The ensuing mechanical response to stressing or straining a structured liquid results in various viscoelastic phenomena, either in the linear region where the microstructure responds linearly with respect to the stress and strain but does not itself change, or in the nonlinear region where the microstructure does change in response to the imposed stresses and strains, but does so reversibly. The complication of thixotropy arises because this reversible, microstructural change itself takes time to come about due to local spatial rearrangement of the components. This frequently found time-response of a microstructure that is itself changing with time makes thixotropic, viscoelastic behaviour one of the greatest challenges facing rheologists today, in terms of its accurate experimental characterisation and its adequate theoretical description. Here a history of thixotropy is given, together with a description of how it is understood today in various parts of the scientific community. Then a mechanistic description of thixotropy is presented, together with a series of applications where thixotropy is important. A list of different examples of thixotropic systems is then given. Finally the various kinds of theories that have been put forward to describe the phenomenon mathematically are listed.

Thixotropy—a review

The development and formulation of printable inks for extrusion-based 3D bioprinting has been a major challenge in the field of biofabrication. Inks, often polymer solutions with the addition of crosslinking to form hydrogels, must not only display adequate mechanical properties for the chosen application but also show high biocompatibility as well as printability. Here we describe a reproducible two-step method for the assessment of the printability of inks for bioprinting, focussing firstly on screening ink formulations to assess fibre formation and the ability to form 3D constructs before presenting a method for the rheological evaluation of inks to characterise the yield point, shear thinning and recovery behaviour. In conjunction, a mathematical model was formulated to provide a theoretical understanding of the pressure-driven, shear thinning extrusion of inks through needles in a bioprinter. The assessment methods were trialled with a commercially available creme, poloxamer 407, alginate-based inks and an alginate-gelatine composite material. Yield stress was investigated by applying a stress ramp to a number of inks, which demonstrated the necessity of high yield for printable materials. The shear thinning behaviour of the inks was then characterised by quantifying the degree of shear thinning and using the mathematical model to predict the window of printer operating parameters in which the materials could be printed. Furthermore, the model predicted high shear conditions and high residence times for cells at the walls of the needle and effects on cytocompatibility at different printing conditions. Finally, the ability of the materials to recover to their original viscosity after extrusion was examined using rotational recovery rheological measurements. Taken together, these assessment techniques revealed significant insights into the requirements for printable inks and shear conditions present during the extrusion process and allow the rapid and reproducible characterisation of a wide variety of inks for bioprinting.

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Proposal to assess printability of bioinks for extrusion-based bioprinting and evaluation of rheological properties governing bioprintability

The yield stress of many yield stress fluids has turned out to be difficult to determine experimentally. This has led to various discussions in the literature about those experimental difficulties, and the usefulness and pertinence of the concept of yield stress fluids. We argue here that most of the difficulties disappear when taking the thixotropy of yield stress fluids into account, and will demonstrate an experimental protocol that allows reproducible data to be obtained for the critical stress necessary for flow of these fluids. As a bonus, we will show that the interplay of yield stress and thixotropy allows one to account for the ubiquitous shear localization observed in these materials. However, due to the thixotropy the yield stress is no longer a material property, since it depends on the (shear) history of the sample.

Yield stress and thixotropy: on the difficulty of measuring yield stresses in practice

Yield stress and thixotropy : on the difficulty of measuring yield stresses in practice

A nonlinear rheological model which accounts for the time-dependent elastic, viscous and yielding phenomena is developed in order to describe the flow behavior of thixotropic materials which exhibit yield stress. A key feature of the formulation is a smooth transition from an ‘elastically’ dominated response to a ‘viscous’ response without a discontinuity in the stress–strain curve. The model is phenomenological and is based on the kinetic processes responsible for structural changes within the thixotropic material. As such, it can predict thixotropic effects, such as stress overshoot during start-up of a steady shear flow and stress relaxation after cessation of flow. Thus this model extends a previously proposed viscoplastic model [J. Rheol. 34 (1991) 647] to include thixotropy. An analysis and comparison to experimental data involving oscillatory shear flow are provided to evaluate the accuracy of the model and to estimate the model parameters in a prototype concentrated suspension. The experiments were conducted using a series of concentrated suspensions of silicon particles and silicon carbide whiskers in polyethylene. The data obtained with this experimental system indicated much better agreement between the theory and experiments that obtained in earlier work.

Transient phenomena in thixotropic systems

In this work, a new model for viscosity decay at constant shear rate is tested and the thixotropic behavior of representative food products is experimentally analyzed. The equilibrium viscosity (or steady‐state viscosity) of some food products, obtained after a sufficiently long time of shear at a constant shear rate, is found to be well represented by the Herschel‐Bulkley model and by an exponential model in which a maximum of two terms of an infinite series are required. The model for viscosity decay, that is, the decrease in viscosity with time at constant shear rate, assumes nth order kinetics for the decay of a structural parameter λ. The rate constant k, for the decay of λ, is found to be a power law function of the shear rate. The equation for structure decay is combined with a scalar constitutive equation for the shear stress and the resulting model represents adequately the data for viscosity decay of foodstuffs in the range of shear rates 50<γ<5420 s−1. Data for suspensions such as tomato juice...

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Papers

Flow Properties of Time‐Dependent Foodstuffs