Distinguishing shear banding from shear thinning in flows with a shear stress gradient

Shear banding occurs in complex fluids that exhibit a non-monotonic constitutive instability, such as wormlike micelles, and potentially also in polymeric fluids with presumably monotonic constitutive behavior. However, velocity profiles for shear thinning fluids in geometries possessing a stress gradient, such as Taylor-Couette flow, could be misidentified as shear banding. To address this, we present a model-free experimental procedure to distinguish shear banding from strong shear thinning using high-resolution velocimetry. The approach is developed and validated using simulations using the d-Giesekus model and is based upon the behavior of the width of the apparent interface between the high and low shear rate regions. It is then tested using experimental data for model wormlike micellar solutions. The method allows shear banding to be distinguished from shear thinning in cases where this difference is otherwise indistinguishable. As a by-product, it also provides an estimate of the stress diffusivities for shear banding fluids.     

Flow of K-BKZ fluids between parallel plates rotating about distinct axes: shear thinning and inertial effects

It has been shown that for any simple fluid, a flow field of the form u = –Ω[y - g(z)], v = Ω[x – f(z], w = 0, which is appropriate for modeling the flow in a orthogonal rheometer, is dynamically possible. The functions f(z) and g(z) depend on the choice of constitutive equation. In the present paper, these are calculated for a class of K-BKZ fluids which exhibit shear thinning. The results are then used to study the interaction of shear thinning and inertial effects on the flow field in an orthogonal rheometer.     

Effects of shear thinning on migration of neutrally buoyant particles in pressure driven flow of Newtonian and viscoelastic fluids

The pattern of cross stream migration of neutrally buoyant particles in a pressure driven flow depends strongly on the properties of the suspending fluid. These migration effects have been studied by direct numerical simulation in planar flow. Shear thinning has a large effect when the inertia or elasticity is large, but only a small effect when they are small. At moderate Reynolds numbers, shear thinning causes particles to migrate away from the centerline, creating a particle-free zone in the core of the channel, which increases with the amount of shear thinning. In a viscoelastic fluid with shear thinning, particles migrate either toward the centerline or toward the walls, creating an annular particle-free zone at intermediate radii. The simulations also give rise to precise determination of slip velocity distributions in the various cases studied.     

Steady shear banding in complex fluids

Shear banding (SB) is manifested by the abrupt “demixing” of the flow into regions of high and low shear rate. In this paper, we first relate analytically the rheological parameters of the fluid with the range of shear rates and stresses of SB occurrence. For this, we accept that the origin of shear banding is constitutive, and adopt a non-linear viscoelastic expression able to accommodate the double-valuedness of the stress with flow intensity, under certain conditions. We then implement the model for the case of pressure driven flow through a cylindrical pipe; we derive approximate expressions for the velocity profile in the two-banded regions (core and outer annular), the overall throughput in the presence or absence of “spurt”, and the radial location limits of the shear rate discontinuity.     

Perspectives on shear banding in complex fluids

In this review, I present an idiosyncratic view of the current state of shear banding in complex fluids. Particular attention is paid to some of the outstanding issues and questions facing the field, including the applicability of models that have “traditionally” been used to model experiments; future directions and challenges for experimentalists; and some of the issues surrounding vorticity banding, which has been discussed theoretically and whose experiments are fewer in number yet, in many ways, more varied in character.     

Phenomenology and physical origin of shear localization and shear banding in complex fluids

We review and compare the phenomenological aspects and physical origin of shear localization and shear banding in various material types, namely emulsions, suspensions, colloids, granular materials, and micellar systems. It appears that shear banding, which must be distinguished from the simple effect of coexisting static-flowing regions in yield stress fluids, occurs in the form of a progressive evolution of the local viscosity toward two significantly different values in two adjoining regions of the fluids in which the stress takes slightly different values. This suggests that from a global point of view, shear banding in these systems has a common physical origin: Two physical phenomena (for example, in colloids, destructuration due to flow and restructuration due to aging) are in competition, and depending on the flow conditions, one of them becomes dominant and makes the system evolve in a specific direction.     

Laminar shear flow of plastic viscoelastic fluids

Summary The theory of plastic viscoelastic fluids was developed by the author to represent the rheological behavior of polymer melts and solutions with high loading of small particles. The present paper develops an asymptotic formulation of the general theory which applies to laminar shear flows. The formulation is analogous to Criminale, Ericksen and Filbey's theory for viscoelastic fluids. We apply this to study plane Poiseuille and Couette flow.With 2 tables     

Sedimentation of particles in shear flows of viscoelastic fluids

An experimental investigation of sedimentation of single particles and concentrated suspensions in Couette flows of viscous and viscoelastic fluids is presented. With the passage from viscous to viscoelastic fluids, a slowing down of the sedimentation was observed. The sedimentation of suspensions in viscoelastic fluids accelerated with increase in the suspension concentration. The development of instabilities during the sedimentation was detected.     

