An account is given of the development of the idea of a yield stress for solids, soft solids and structured liquids from the beginning of this century to the present time. Originally, it was accepted that the yield stress of a solid was essentially the point at which, when the applied stress was increased, the deforming solid first began to show liquid-like behaviour, i.e. continual deformation. In the same way, the yield stress of a structured liquid was originally seen as the point at which, when decreasing the applied stress, solid-like behaviour was first noticed, i.e. no continual deformation. However as time went on, and experimental capabilities increased, it became clear, first for solids and lately for soft solids and structured liquids, that although there is usually a small range of stress over which the mechanical properties change dramatically (an apparent yield stress), these materials nevertheless show slow but continual steady deformation when stressed for a long time below this level, having shown an initial linear elastic response to the applied stress. At the lowest stresses, this creep behaviour for solids, soft solids and structured liquids can be described by a Newtonian-plateau viscosity. As the stress is increased the flow behaviour usually changes into a power-law dependence of steady-state shear rate on shear stress. For structured liquids and soft solids, this behaviour generally gives way to Newtonian behaviour at the highest stresses. For structured liquids this transition from very high (creep) viscosity (>106 Pa.s) to mobile liquid (

The yield stress—a review or ‘παντα ρει’—everything flows?

The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

A fundamental study of the deposition and aging of a thin incipient wax-oil gel that is formed during the flow of waxy oils in cooled pipes was performed. The solubility of high molecular weight paraffins in naphthenic, aromatic or paraffinic solvents is very low and decreases rapidly with decreasing temperature. This property of the paraffins leads to the formation of gels of complex morphology that deposit on the cold walls of the subsea pipelines during the flow of waxy crudes. This deposition reduces the pipe diameter and decreases the flow capacity of the pipe. These wax-oil gels contain a large fraction of oil trapped in a 3-D network structure of the wax crystals that behaves as a porous medium. After the incipient gel is formed, wax molecules continue to diffuse into this structure, thereby increasing its wax content. A model system of wax and oil mixture was used to understand the aging process of the wax-oil gels, which hardens the wax deposit with time. To understand the physics of the aging process for incipient thin-film deposits, a series of laboratory flow loop experiments was performed. The aging process was a counterdiffusion phenomenon with a critical carbon number above which wax molecules diffuse into the gel deposit and below which oil molecules diffuse out of the deposit. The aging rate of the gel deposit depends on the oil flow rate and the wall temperature. A mathematical model developed predicted the growth and wax content of the gel deposit on externally cooled pipe walls. The theory agreed with experiments excellently for thin gels.

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Formation and Aging of Incipient Thin Film Wax-Oil Gels

Yield stress fluids are encountered in a wide range of applications: toothpastes, cements, mortars, foams, muds, mayonnaise, etc. The fundamental character of these fluids is that they are able to flow (i.e., deform indefinitely) only if they are submitted to a stress above some critical value. Otherwise they deform in a finite way like solids. The flow characteristics of such materials are difficult to predict as they involve permanent or transient solid and liquid regions that are generally hard to locate a priori. Here we review the present state of the art as it appears from experimental data for flows of simple (non-thixotropic) yield stress fluids under various conditions, viz., uniform flows in straight channels or rheometrical geometries, complex stationary flows in channels of varying cross-section such as extrusion, expansion, flow through a porous medium, transient flows such as flows around obstacles, spreading, spin-coating, squeeze flow, and elongation. The effects of surface tension, confinement, and secondary flows are also reviewed. We focus especially on experimental work identifying internal flow characteristics that can be compared with numerical predictions. It is shown in particular that: (i) deformations in the solid regime can play a critical role in transient flows; (ii) the yield character is not apparent in the flow field when the boundary conditions impose large deformations; (iii) the yield character is lost in secondary flows.

Yield stress fluid flows: A review of experimental data

https://pureadmin.qub.ac.uk/ws/files/202071352/20200310_Paper_on_Physics_in_DFC_revised_1_.pdf

Extrusion-based additive manufacturing with cement-based materials – Production steps, processes, and their underlying physics: A review

A novel approach for modeling the mechanical behavior of thixotropic viscoplastic fluids is presented. Non-monotonic flow curves, stress overshoot during microstructure breakdown flows at constant shear rate, and viscosity bifurcation are some of the common aspects of structured fluids that are predicted by the new model. It involves two evolution equations, one for the stress and the other for the structure parameter. Simple ideas are employed to describe the microstructure, and, as a result, a model with a clear physical basis is obtained. In addition to the flow curve, which by construction is exactly predicted, it is shown that the model is able to predict correctly the behavior observed in the usual rheometric transient flows, among which abrupt changes in shear rate (microstructure buildup or breakdown experiments) and abrupt changes in shear stress (viscosity bifurcation experiments). The model is frame-indifferent and applicable to complex flows.

Modeling the thixotropic behavior of structured fluids

A constitutive model for structured fluids is presented. Its predictive capability includes thixotropy, viscoelasticity and yielding behavior. It is composed by two differential equations, one for the stress and the other for the structure parameter—a scalar quantity that represents the structuring level of the fluid. The equation for stress is obtained in accordance with a simple mechanical analog composed by a structuring-level-dependent Maxwell element in parallel with a Newtonian element, leading to an equation of the same form as the Jeffreys (or Oldroyd-B) equation. The relaxation and retardation times that arise are functions of the structure parameter. The ideas found in de Souza Mendes, J. Non-Newtonian Fluid Mech., 2009, 164, 66 are employed for the structure parameter equation as well as for the dependencies on the structure parameter of the structural viscosity and structural shear modulus. The model is employed in constant-rate, constant-stress, and oscillatory shear flows, and its predictive capability is shown to be excellent for all cases.

Thixotropic elasto-viscoplastic model for structured fluids

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 unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids

The literature on thixotropy modeling is reviewed, with particular emphasis on models for yield stress materials that possess elasticity. The various possible approaches that have been adopted to model the different facets of the mechanical behavior of this kind of materials are compared and discussed in detail. An appraisal is given of the advantages and disadvantages of algebraic versus differential stress equations. The thixotropy phenomenon is described as a dynamical system whose equilibrium locus is the flow curve, and the importance of using the flow curve as an input of the model is emphasized. Different forms for the evolution equation for the structure parameter are analyzed, and appropriate choices are indicated to ensure a truthful description of the thixotropy phenomenon.

A critical overview of elasto-viscoplastic thixotropic modeling

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.

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Paulo R. de Souza Mendes

Papers

Modeling the thixotropic behavior of structured fluids

Thixotropic elasto-viscoplastic model for structured fluids

A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids

A critical overview of elasto-viscoplastic thixotropic modeling

Bingham’s model in the oil and gas industry