolar squirmers show shear thickening while polar ones develop a shear thinning response to the applied shear. We show that the detailed coupling of the squirmers to the bounding walls has a strong influence on the structure of the suspension and the development of shear bands.

A comparison of the colloidal stabilization of aqueous titanium carbide suspensions using anionic and cationic dispersants

The aqueous colloidal stability of titanium carbide (TiC) suspensions has been assessed using both anionic and cationic dispersants. The zeta potential of TiC suspensions, both without and with polyelectrolyte addition, is examined as a function of pH and the relative responses of the polyelectrolytes are compared. Without a dispersant, the TiC powder used shows an isoelectric point at ~ pH 2.6. The use of an anionic polyelectrolyte, an ammonium salt of polymethacrylate (PMA-NH 4) does not significantly alter the isoelectric point. Conversely, the addition of a cationic dispersant, polyethylenimine (PEI) with a molecular weight of either 1800 or 10,000, significantly alters the isoelectric point. The rheological behaviour of the TiC suspensions was examined using a concentric cylinder geometry. In each case a shear thinning response is observed, and a transition to shear thickening is seen on all the PMA-NH 4 trials, and some, but not all, of the PEI experiments at high shear rates (~ 600 s − 1 ). The PMA-NH 4 was found to produce optimum slip stability at lower concentrations, (~ 0.02 wt.%) versus the PEI, which obtained the same slip stability at concentrations of ~ 0.30 wt.%. However, increasing the PMA-NH 4 concentration does not provide increased stability; above this point it begins to degrade the slip properties through increasing viscosity. Conversely, the PEI does not exhibit a plateau and subsequent drop off of the slip stability with increasing concentration for the dispersant range studied. For TiC, both polyelectrolytes appear to be suitable dispersants for processing at their respective regions of the pH scale. The PMA-NH 4 provides sufficient stability at ~ pH 8.5, and the PEI provides essentially equal stability in the pH 4.5 region for the concentrations examined.

Response of an emulsion of leaky dielectric drops immersed in a simple shear flow: Drops less conductive than the suspending fluid

Direct numerical simulations of the effects of an electric field on an emulsion of drops are presented. A simple shear flow configuration is adopted where the electric field is applied perpendicular to the sliding plates. Both the drops and the suspending fluid are assumed to behave as leaky dielectric fluids. Here, drops less conductive than the suspending fluid with an electrical conductivity ratio smaller than the dielectric permittivity ratio are considered. This combination of electrical properties leads to a viscous fluid motion from the poles to the equator. The response of an emulsion is governed by the competition between the electrical forces, the fluid shear, and the capillary forces. The Mason number [Mn=(3λ+2)μγ̇∕6(λ+1)ε0β2E∞2] and the electric capillary number [Ce=ε0β2E∞2a∕γ] are used to describe the response of the systems. As previously observed in experiments at low shear rates, Mn<0.2, the drops aggregate in chains that tilt under a shear. The competition between the electrical forces and the fluid shear results in shorter chains at intermediate shear rates, 0.2<Mn<2.0. As the fluid shear becomes stronger than the electrical attraction, Mn>2.0, the chains of drops break up. The rheological properties mainly depend on the emulsion microstructure. The effective viscosity exhibits a strong shear-thinning response because the chains of drops, which appear at low shear rates, increase the resistance of the system to shear. As the chains shorten and break up, the effective viscosity decreases. The elastic properties of the emulsion are also affected by the presence of the electric field. Normal stress differences arise as a consequence of the deformation of the drops and the surface tension acting on the interface between the fluids. The shape of the drops is determined by the deformation caused by the viscous forces and the deformation due to the electric stresses. At low shear rates, the electric effects are predominant and the application of an electric field leads the drops to deform into oblate shapes. The oblate deformation results in higher stresses in the direction parallel to the shearing motion than perpendicular to it, which results in a significant increase in the first normal stress difference. As the shear rate is increased, the oblate deformation is supplemented by the deformation due to the fluid shear. The deformation caused by the electric field is also responsible for the negative magnitude of the second normal stress difference in three-dimensional emulsions.

