The focus of this paper was to gain a true understanding of the impact of a multifunctional epoxide (Joncryl®;ADR-4368) on the interfacial properties of biopolymer blends based on poly(lactic acid) (PLA) and poly(butylene adipate-co-terephthalate) (PBAT). The effect of Joncryl on the shear rheological, morphological, and interfacial properties of the blends was systematically investigated. For the deformed drop retraction experiments, different sandwich model systems (droplet/matrix), representing various scenarios of compatibilization, were prepared, aiming to probe the role of the epoxy-functionalized chains on the interface. The decrease of the interfacial tension in the modified/compatibilized PLA_PBAT and the formation of the PLA-Joncryl-PBAT copolymer were highlighted. A new relaxation peak relative to this copolymer was detected by the relaxation spectrum. Transient start-up shear and nonlinear stress relaxation experiments were carried out and confirmed the obtained results. In addition, the interface contribution was demonstrated using the Lee and Park model. The relaxation time increased with the amount of added Joncryl. Hence, the coexistence of chain extension/branching chains coupled to the PLA-Joncryl-PBAT copolymer formation had to be taken into account to explain the improved mechanical properties.

The current state of understanding for solution conformations of flexible polymers and their linear viscoelastic response is reviewed. Correlation length, tube diameter, and chain size of neutral polymers in good solvent, neutral polymers in theta-solvent, and polyelectrolyte solutions with no added salt are compared as these are the three universality classes for flexible polymers in solution. The 1956 Zimm model is used to describe the linear viscoelasticity of dilute solutions and of semidilute solutions inside their correlation volumes. The 1953 Rouse model is used for linear viscoelasticity of semidilute unentangled solutions and for entangled solutions on the scale of the entanglement strand. The 1971 de Gennes reptation model is used to describe linear viscoelastic response of entangled solutions. In each type of solution, the terminal dynamics, reflected in the terminal modulus, chain relaxation time, specific viscosity, and diffusion coefficient are reviewed with experiment and theory compared. Overall, the agreement between theory and experiment is remarkable, with a few unsettled issues remaining.

This paper presents both experimental and modeling studies of viscoelastic properties of MR elastomers under harmonic loadings. Magnetorheological elastomer (MRE) samples were fabricated by mixing carbonyl iron power, silicone oil, and silicone rubber and cured under a magnetic field. Its steady-state and dynamic properties were measured by using a parallel-plate rheometer. Various sinusoidal loadings, with different strain amplitude and frequencies, were applied to study the stress responses. The stress–strain results demonstrated that MR elastomers behave as linear visocoelastic properties. Microstructures of MRE samples were observed with a scanning electron microscope. A four-parameter linear viscoelatic model was proposed to predict MRE performances. The four parameters under various working conditions (magnetic field, strain amplitude, and frequency) were identified with the MATLAB optimization algorithm. The comparisons between the experimental results and the model predictions demonstrate that the four-parameter viscoelastic model can predict MRE performances very well. In addition, dynamic properties of MRE performances were alternatively represented with equivalent stiffness and damping coefficients.

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.

Numerical simulations of viscoplastic fluid flows have provided a better understanding of fundamental properties of yield stress fluids in many applications relevant to natural and engineering sciences. In the first part of this paper, we review the classical numerical methods for the solution of the non-smooth viscoplastic mathematical models, highlight their advantages and drawbacks, and discuss more recent numerical methods that show promises for fast algorithms and accurate solutions. In the second part, we present and analyze a variety of applications and extensions involving viscoplastic flow simulations: yield slip at the wall, heat transfer, thixotropy, granular materials, and combining elasticity, with multiple phases and shallow flow approximations. We illustrate from a physical viewpoint how fascinating the corresponding rich phenomena pointed out by these simulations are.

High solid dispersions are soft materials made of colloidal or non-colloidal particles dispersed at high volume fractions in a liquid matrix. They include hard sphere glasses, colloidal pastes, concentrated emulsions, foams, and vesicles. These materials are prone to exhibit different kinds of flow heterogeneities: shear banding, wall slip, and fracture. While wall slip is often considered as a nuisance by experimentalists, it appears to be a fundamental component to the way that high solid dispersions respond to mechanical deformation. Moreover, the ability of soft materials to slip onto surfaces allows them to move readily and efficiently in many natural phenomena and industrial processes. This review surveys recent developments and current research in the field. Topics like wall slip detection and control, microscopic modeling for rigid and soft particles materials, and the relation between wall slip and other flow heterogeneities are discussed. We also identify important open issues for future research.

