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© 2018 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Supplementary Raw Research Data, is open data under the CC BY license http://creativecommons.org/licenses/by/4.0/ This author accepted manuscript is made available following 24 month embargo from date of publication (October 2018) in accordance with the publisher’s archiving policy, The start-up flow of a Bingham plastic in a channel is considered and Safronchik’s solution [1] for the initial evolution of the yield surface and the core velocity is revisited. Stricter time bounds for the validity of the above solution are derived and the solution is extended to include the velocity profile in the evolving yielded zone. Comparisons are made with another approximate solution derived under the assumption that the velocity in the yielded zone is parabolic adjusting with the evolving yield surface. This approximation performs well for small values of the yield stress, or, equivalently, for large values of the imposed pressure gradient.

We provide benchmark results for a transient variant of the lid-driven cavity problem, where the lid motion is suddenly stopped and the flow is left to decay under the action of viscosity. Results include Newtonian as well as Bingham flows, the latter having finite cessation times, for Reynolds numbers Re ∈ [1, 1000] and Bingham numbers Bn ∈ [0, 10]. The finite-volume method and Papanastasiou regularisation were employed. A combination of Re and Bn, the effective Reynolds number, is shown to convey more information about the flow than either Re or Bn alone. A time scale which characterises the flow independently of the geometry and flow parameters is proposed. © 2015, Springer-Verlag Berlin Heidelberg. 55 1 51 66 Cited By :6

We analyse the circular Couette flow of Herschel–Bulkley fluids to investigate the validity of the assumption that the rate of strain distributions across the gap share a common point. It is demonstrated that this is true only with fully-yielded Bingham -plastic flow. In other cases, e.g., in partially-yielded Bingham-plastic flow or fully-yielded Herschel–Bulkley flow, the common point for the fully-yielded Bingham case provides a good approximation for determining material constants only if the gap is sufficiently small. We also revisit the important issue of determining material properties of viscoplastic fluids by using “true values” for the rate of strain and demonstrate that the material properties can be very different from those obtained using “apparent’ values for the rate of strain. 260 101 108

We study the flow of a thixotropic fluid around a cylinder. The rheology of the fluid is described by means of a structural viscoplastic model based on the Bingham constitutive equation, regularised using the Papanastasiou regularisation. The yield stress is assumed to vary linearly with the structural parameter, which varies from zero (completely broken structure) to one (fully developed skeleton structure), following a first-order rate equation which accounts for material structure break-down and build-up. The results were obtained numerically using the Finite Element Method. Simulations were performed for a moderate Reynolds number of 45, so that flow recirculation is observed behind the cylinder, but vortex shedding does not occur. The effects of the Bingham number and of the thixotropy parameters are studied. The results show that the viscous character of the flow can be controlled within certain limits through these parameters, despite the fact that the Reynolds number is fixed. © 2014 Elsevier B.V. 220 44 56 Cited By :2

The objective of this presentation is to show and explain why semisolid slurries can fill thin sections at seemingly unlimited flow velocity the suitability of SSM parts with very thin sections is a characteristic of the process that is often overlooked by the industry. This characteristic provides a unique opportunity for new advanced applications of the process, not possible by other existing metal-mold casting methods. © (2015) Trans Tech Publications, Switzerland. 217-218 159 165 159-165

An essential element for the integration of a semisolid process in the production of complex commercial components is the availability of accurate mathematical and computational tools that could describe both the rheological behavior and the material characteristics of the suspension, which are strongly affected from its internal structure and its evolution during deformation. In this study we considered the squeeze flow experiment, which is a standard method used to determine material properties of semisolid slurries, where a fixed amount of material is compressed from its topside either under constant load or constant velocity, while the bottom side remains fixed. Through high fidelity computational modeling we simulated the classical compression experiment by including the effects of thixotropy in order to demonstrate its role in determining material constants. More specifically a structural viscoplastic model based on the Bingham plastic constitutive equation is proposed. The yield stress is assumed to vary linearly with the structural parameter which follows a first-order rate equation accounting for the material structure break-down and build-up. The development of the yielded/unyielded regions in relation to material structural changes is analyzed. Furthermore, we performed also simulations, where the compression is interrupted for a short time, in order to study the material internal structure after a short relaxation time. © (2015) Trans Tech Publications, Switzerland. 217-218 121 129 Sponsors: Conference code: 107639