A Quantitative Solution for the Full Shear-Thinning EHL Point Contact Problem Including Traction

We present a realistic elastohydrodynamic lubrication (EHL) simulation in point contact using a Carreau-like model for the shear-thinning response and the Doolittle-Tait free-volume viscosity model for the piezoviscous response. The liquid lubricant modeled is a high-viscosity polyalphaolefin which has been shown by high-pressure viscometry to possess a relatively low threshold for shear-thinning as a single-component liquid lubricant. As a result, the measured EHL film thickness is about one-half of the Newtonian prediction. We derived and numerically solved the two-dimensional generalized Reynolds equation for the modified Carreau model based on Greenwood. In this simulation, viscosity was not treated as an adjustable parameter; the models used for the pressure and shear dependence of viscosity were obtained entirely from viscometer measurements. Truly remarkable agreement is found in the comparisons of simulation and experiment for traction coefficient and for film thickness in both pure rolling and sliding cases.

A Reynolds–Ellis equation for line contact with shear-thinning

A form of the Reynolds equation is lacking for the general shear-thinning that evolves from linear response at low stress to power-law at high stress. The Ellis model is a reasonable description of the shear-thinning response at elevated pressure of those liquid lubricants with a strong dependence of viscosity on shear, that is, for a power-law exponent less than ½. A one-dimensional Reynolds–Ellis equation has been derived that can be written d d x { p ′ h 3 12 μ + Γ μ p ′ 2 [ ( τ m − ϕ 1 n + 2 + ϕ ) | τ m − ϕ | 1 n + 1 − ( τ m + ϕ 1 n + 2 − ϕ ) | τ m + ϕ | 1 n + 1 ] } = u ¯ d h d x . This reduces to the one-dimensional form of Greenwood's Reynolds–Rabinowitsch equation for n=1/3. Simple Grubin style solutions to the EHL line contact problem show that the new generalized Reynolds equation is an accurate form for an Ellis fluid. Unfortunately, the Ellis model is not ideal, as the transition to shear-thinning becomes extremely broad for n<1/2. The Ellis model does, however, provide an exact solution for a sliding line contact for a liquid that possesses a zero shear viscosity along with a variable power-law exponent, and it may be unique in this respect. Future work should consider a two-dimensional Reynolds equation for more accurate models of moderately shear-thinning lubricants such as Carreau.

Nano- to Microscale Dynamics of P-Selectin Detachment from Leukocyte Interfaces. II. Tether Flow Terminated by P-Selectin Dissociation from PSGL-1

We have used a biomembrane force probe decorated with P-selectin to form point attachments with PSGL-1 receptors on a human neutrophil (PMN) in a calcium-containing medium and then to quantify the forces experienced by the attachment during retraction of the PMN at fixed speed. From first touch to final detachment, the typical force history exhibited the following sequence of events: i), an initial linear-elastic displacement of the PMN surface, ii), an abrupt crossover to viscoplastic flow that signaled membrane separation from the interior cytoskeleton and the beginning of a membrane tether, and iii), the final detachment from the probe tip most often by one precipitous step of P-selectin:PSGL-1 dissociation. Analyzing the initial elastic response and membrane unbinding from the cytoskeleton in our companion article I, we focus in this article on the regime of tether extrusion that nearly always occurred before release of the extracellular adhesion bond at pulling speeds ≥1μm/s. The force during tether growth appeared to approach a plateau at long times. Examined over a large range of pulling speeds up to 150μm/s, the plateau force exhibited a significant shear thinning as indicated by a weak power-law dependence on pulling speed, f∞=60 pN(νpull/μm/s)0.25. Using this shear-thinning response to describe the viscous element in a nonlinear Maxwell-like fluid model, we show that a weak serial-elastic component with a stiffness of ∼0.07 pN/nm provides good agreement with the time course of the tether force approach to the plateau under constant pulling speed.

