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An isothermal and incompressible flow of a magnetohydrodynamici (MHD) viscoplastic fluid has been examined while passing through the area among two co-rotating rolls. Applying lubrication approximation theory (LAT), the basic flow equations of mass and momentum are derived and subsequently non-dimensionalized. Exact solutions of velocity and pressure gradient distributions are evaluated. To evaluate the complex integrals, Trapezoidal rule for numerical integration is used. The significant engineering parameters like, the roll separation force, maximum pressure and the power transferred to the fluid by the rolls, are also numerically computed. The results demonstrate that the velocity field and pressure gradient are significantly affected due to the presence of the viscoplastic parameter. Magnetic field is found to be the controlling parameter for power input, separating force, and distance among attachment and detachment points, being extremely beneficial for the roll coating process. It has been learnt through this study that MHD can be an effective tool in the coating industry to regulate the engineering quantities in which coating thickness is the most important.

Yield-stress materials such as structurally complex formulations of paints, slurries, and waxes have been long ubiquitous in the coating industry, though the practice of coating engineering remains largely empirical as the fundamental role of viscoplasticity due to the yield stress of the coating material in most coating applications is still unclear. Here, we couple a recent harmonic mean viscosity regularization for the Bingham model with a well-established finite element/elliptic mesh generation method for free surface flows to present a detailed computational study of slot coating applications of viscoplastic materials. By neglecting inertia and focusing on the downstream section of a slot coater, we introduce suitable dimensionless parameters to discuss a comprehensive set of results that unravels a striking impact of viscoplasticity on the flow dynamics and low-flow limit. We show that viscoplastic effects have major implications to the velocity field and recirculation pattern in the coating bead as well as to the development length and free surface in the film formation region. Most importantly, we find that viscoplastic effects markedly widen the operating window of the process, delaying the onset of the low-flow limit and thereby suggesting that structurally complex yield-stress materials may be used to coat thinner films and/or at higher speeds than predicted by the standards far established for simple Newtonian liquids. • Finite element simulations of slot coating flows of regularized Bingham materials. • Viscoplasticity affects the velocity field and recirculation pattern in the coating bead. • Viscoplasticity affects the development length and free surface in the film formation region. • Viscoplasticity widens the operating window of the low-flow limit of the process. • Bingham materials can be used to coat thinner and/or faster than simple Newtonian liquids. [ABSTRACT FROM AUTHOR]

An isothermal and incompressible flow of a magnetohydrodynamici (MHD) viscoplastic fluid has been examined while passing through the area among two co-rotating rolls. Applying lubrication approximation theory (LAT), the basic flow equations of mass and momentum are derived and subsequently non-dimensionalized. Exact solutions of velocity and pressure gradient distributions are evaluated. To evaluate the complex integrals, Trapezoidal rule for numerical integration is used. The significant engineering parameters like, the roll separation force, maximum pressure and the power transferred to the fluid by the rolls, are also numerically computed. The results demonstrate that the velocity field and pressure gradient are significantly affected due to the presence of the viscoplastic parameter. Magnetic field is found to be the controlling parameter for power input, separating force, and distance among attachment and detachment points, being extremely beneficial for the roll coating process. It has been learnt through this study that MHD can be an effective tool in the coating industry to regulate the engineering quantities in which coating thickness is the most important. [ABSTRACT FROM AUTHOR]

This paper analyzes the effects of yield stress and nanoparticles transport on the natural convection of viscoplastic Casson nanofluids. The non-linear coupled partial differential equations are solved numerically using Buongiorno's mathematical model. The governing parameters for the problem are the Rayleigh number (Ra), yield number (Y ), and thermophoresis and Brownian motion parameters (Nt&Nb). The effects of these parameters on the fluid flow, heat and mass transfer, and the shape of yielded and unyielded regions are examined and discussed in detail. The results demonstrate that the heat and mass transfer rates increase as the Rayleigh number increases, while the opposite behaviors are observed with increasing the yield number. The fluid is difficultly yielded at low Rayleigh number. The heat and mass transfer are primarily due to conduction at the high values of the yield number. The main effect of thermophoresis and Brownian motion parameters is on temperature and concentration distribution in the cavity. These parameters also show significant impacts on critical heat and mass transfer. [ABSTRACT FROM AUTHOR]

In this paper, we address the numerical aspects and implementation of a nonlinear viscoplastic model of the mechanical behaviour of brain tissue to simulate the dynamic responses related to impact loads which may cause traumatic injury. Among the various viscoelastic models available, we deliberately considered modifying the Norton–Hoff model in order to introduce non-typical viscoplastic softening behaviour that imitates a brain’s response just several milliseconds after a rapid impact. We describe the discretisation and three dimensional implementation of the model, with the aim of obtaining accurate numerical results in a reasonable computational time. Due to the large scale and complexity of the problem, a parallel computation technique, using a space–time finite element method, was used to facilitate the computation boost. It is proven that, after calibrating, the introduced viscoplastic-softening model is better suited for modelling brain tissue behaviour for the specific case of rapid impact loading rather than the commonly used viscoelastic models.