In this work we revisit the issue of obtaining true material constants for semisolid slurries. Therefore, we consider the circular Couette flow of Herschel-Bulkley fluids. We first show how true constants can be obtained using an iterative procedure from experimental data to theory and vice versa. The validity of the assumption that the rate-of-strain distributions across the gap share a common point is also investigated. It is demonstrated that this is true only for fully-yielded Bingham plastics. In other cases, e.g., for partially-yielded Bingham plastics or fully-yielded Herschel-Bulkley materials, the common point for the fully-yielded Bingham case provides a good approximation for determining the material constants only if the gap is sufficiently small. It can thus be used to simplify the iterative procedure in determining the material constants. © 2016 Trans Tech Publications, Switzerland. 256 153 172 Sponsors: Conference code: 184809

A standard method used to determine material properties of semi-solid slurries is the squeeze flow experiment a fixed amount of material is squeezed under constant force or velocity and the relation between the force and the displacement of the sample provides information about the rheology of the slurry. The objective of this work is to contribute to the further development of the squeeze flow methodology in order to accurately determine material properties. This is achieved by a model that accounts for the finite yield stress and the thixotropy of the slurry. More specifically a structural viscoplastic model based on the Bingham plastic constitutive equation is proposed. The yield stress is assumed to vary linearly with the structural parameter which follows a first-order rate equation accounting for the material structure break-down and build-up. Numerical experiments of squeeze flow under either constant load or constant velocity are presented and discussed. Comparisons with their non-thixotropic counterparts are made in the case of compression under constant load. The development of the yielded/unyielded regions in relation to material structural changes is analyzed. The numerical results show that initially thixotropy does not affect the flow. However, once the structure is destroyed, the unyielded regions grow slower than the non-thixotropic case allowing for longer compression of the sample. Under constant force the structure may be destroyed at the early stages of the compression but at a later time it re-builds steadily till the cessation of the flow experiment. Under constant velocity, however, the structure is destroyed steadily. Depending then on the case, the final internal structure of the squeezed material can vary significantly. This is an important issue that needs to be taken into consideration in the evaluation of the material parameters. © 2012 Elsevier B.V. 193 103 115 Cited By :13

The 3rd meeting on “Viscoplastic Fluids: From Theory to Application” was held in the lovely coastal city of Limassol, Cyprus. It was organized by the Hellenic Society of Rheology, under the auspices of ESR, with the help and encouragement of Neil Balmforth and Ian Frigaard, who organized the 1st meeting held in Banff, Canada (22–27 October 2005). The 2nd meeting took place in Monte Verita, Switzerland (14–18 October 2007). The goal of these workshops is to promote interactions between people from different communities working on viscoplastic fluids. With 50 registered participants from 13 countries (see Table 1 and Fig. 1), the workshop was really an international event. The scientific program consisted of 28 oral communications, five poster contributions, and three invited talks. The workshop spanned different topics, such as physical processes involved in yielding, fluid mechanics, and industrial and other applications. All aspects were studied through experiments, numerical simulation, and mathematical modelling. A brief summary of the different presentations follows.