Molecular orientation, “Region I” shear thinning and the cholesteric phase in aqueous hydroxypropylcellulose under shear

Birefringence and flow visualization are used to study molecular orientation, texture, and the cholesteric nature of a 60 wt% aqueous hydroxypropylcellulose solution at low to moderate shear rates. There is a sharp transition in behavior at a shear rate near 0.5 s^–1. Below this rate, the sample shows “Region I” shear thinning, takes on a frosted appearance, has low flow-induced orientation, and exhibits faint optical diffraction characteristic of cholesteric liquid crystals. Upon flow cessation from low rates, a highly organized cholesteric phase showing bright optical diffraction is re-formed in around 5min. Above the critical shear rate, the sample exhibits much higher orientation and a striped texture which is readily apparent with or without polarized light illumination. Upon flow cessation, molecular orientation decays significantly for up to around 400 s; however, the striped textures established during shear persist. It is suggested that persistence of the cholesteric phase under shear is responsible for the occurrence of Region I shear thinning at low shear rates in this solution.     

The behaviour of field-responsive fluids during shear start-up

The application of an external field (magnetic or electric) to suspensions of particles in a carrier liquid often causes a dramatic increase in the flow resistance. The transient stress response of these systems during the start-up of shear flow was studied as a function of the shear rate, using a system of carbonyl iron particles dispersed in paraffinic spindle oil under magnetic flux densities up to 0.57 T. It was found that initially the stress increased in proportion to the applied strain, reaching a plateau value at a characteristic strain of 0.2. Similar strain dependence of the transient stress behaviour was observed for shear rates spanning the range 0.01 s^–1 to 10 s^–1, suggesting that strain-governed deformation and rupture of the particle aggregates in the fluid was the main contribution to the response. In addition, the steady state flow curves of these fluids were obtained over the shear rate range 0.1 to 100 s^–1.     

Study of magnetorheological fluids at high shear rates

The tunable rheological properties of magnetorheological (MR) materials at high shear rates are studied using a piston-driven flow-mode-type rheometer. The proposed method provides measurement of the apparent viscosity and yield stress of MR fluids for a shear rate range of 50 to 40,000 s⁻¹. The rheological properties of a commercial MR fluid, as well as a newly developed MR polymeric gel, and a ferrofluid-based MR fluid are investigated. The results for apparent viscosity and dynamic and static shear stresses under different applied magnetic fields are reported.     

An apparent viscosity function for shear thickening fluids

A new apparent viscosity function for shear thickening fluids is proposed, contemplating the three characteristic regions typically exhibited by these materials: slight shear thinning at low shear rates, followed by a sharp viscosity increase over a threshold shear rate value (critical shear rate), and a subsequent pronounced shear thinning region at high shear rates. The proposed function has a continuous derivative, making it appropriate in numerical simulations. Moreover, the function is shown to provide an excellent fit to several independent experimental data sets.     

E-FiRST: Electric field responsive shear thickening fluids

A novel electrorheological (ER) effect is presented where the application of an electric field, orthogonal to the vorticity-flow plane, increases the critical hydrodynamic stress required to shear thicken concentrated, colloidal dispersions (the E-FiRST effect). The shear thickening behavior of a Brownian charge stabilized dispersion (226 nm silica in 4-methylcyclohexanol at 53, 50. and 41 vol.%) is studied in the presence of an electric field as a function of the field strength and coupling parameter ( ß) where the latter is a function of a.c. field frequency due to diffusion limitations on the polarization of the particles' double layer. A mechanism is proposed whereby the applied electric field suppresses the formation of the self-organized hydrocluster microstructure responsible for shear thickening, thus delaying the onset of shear thickening to higher applied shear stresses. A Mason-number type scaling law is found to scale the effect, which supports the proposed mechanism.     

On the propagation of shear oscillations in inelastic power-law fluids

A similarity solution is presented to the problem of oscillatory flow produced by an oscillating flat plate in a semi-infinite sea of an inelastic power-law fluid. The physical relevance of the similarity solution is discussed in relation to actual oscillatory flows.     

Droplet deformation of a strongly shear thinning dense suspension of polymeric micelles

We investigated the deformation of a strong shear thinning droplet undergoing simple shear flow in a Newtonian liquid. The droplet was an aqueous solution of poly(ethylene oxide) end capped with an alkyl group that forms spherical micelles in aqueous solution. At high concentrations and below a critical temperature, the jammed micelles showed strong shear thinning behaviour, and neither a yield stress nor a Newtonian viscosity was observed. At small shear rates, the droplet rotated and aligned in the flow, but did not deform or only very weakly. At high shear rates, the droplet deformation increased with increasing shear rate. The deformed droplet did not relax after the shear was stopped except for a modest rounding of the edges. For each shear rate, an apparent viscosity, η _ad, of the equivalent Newtonian droplet was calculated assuming affine deformation. η _ad showed a power law dependence on the capillary number Ca with an exponent of − 1.8 and was larger than the shear viscosity of the micelle suspension at the same shear rates. The results were explained by the existence of a strong gradient of the viscosity inside the droplet leading to a very low viscosity fluid layer near the droplet/matrix interface.     

Control of homogeneous shear flow of multimode Maxwell fluids

We consider a homogeneous parallel shear flow of a multimode Maxwell fluid. This problem results in a set of ordinary differential equations for the stresses. In this system, we view the shear rate as a control and consider the problem of steering the system to a given state of stress. The objective is to steer the system from given initial stresses to a final state of stress, allowing the shear rate to vary in an arbitrary fashion. We show that this problem is related to a calculus of variations problem. For the case of two modes, we obtain a characterization of the set of achievable streses.