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.

We explore the utility of strain-controlled large amplitude oscillatory shear (LAOS) deformation for identifying and characterizing apparent yield stress responses in elastoviscoplastic materials. Our approach emphasizes the visual representation of the LAOS stress response within the framework of Lissajous curves with strain, strain rate, and stress as the coordinate axes, in conjunction with quantitative analysis of the corresponding limit cycle behavior. This approach enables us to explore how the material properties characterizing the yielding response depend on both strain amplitude and frequency of deformation. Canonical constitutive models (including the purely viscous Carreau model and the elastic Bingham model) are used to illustrate the characteristic features of pseudoplastic and elastoplastic material responses under large amplitude oscillatory shear. A new parameter, the perfect plastic dissipation ratio, is introduced for uniquely identifying plastic behavior. Experimental results are presented for two complex fluids, a pseudoplastic shear-thinning xanthan gum solution and an elastoviscoplastic invert-emulsion drilling fluid. The LAOS test protocols and the associated material measures provide a rheological fingerprint of the yielding behavior of a complex fluid that can be compactly represented within the domain of a Pipkin diagram defined by the amplitude and timescale of deformation.

The rheological properties of complex fluid interfaces are of prime importance in a number of technological and biological applications. Whereas several methods have been proposed to measure the surface rheological properties, it remains an intrinsically challenging problem due to the small forces and torques involved and due to the intricate coupling between interfacial and bulk flows. In the present work, a double wall-ring geometry to measure the viscoelastic properties of interfaces in shear flows is presented. The geometry can be used in combination with a modern rotational rheometer. A numerical analysis of the flow field as a function of the surface viscoelastic properties is presented to evaluate the non-linearities in the surface velocity profile at a low Boussinesq number. The sensitivity of the geometry, as well as its applicability, are demonstrated using some reference Newtonian and viscoelastic fluids. Oscillatory and steady shear measurements on these reference complex fluid interfaces demonstrate the intrinsic sensitivity, the accuracy, and the dynamic range of the geometry when used in combination with a sensitive rheometer.

A constitutive model for elasto-viscoplastic thixotropic materials is proposed. It consists of two differential equations, one for the stress and the other for the structure parameter, a scalar quantity that indicates the structuring level of the microstructure. In contrast to previous models of this kind, the structure parameter varies from zero to a positive and typically large number. The lower limit corresponds to a fully unstructured material, whereas the upper limit corresponds to a fully structured material. When the upper limit is finite, the model represents a highly shear-thinning, thixotropic, and viscoelastic liquid that possesses an apparent yield stress. When it tends to infinity, the behavior of a true yield-stress material is achieved. Predictions for rheometric flows such as constant shear rate tests, creep tests, SAOS, and large-amplitude oscillatory shear (LAOS) are presented, and it is shown that, in all cases, the trends observed experimentally are faithfully reproduced by the model. Within the framework of the model, simple explanations are given for the avalanche effect and the shear banding phenomenon. The LAOS results obtained are of particular importance because they provide a piece of information that so far is absent in the literature, namely a quantitative link between the Lissajous–Bowditch curve shapes and rheological effects such as elasticity, thixotropy, and yielding.

A concept of viscoplasticity advanced exactly one century ago by Bingham appears very fruitful because there are many natural and artificial materials that demonstrate viscoplastic behavior, i.e., they are able to pass from a solid to a liquid state under the influence of applied stress. However, although this transition was originally considered as a jump-like phenomenon occurring at a certain stress—the yield stress—numerous subsequent studies have shown that the real situation is more complicated. A long-term discussion about the possibility of flow at low stresses less than the yield stress came to today’s conclusion denying this possibility as being opposite to the existence of the maximal Newtonian viscosity in viscoelastic polymeric fluids. So, there is a contradiction between the central dogma of rheology which says that “everything flows” and the alleged impossibility for flow at a solid-like state of viscoplastic fluids. Then, the concept of the fragile destruction of an inner structure responsible for a solid-like state at the definite (yield) stress was replaced by an understanding of the yielding as a transition extending over some stress range and occurring in time. So, instead of the yield stress, yielding is characterized by the dependence of durability (or time-to-break) on the applied stress. In this review, experimental facts and the new understanding of yielding as a kinetic process are discussed. Besides, some other alternative methods for measuring the yield stress are considered.

On a series of examples from the field of viscoelasticity we demonstrate that it is possible to attribute physical meaning to initial conditions expressed in terms of Riemann–Liouville fractional derivatives, and that it is possible to obtain initial values for such initial conditions by appropriate measurements or observations.