The High Pressure Rheology of Mixtures

The Newtonian mixing rules for several binary systems have been experimentally investigated. Some systems show non-ideal mixing response and for some systems the non-ideal response is pressure-dependent, yielding an opportunity for manipulation of the pressure-viscosity behavior to advantage. The mixing of differing molecular weight “straight cuts” can produce very different pressure-viscosity response. This behavior underscores the difficulty in predicting the pressure-viscosity coefficient based upon chemical structure and ambient viscosity since the molecular weight distribution is also important, but it also provides another opportunity to control the high-pressure response by blending. The first experimental observation of double shear-thinning within a single flow curve is reported. Blending then provides the capability of adjusting not only the Newtonian viscosity but also the non-Newtonian shear-thinning response as well.

Numerical simulation of atomization gas flows : S.D.Ridder et al. (National Inst. for Standards and Technology, Gaithersburg, USA.)

3D printing metals via material extrusion utilizes a metal particle reinforced polymer matrix composite (PMC) as the filament which is typically made with gas-atomized powders as fillers. Its rheological behavior limits the maximum metal content of the printed green composite which, consequently, hinders further reductions to part porosity and shrinkage. In this paper, the scaling of the dynamic viscosity of melt-extruded PMC filaments made of PLA and Ni-Cu gas-atomized powders is studied as a function of the metal’s volumetric content and feedstock pre-mixing strategies and correlated to its extrudability performance. Extrudable and uniform filaments with the highest metal content of 63.4 vol% were produced by employing solution-mixing of the PMC feedstock and compared to physical mixing which only reached 54 vol%. After sintering, the improved metal content of 3D printed parts from solution-mixing reduced linear shrinkage by 76% in comparison to physical mixing, resulting in an absolute shrinkage value of 0.49%. By characterizing the PMC feedstock via flow-sweep rheology tests, a distinct extension of the shear-thinning zone towards high shear rates (i.e. 100 s−1) at high metal content was observed for the case of solution-mixed feedstock – a result that is attributed to the improved adhesion of the PMCs to the walls of the rheometer. PMCs with such characteristics correlated well to favorable extrudability and windability test outcomes (i.e. no particle jamming or metal accumulation at the die). The Krieger-Dougherty analytical model was employed to predict the zero-shear rate viscosity as a function of the metal content in the PMCs, however, the latter property is not necessarily correlated to the viscosity at high shear rates (10–1000 s−1) due to a complex shear thinning response. Since PMCs experience high shear rates in the die orifice, additional theoretical models are needed to predict shear-thinning at high metal content in PMCs and, thus, improve our prediction of PMC’s rheology, its design, and extrudability to maximize its metal content.

The Cox–Merz rule extended: A rheological model for concentrated suspensions and other materials with a yield stress

A nonlinear rheological model combining elastic, viscous, and yielding phenomena is developed in order to describe the rheological behavior of materials which exhibit a yield stress. A key feature of the formulation is the incorporation of a recoverable strain; it has a maximum value equal to the critical strain at which the transition from an elastic solid-like response to a viscous shear thinning response occurs. An analysis is presented to enable determination of all the model parameters solely from dynamic measurements which are easily accessible experimentally. A rigorous correlation, analogous in form to the Cox–Merz rule, is shown to exist between the steady shear viscosity and the complex dynamic viscosity in terms of a newly defined ‘‘effective shear rate.’’ Experimental data obtained for a 70 vol % suspension of silicon particles in polyethylene indicate agreement with theoretical predictions for both the dynamic and steady shear behavior.

The influence of processing on biopolymeric structures

AbstractMaize grits and maize starch were extruded under a number of conditions using a twin screw extruder. Under equilibrium operation the extruder was dead stopped and the barrel contents removed. Samples from the raw input to the extrudate were examined using scanning electron microscopy, water solubility and aqueous dispersion rheology. The extrusion process results in deformation of the starch granular structure and the production of a new texture corresponding to a marked increase in solubility. Raw maize dispersions are characterised by low viscosity and dilatancy, whereas their heat treatment results in a viscous, shear thinning response. Extrusion results in a tendency to Newtonian behaviour in the limit of high shear and low moistures. This behaviour has been attributed to the reduced swelling functionality of the starch as a function of extrusion which causes a breakdown of the starch granules.