The objective of this review is to examine how the concept of plasticity is used in geophysical fluid dynamics. Rapid mass movements such as snow avalanches or debris flows involve slurries of solid particles (ice, boulder, clay, etc.) within an interstitial fluid (air, water). The bulk behavior of these materials has often been modeled as plastic materials, i.e., a plastic material yields and starts to flow once its stress state has significantly departed from equilibrium. Two plastic theories are of common use in fluid dynamics: Coulomb plasticity and viscoplasticity. These theories have little in common, since ideal Coulomb materials are two-phase materials for which pore pressure and friction play the key role in the bulk dynamics, whereas viscoplastic materials (e.g., Bingham fluids) typically behave as single-phase fluids on the macroscopic scale and exhibit a viscous behavior after yielding. Determining the rheological behavior of geophysical materials remains difficult because they encompass coarse, irregular particles over a very wide range of size. Consequently, the true nature of plastic behavior for geophysical flows is still vigorously debated. In this review, we first set out the continuum-mechanics principles used for describing plastic behavior. The notion of yield surface rather than yield stress is emphasized in order to better understand how tensorial constitutive equations can be derived from experimental data. The notion of single-phase or two-phase behaviors on the macroscopic scale is then examined using a microstructural analysis on idealized suspensions of spheres within a Newtonian fluid; for these suspensions, the single-phase approximation is valid only at very high or low Stokes numbers. Within this framework, the bulk stress tensor can also be constructed, which makes it possible to give a physical interpretation to yield stress. Most of the time, depending on the bulk properties (especially, particle size) and flow features, bulk behavior is either Coulomb-like or viscoplastic in simple-shear experiments. The consequences of the rheological properties on the flow features are also examined. Some remarkable properties of the governing equations describing thin layers flowing down inclined surfaces are discussed. Finally, the question of parameter fitting is tackled: since rheological properties cannot be measured directly in most cases, they must be evaluated from field data. As an example, we show that the Coulomb model successfully captures the main traits of avalanche motion, but statistical analysis demonstrates that the probability distribution of the friction coefficient is not universal.

/pdf/plasticity-and-geophysical-flows-a-review-4bos64lahx.pdf

Plasticity and geophysical flows: A review

This paper gives details of new data on neutralized Carbopol 940 dispersions. Appropriate techniques have been used to characterize the physical properties of the bulk gel and inter-phase slip at the wall. Previously published data are analysed and used wherever possible. Terminology and measurement difficulties are also addressed. The structure of Carbopol dispersions can be described in terms of polydisperse glasses made of individual swollen hydrophylic elastic sponges. They display elastoplasticity, and significant dissipation both below and above their yield stress. Hardly any creep was observed over 10 months of experiments. Scaling laws are proposed for Carbopol mechanical properties as a function of concentration. Carbopol behaviour varies with the value of concentration, and in particular when comparing percolation concentration with close-packing concentration. Constitutive equations for bulk shear stresses and for friction slip at the wall can be deduced from contact mechanics which fit rheometry data and scaling laws. Herschel–Bulkley constitutive equations may be used by ignoring elasticity, normal shear stresses and transients.

Carbopol gels: Elastoviscoplastic and slippery glasses made of individual swollen sponges: Meso- and macroscopic properties, constitutive equations and scaling laws

Novel manufacturing techniques such as additive manufacturing (AM, also referred to as 3D printing) will play a critical role in building a sustainable future. AM will reduce waste, energy consumption and production time by eliminating the need to assemble components. It will also enable the mass customization of complex devices. To reach their full potential, additive manufacturing technologies should be able to combine different materials in a single processing step. Although the development of multi-material printing is in its infancy, it could have a massive impact in fields as diverse as energy storage and generation, electronic devices, healthcare or structural composites to name a few. Here we provide a critical perspective on the advances and potential of multi-material printing using direct extrusion-based printing, also known as direct ink writing (DIW) or robocasting. We will show examples of devices and structures combining a wide range of materials from ceramics to metals, polymers and carbon with particular focus on three promising applications: energy storage, lightweight composites and sensors. The goals are to assess the progress made so far, to point out specific challenges and areas for further development and to provide guidelines to those interested in multi-material DIW.