The flow and shape evolution during the compression of a finite amount of a Bingham plastic is investigated by means of numerical simulations. The problem relates to the popular compression test used for the rheological characterization of non-Newtonian fluids. The flow is modelled in Lagrangian coordinates using the Papanastasiou regularization for the Bingham plastic and a mixed-Galerkin finite element method. Simulations have been performed for compression under both constant load and constant velocity. Results for various Reynolds and Bingham numbers are presented and discussed. © 2007 Elsevier B.V. All rights reserved. 143 1 38 47 Cited By :15

Semisolid materials are suspensions of metal alloys which are processed while in a mushy state. In this state, the suspensions behave as viscoplastic materials with time-dependent material properties. During processing, the material is injected at high speed into a mold cavity with the process lasting only fractions of a second. The short-term transient material response is thus very important for the understanding of the rheology and the further development of the process. A theory based on the Herschel-Bulkley flow model appropriate for the short-term breakage of welded bonds in semisolid metal slurries is proposed. The "strength" of the slurry due to these bonds is assumed to be a function of a coherency parameter which is proportional to the number of welded bonds that break during the application of shear. The evolution of this parameter is described by a first-order kinetics. Using a novel and simple computational method, well suited for free and moving-boundary problems, we study the flow between two coaxial cylinders and obtain accurate results for the evolution of the structure, the extent of the yielded domain and the evolution of the stress. The results and conclusions apply directly to the design and analysis of rotational rheometer experiments for semisolid metal slurries and suspension systems exhibiting similar behavior. © 2006 Elsevier B.V. All rights reserved. 142 1-3 199 206 Cited By :16

A solar-heating-and-cooling (SHC) system, consisting of a flat-plate solar collector array, a hot water storage tank, and an absorption chiller unit is designed and modeled to satisfy thermal loads (space heating, domestic hot water, and space cooling). The system is applied for Nicosia, Cyprus, a location with prolonged summer-like conditions, where heating demand is moderate, while space cooling demand is comparatively very high. The study investigates the potential of a solar system installed and operated onsite in a detached single-family household to satisfy all necessary thermal loads. The hot water storage tank is also connected to an auxiliary heater (diesel-fired boiler) to supplement solar heating, when needed. The main purpose of the study is to model the overall system and contact a parametric study that will determine the optimum economic system performance in terms of design parameters. The system is compared, through a cost analysis, to an electric heat pump (EHP) system. It is found that the optimum system combination of solar collector area and volumetric capacity of the hot water storage tank is 70m2 and 2000L, respectively. The total annualized cost (in USD) for the optimum SHC system is $3,719. The sensitivity analysis showed that the SHC system would be unfavorable to compete with EHP technology, if the solar collector cost is above $360/m2. © 2015 Elsevier Ltd. 117 59 73 59-73

We investigate numerically the interactions of two-dimensional jets of Bingham plastic and Herschel-Bulkley fluids with a vertical surface at a distance from the die exit. This problem simulates the early stages of filling of a planar cavity. Our main objective is to explain the flow instabilities observed during the processing of semisolid materials. The effects of the Reynolds and Bingham numbers and of the inlet boundary conditions on both the filling and the stability of the jet are established by means of numerical time-dependent calculations. © 2003 Elsevier B.V. All rights reserved. 116 1 19 32 Cited By :31

We extend our recent work on the creeping flow of a Bingham fluid in a lid-driven cavity, to the study of inertial effects, using a finite volume method and the Papanastasiou regularisation of the Bingham constitutive model (Papanastasiou, 1987) [7]. The finite volume method used belongs to a very popular class of methods for solving Newtonian flow problems, which use the SIMPLE algorithm to solve the discretised set of equations, and have matured over the years. By regularising the Bingham constitutive equation it is easy to extend such a solver to Bingham flows since all that this requires is to modify the viscosity function. This is a tempting approach, since it requires minimum programming effort and makes available all the existing features of the mature finite volume solver. On the other hand, regularisation introduces a parameter which controls the error in addition to the grid spacing, and makes it difficult to locate the yield surfaces. Furthermore, the equations become stiffer and more difficult to solve, while the discontinuity at the yield surfaces causes large truncation errors. The present work attempts to investigate the strengths and weaknesses of such a method by applying it to the lid-driven cavity problem for a range of Bingham and Reynolds numbers (up to 100 and 5000 respectively). By employing techniques such as multigrid, local grid refinement, and an extrapolation procedure to reduce the effect of the regularisation parameter on the calculation of the yield surfaces (Liu et al., 2002) [55], satisfactory results are obtained, although the weaknesses of the method become more noticeable as the Bingham number is increased. © 2014 Elsevier B.V. 208-209 88 107 Cited By :15