The paper develops a general scheme for viscoelastic materials, where the constitutive properties are described by means of measures of strain, stress, heat flux, and their time derivatives. The constitutive functions are required to be consistent with the second law of thermodynamics. Indeed, a new view is associated with the second law: the non-negative expression of the entropy production is set equal to a further constitutive function. The introduction of the entropy production as a constitutive function allows for a much wider range of models. Within this range, a scheme to obtain nonlinear models of thermo-viscoelastic materials subject to large deformations is established. Notably, the Kelvin–Voigt, Maxwell, Burgers, and Oldroyd-B viscoelastic models, along with the Maxwell–Cattaneo heat conduction, are obtained as special cases. The scheme allows also for modelling the visco-plastic materials, such as the Prandtl–Reuss work-hardening function and the Bingham–Norton fluid.

We report experimental microfluidic measurements and theoretical modeling of elastoviscoplastic materials under steady, planar elongation. Employing a theory that allows the solid state to deform, we predict the yielding and flow dynamics of such complex materials in pure extensional flows. We find a significant deviation of the ratio of the elongational to the shear yield stress from the standard value predicted by ideal viscoplastic theory, which is attributed to the normal stresses that develop in the solid state prior to yielding. Our results show that the yield strain of the material governs the transition dynamics from the solid state to the liquid state. Finally, given the difficulties of quantifying the stress field in such materials under elongational flow conditions, we identify a simple scaling law that enables the determination of the elongational yield stress from experimentally measured velocity fields. [ABSTRACT FROM AUTHOR]

The main purpose of our work is to show the impact of some pertinent parameters; such Lewis and solutal Rayleigh numbers as well as the buoyancy and the aspect ratios; on a viscoplastic materials’ double-diffusive convection which occurs within an SiC annulus; contained between a cold “and less concentric” outer circular cylinder and a hot “and concentric” inner one, to come out with innovative correlations what predict the mean transfer rates into such annulus. To do so, the physical model for the momentum conservation equation is made using the Brinkman extension of the classical Darcy equation. The set of coupled equations is solved using the finite volume method and the SIMPLER algorithm. To handle the cylinder shape in Cartesian coordinates; the Cartesian Cut-Cell approach was adopted. Subsequently, inclusive correlations of overall transfers within such viscoplastic porous annulus are set forth as a function of the governing parameters; which foresee with ±2 to ±3% the numerical predictions. Noted that the validity of the computing code was ascertained by comparing its results with experimental data and numerical ones; already available in the literature. [ABSTRACT FROM AUTHOR]

Drop coalescence in viscoplastic materials is present in various industrial applications and the environment. The plasticity of the surrounding material affects drop rise, collision, and film drainage dynamics, and knowledge about these is essential for designing and operating industrial mixer and separator units. Despite its importance, the coalescence of drops in yield stress materials is not entirely understood. In this work, we investigate the effects of the surrounding material plasticity on the rise and interfacial coalescence initiation of Newtonian drops using direct numerical simulations. Plastic effects contribute to the formation of smaller and spherical films, which facilitate the film drainage process on the one hand, but also to an increase in the resistance of the film to flow, which makes the drainage process more difficult on the other hand. The fluids' interfaces are less deformable for high surface tension regimes, and the flow resistance effects become more significant than the film shape change effects. As a result, the drainage time tends to increase with the level of plasticity. For low surface tension regimes, the fluid interface is more deformable, and film drainage time tends to decrease with an increase in the level of plasticity. [Display omitted] • Plastic effects contribute to the formation of a smaller and spherical film. • Plastic effects increase the resistance of the film to flow. • For high surface tension regimes, plasticity tends to increase the drainage time. • For low surface tension regimes, plasticity tends to decrease the drainage time. [ABSTRACT FROM AUTHOR]

An experimental and numerical investigation of the rotational rheometry of yield-stress materials is performed, using waterbased Carbopol dispersions. The flow and fluid characterization in different rheometer geometries, namely the smooth Couette, the grooved Couette, and the vane-in-cup are analysed. The bi-dimensional flow governing equations are solved numerically, using the finite volume method and Fluent software (Ansys Inc.). The viscoplastic behavior of Carbopol dispersions is modeled using the Generalized Newtonian constitutive equation with the regularized viscoplastic viscosity function proposed by de Souza Mendes and Dutra [1], herein called SMD function. The flow pattern and the presence of apparent wall slip in rheometric measurements of yield-stress materials are investigated and discussed.