/pdf/direct-ink-writing-advances-in-multi-material-structures-for-4zfcecrv3i.pdf

Direct ink writing advances in multi-material structures for a sustainable future

Linear low-density polyethylene (LLDPE) based composites were prepared by melt compounding with 1, 2, 3 and 4 vol% of various kinds of amorphous silicon dioxide (SiO2) micro- and nanoparticles. Dynamic rheological tests in parallel plate configuration were conducted in order to detect the role of the filler morphology on the rheological behaviour of the resulting micro- and nanocomposites. A strong dependence of the rheological parameters from the filler surface area was highlighted, with a remarkable enhancement of the storage shear modulus (G') and of the viscosity (η) in fumed silica nanocomposites and in precipitated silica microcomposites, while glass microbeads only marginally affected the rheologi- cal properties of the LLDPE matrix. This result was explained considering the formation of a network structure arising from particle-particle interactions due to hydrogen bonding between silanol groups. A detailed analysis of the solid like behav- iour for the filled samples at low frequencies was conducted by fitting viscosity data with a new model, based on a modifi- cation of the original De Kee-Turcotte expression performed in order to reach a better modelling of the high-frequency region.

http://www.expresspolymlett.com/letolt.php?file=EPL-0001281&mi=c

Linear low-density polyethylene/silica micro- and nanocomposites: dynamic rheological measurements and modelling

The boundary-layer flow due to a rotating disk is considered for a number of generalised Newtonian fluid models. In the limit of large Reynolds number the flow inside the three-dimensional boundary-layer is determined via a similarity solution. Results for power-law and Bingham plastic fluids agree with previous investigations. We present solutions for fluids that adhere to the Carreau viscosity model. It is well known that unlike the power-law and Bingham models the Carreau model is applicable for vanishingly small, and infinitely large shear rates, as such we suggest these results provide a more accurate description of non-Newtonian rotating disk flow.

https://radar.brookes.ac.uk/radar/file/04967678-2027-47d2-8878-f8038dd482a5/1/griffiths2015flow.pdf

Flow of a generalised Newtonian fluid due to a rotating disk

A modified Herschel–Bulkley model [E. Mitsoulis, S.S. Abdali, Flow simulation of Herschel–Bulkley fluids through extrusion dies, Can. J. Chem. Eng. 71 (1993) 147–160] predicts an infinite apparent viscosity at vanishing shear rate. Furthermore, the dimensions of one parameter depend on another parameter. In this contribution, we propose a generalized model based on earlier work by De Kee and Turcotte [D. De Kee, G. Turcotte, Viscosity of biomaterials. Chem. Eng. Commun. 6 (1980) 273–282] and on the work of Papanastasiou [T.C. Papanastasiou, Flows of materials with yield, J. Rheol. 31 (1987) 385–404] to solve the problems associated with the modified Herschel–Bulkley model. Compared to the responses of the Papanastasiou model and the modified Herschel–Bulkley model, the proposed generalized model provides the expected improvements and is capable of predicting successfully the rheological behavior (viscosity and yield stress) of Carbopol 980 dispersions.

Non-Newtonian fluids with a yield stress

We performed a numerical study for the cessation of Couette flow of non-Newtonian fluids with a yield stress. We solved this problem by employing our recently developed constitutive model for such fluids [H. Zhu, Y.D. Kim, D. De Kee, Non-Newtonian fluids with a yield stress, J. Non-Newton. Fluid Mech. 129 (2005) 177]. In the numerical simulation we adopted the finite volume method with an implicit scheme in time. We computed the finite stopping times for fluids with different yield stresses and shear thinning properties. Our numerical results show that the yield stress play a important role in determining the finite stopping times for non-Newtonian fluids with a yield stress; on the other hand, the shear thinning property does affect the finite stopping times in that the larger the degree of shear thinning, the longer the finite stopping time. The present study is an extension of the previous work by Chatzimina et al. [M. Chatzimina, G.C. Georgiou, I. Argyropaidas, E. Mitsoulis, R.R. Huilgol, Cessation of Couette and Poiseuille flows of a Bingham plastic and finite stopping times, J. Non-Newton. Fluid Mech. 129 (2005) 117], in which only Bingham fluids are considered.

A numerical study for the cessation of Couette flow of non-Newtonian fluids with a yield stress

Flow-induced structural anisotropy could result when a complex fluid system is removed from equilibrium by means of hydrodynamic forces. In this paper, a general theory is developed to model flow-induced anisotropic behavior of complex viscoelastic systems such as polymer solutions/melts and suspensions. The rheological properties are characterized by viscosity and relaxation time tensors. We consider a second-rank tensor as a measure of the microstructure. We consider the effect of the flow on the structural changes, i.e. the evolution of the microstructure tensor is governed by a relaxation-type differential equation. We also propose that the viscosity and the relaxation time tensors depend on the second-rank microstructure tensor, that is as the microstructure tensor changes with the applied rate of deformation, the viscosity and relaxation time tensors evolve accordingly. As an example we consider the elongational flows of two complex fluids.

H. Zhu

Papers

Non-Newtonian fluids with a yield stress

A numerical study for the cessation of Couette flow of non-Newtonian fluids with a yield stress

A constitutive model for flow-induced anisotropic behavior of viscoelastic complex fluids