In this paper we study steady flow of Herschel-Bulkley fluids in a canonical three-dimensional expansion. The fluid behavior was modeled using a regularized continuous constitutive relation, and the flow was obtained numerically using a mixed-Galerkin finite element formulation with a Newton-Raphson iteration procedure coupled to an iterative solver. Results for the topology of the yielded and unyielded regions, and recirculation zones as a function of the Reynolds and Bingham numbers and the power-law exponent, are presented and discussed for a 2:1 and a 4:1 expansion ratio. The results reveal the strong interplay between the Bingham and Reynolds numbers and their influence on the formation and break up of stagnant zones in the corner of the expansion and on the size and location of core regions. © 2001 Elsevier Science B.V. All rights reserved. 100 77 96 77-96

Herschel-Bulkley fluids are materials that behave as rigid solids when the local stress τ is lower than a finite yield stress τ0, and flow as nonlinearly viscous fluids for τ > τ0. The flow domain then is characterized by two distinct areas, τ τ0. The surface τ = τ0 is known as the yield surface. In this paper, by using analytic solutions for antiplane shear flow in a wedge between two rigid walls, we discuss the ability of regularized Herschel-Bulkley models such as the Papanastasiou, the bi-viscosity and the Bercovier and Engelman models in determining the topography of the yield surface. Results are shown for different flow parameters and compared to the exact solutions. It is concluded that regularized models with a proper choice of the regularizing parameters can be used to both predict the bulk flow and describe the unyielded zones. The Papanastasiou model predicts well the yield surface, while both the Papanastasiou and the bi-viscosity models predict well the stress field away from τ = τ0. The Bercovier and Engelman model is equivalent to the Papanastasiou model provided a proper choice of the regularization parameter δ is made. It is also demonstrated that in some cases the yield surface can be effectively recovered using an extrapolation procedure based upon an analytical representation of the solution. © 1999 The Society of Rheology. 43 463 483 463-483

We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385-404]. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely deteriorates as the Bingham number increases, with a corresponding increase in the non-linearity of the equations. It is shown that using the SIMPLE algorithm in a multigrid context dramatically improves convergence, although the multigrid convergence rates are much worse than for Newtonian flows. The numerical results obtained for Bingham numbers as high as 1000 compare favourably with reported results of other methods. © 2013 Elsevier B.V.. 195 19 31 Cited By :18

The purpose of this work is to simulate shear rejuvenation and aging effects in shear thinning yield stress fluids in a typical rotational rheometer and to provide a common framework to describe the behavior of yield stress materials in general. This is particularly important in the determination of material constants under both steady and unsteady conditions. The breakdown and buildup of structure are studied using a theory based on the Herschel-Bulkley flow model that it is consistent with experimental data. The theory is implemented using a novel computational method. Interestingly, the simulations reveal the existence of time-dependent shear banding that occurs within the gap when the macroscopically imposed shear rate is below a certain critical value. Shear banding is analyzed in detail and results showing the effects of major parameters on the phenomenon are presented. © 2009 Elsevier B.V. All rights reserved. 158 1-3 6 17 Cited By :22

The time-dependent, compressible extrusion of a Carreau fluid is solved over the reservoir-die-extrudate region using finite elements in space and a fully implicit scheme in time. A nonmonotonic slip law based on experimental data on polyethylene melts is assumed to hold along the die wall and the velocity at the entrance of the reservoir is taken to be fixed and uniform. As in the case of the extrudate-swell flow, the combination of compressibility and nonlinear slip leads to self-sustained oscillations of the pressure drop and of the mass flow rate in the unstable regime. The effects of the reservoir volume, the imposed flow rate, and the capillary length on the amplitude and the frequency of the pressure and free surface oscillations are studied and comparisons are made with experimental observations. © 2006 Elsevier B.V. All rights reserved. 146 1-3 30 44 Cited By :16