Yield stress fluid flows occur in a great many operations and unit processes within the oil and gas industry. This paper reviews this usage within reservoir flows of heavy oil, drilling fluids and operations, wellbore cementing, hydraulic fracturing and some open-hole completions, sealing/remedial operations, e.g., squeeze cementing, lost circulation, and waxy crude oils and flow assurance, both wax deposition and restart issues. We outline both rheological aspects and relevant fluid mechanics issues, focusing primarily on yield stress fluids and related phenomena.

The main purpose of this paper is to provide an easy-to-use approximation formula for the inverse Langevin function. The mathematical complexity of this function makes it unfeasible for an analytical manipulation and inconvenient for computer simulation. This situation has motivated a series of papers directed on its approximation. The best known solution is given by Cohen. It is used in a lot of statistically based models of rubber-like materials. The formula is derived from rounded Padé approximation [3/2]. The main idea of the presented approach in this paper relies on improvement of the precision of approximation formula for the inverse Langevin function by using multipoint Padé approximation method. We focused our study strongly on obtaining a simple and accurate approximation. It is assumed that the proposed approximation formula may be considered a useful tool for verification of the results obtained in other ways. Our results are supported by investigating several numerical examples. The paper also presents a few applications of computer software named Mathematica which can be used to calculate symbolically one point Padé approximants and numerically multipoint Padé approximants. Using this software, we showed also how to compute higher order derivatives of the inverse function in a simple and elegant way. This issue was discussed by Itskov et al.

A century ago, and more than a decade before the term rheology was formally coined, Bingham introduced the concept of plastic flow above a critical stress to describe steady flow curves observed in English china clay dispersions. However, in many complex fluids and soft solids, the manifestation of a yield stress is also accompanied by other complex rheological phenomena such as thixotropy and viscoelastic transient responses, both above and below the critical stress. In this perspective article, we discuss efforts to map out the different limiting forms of the general rheological response of such materials by considering higher dimensional extensions of the familiar Pipkin map. Based on transient and nonlinear concepts, the maps first help organize the conditions of canonical flow protocols. These conditions can then be normalized with relevant material properties to form dimensionless groups that define a 3D state space to represent the spectrum of thixotropic elastoviscoplastic (TEVP) material responses.

Viscoplasticity is characterized by a yield stress, below which the materials will not deform and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the Herschel-Bulkley model and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a regularization parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a bubble and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown. The above-mentioned viscoplastic models leave undetermined the stress and elastic deformation in the solid region. Moreover, deviations have been reported between predictions with these models and experiments for flows around particles using Carbopol, one of the very often used and heretofore widely accepted as a simple “viscoplastic” fluid. These have been partially remedied in very recent studies using the elastoviscoplastic models proposed by Saramito.

Yield stress fluid flows occur in a great many operations and unit processes within the oil and gas industry. This paper reviews this usage within reservoir flows of heavy oil, drilling fluids and operations, wellbore cementing, hydraulic fracturing and some open-hole completions, sealing/remedial operations, e.g., squeeze cementing, lost circulation, and waxy crude oils and flow assurance, both wax deposition and restart issues. We outline both rheological aspects and relevant fluid mechanics issues, focusing primarily on yield stress fluids and related phenomena.

It is now 30 years since Barnes and Walters published a provocative paper in which they asserted that the yield stress is an experimental artifact. We now know that the situation is far more complicated than understood at the time, and that the mechanics of the solid material prior to yielding must be considered carefully. In this paper, we examine the response of a well-studied "simple" yield-stress material, namely a Carbopol gel that exhibits no thixotropy, and demonstrate the significance of the pre-yielding behavior through a number of elementary measurements.

Recent experimental techniques used to investigate shear banding are reviewed. After recalling the rheological signature of shear-banded flows, we summarize the various tools for measuring locally the microstructure and the velocity field under shear. Local velocity measurements using dynamic light scattering and ultrasound are emphasized. A few results are extracted from current works to illustrate open questions and directions for future research.

It is now 30 years since Barnes and Walters published a provocative paper in which they asserted that the yield stress is an experimental artifact. We now know that the situation is far more complicated than understood at the time, and that the mechanics of the solid material prior to yielding must be considered carefully. In this paper, we examine the response of a well-studied “simple” yield-stress material, namely a Carbopol gel that exhibits no thixotropy, and demonstrate the significance of the pre-yielding behavior through a number of elementary measurements.