Numerical simulations are undertaken for the transient squeeze flow between parallel plates under a constant load. The conservation equations are solved via the finite element method in space and the Crank-Nicolson method in time. The constitutive equation used to describe the semi-concentrated fiber suspension is an integral equation proposed by Dinh and Armstrong for fiber-filled Newtonian liquids. New results are obtained for both random and aligned fibers and for different levels of squeeze force, and these are compared with the corresponding Newtonian ones, which are slightly lower. The fiber orientation in the flow field is also obtained for different points in the material. © 2006 Elsevier B.V. All rights reserved. 146 114 124 114-124

The present study concentrates on Bingham fluid filling of a 2-D cavity and examines the relative importance of inertial, viscous and yield stress effects on the filling profile. The results presented are obtained using PAM-CAST/SIMULOR, which was modified by introducing a regularized Bingham fluid constitutive relation. The results identify five different flow patterns: `mound', `disk,' `shell,' `bubble,' and a `transition flow' between that of mound and bubble patterns. A complete map of the flow patterns as a function of the Reynolds and Bingham numbers is also presented and discussed using dimensional and physical arguments within a simplified theoretical framework. 96 383 403 383-403

The flow development of Herschel-Bulkley fluids in a sudden three-dimensional square expansion is studied numerically. The flow is modeled using the mixed-Galerkin finite element formulation to solve the conservation of mass and momentum equations. The Herschel-Bulkley material behavior is described using a regularized model based on the Papanastasiou model. Solutions are obtained for a downstream-to-upstream expansion ratio of 2:1 and for a wide range of pressure gradient values and rheological parameters. The results show that, during the evolution of the flow, two core regions and dead zones at the corners are formed. The extent of the core regions decreases with the pressure gradient and the Reynolds number, and increases with the power-law index. It is also found that the volume flow rate at steady flow increases with the pressure gradient, power-law index, and Reynolds number. © 7999 The Society of Rheology. 43 485 498 485-498

The interest in the theoretical investigation of the flow behavior of fiber suspensions during manufacturing processes has increased considerably due to the increased interest in the use of composite materials. The unsteady flow of semi-concentrated fiber suspensions in two dimensions is investigated using the Generalized Eulerian-Lagrangian (GEL) formulation. The integral constitutive relation proposed by Dinh and Armstrong is used to express the stress tensor. Currie approximation is then used to express the integral expression using a differential expression involving the finite deformation (Finger and Cauchy) tensors and their invariants. A semi-implicit finite difference scheme is developed which expresses the finite deformation tensors in terms of the kinematics of the flow. The evolution of fiber orientation is also likewise expressed in terms of the flow kinematics. In order to determine the accuracy of the semi-implicit finite difference scheme, numerical results are compared with exact analytic solutions for a radially diverging source flow. The numerical efficiency and ease of implementation of the method are discussed. The method is then used to simulate the filling of a simple two-dimensional injection molding cavity. © 1994. 55 115 136 115-136

The extrusion of a rod-like fiber suspension is a Newtonian solvent, as a first step to the fast and inexpensive production of composite materials, is investigated. The analysis is carried out by means of an integral constitutive equation for a non-dilute suspension, streamlined finite element for liquid with memory, and Newton iteration of nonlinear integro-differential equations. The predictions show substantial differences between dilute and nondilute fiber suspension regarding the processing conditions (pressure drop, velocity distribution, die-swell) and the resulting fiber orientation. Nondilute fiber suspensions exhibit substantial shear-thinning and negligible elasticity as evidenced by the small die-swell, and fiber concentration viscosity-thickening as evidenced by the large pressure drop. The fiber orientation is computed by solving the orientation distribution function along selected streamlines of the complex velocity field. It is shown that the fiber orientation far downstream can be made independent of the random fiber orientation at the inlet. © 1987. 25 313 328 313-328