Highlights • The circular Couette flow of Herschel–Bulkley fluids is analysed. • The conditions under which the rates of strain share a common point are specified. • The errors when using apparent instead of true shear rates are highlighted. • The errors in the calculated material parameters are discussed. • The findings of the present work are demonstrated on experimental data. Abstract 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. [ABSTRACT FROM AUTHOR]

An elastic-viscoplastic model (Ulrich, 2013) is combined to a multi-phase SPH formulation (Hu and Adams, 2006; Ghaitanellis et al., 2015) to model granular flows and non-cohesive sediment transport. The soil is treated as a continuum exhibiting a viscoplastic behaviour. Thus, below a critical shear stress ( i.e. the yield stress), the soil is assumed to behave as an isotropic linear-elastic solid. When the yield stress is exceeded, the soil flows and behaves as a shear-thinning fluid. A liquid-solid transition threshold based on the granular material properties is proposed, so as to make the model free of numerical parameter. The yield stress is obtained from Drucker–Prager criterion that requires an accurate computation of the effective stress in the soil. A novel method is proposed to compute the effective stress in SPH, solving a Laplace equation. The model is applied to a two-dimensional soil collapse (Bui et al., 2008) and a dam break over mobile beds (Spinewine and Zech, 2007). Results are compared with experimental data and a good agreement is obtained. [ABSTRACT FROM AUTHOR]

We have modeled an incompressible, non-isothermal flow of a magnetohydrodynamic (MHD) viscoplastic fluid when it passes through the tapered area between two co-rotating rolls. The basic conservation equations like mass, momentum, and energy based on the lubrication approximation theory (LAT) are developed, non-dimensionalized, and solved exactly for the velocity-, pressure gradient-, and temperature-distribution. The value of λ, where the sheet leaves the rolls, is calculated using Simpson’s 1/3 formula for numerical integration along with the modify regula-falsi method. Moreover, quantities of engineering interest such as extreme pressure, the roll separation force and the power transferred to the fluid by the rolls are also computed. The results show that the inclusion of the viscoplastic parameter affects the velocity field, pressure gradient-, and temperature-distribution substantially. It is found that the magnetic field provides a mechanism to control power transmission, separation force, and distance between attachment and detachment points, which are very useful for the calendering process. [ABSTRACT FROM AUTHOR]

The aim of this work is to present a computationally efficient algorithm to simulate the deformations suffered by a viscoplastic body in a solidification process. This type of problems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. In our previous papers, this difficulty has been solved by means of a duality method, known as Bermúdez–Moreno algorithm, involving a multiplier which was computed with a fixed point algorithm or a Newton method. In this paper, we will improve the former algorithms by means of a generalized duality method with variable parameters and we will present numerical results showing the applicability of the resultant algorithm to solidification processes. Furthermore, we will describe a numerical procedure to choose a constant parameter for the Bermúdez–Moreno algorithm which gives good results when it is applied to solidification processes. [ABSTRACT FROM AUTHOR]

Abstract: The inertialess immiscible displacement of a viscoplastic material by a second viscoplastic material in a pressure-driven capillary plane channel is numerically analyzed. The fluids are modeled as Bingham materials with a regularization function proposed by Papanastasiou (1987). We use an elliptic mesh generation technique, coupled with the Galerkin finite element method, to compute the velocity field and determine the position and shape of the interface. The main focus of the present paper is to investigate the fraction of mass attached to the wall and the flow regimes as functions of the capillary number, the viscosity ratio, and the yield numbers, defined as the ratio of the yield stress to the characteristic viscous stress, of the displacing and displaced materials. We also show the yielding and unyielding zones of several representative cases. We have constructed maps of the streamlines in the Cartesian space defined by the yield numbers and capillary numbers for fixed viscosity ratio in order to capture the bypass and recirculating flow regimes. We show that for the cases we analyzed, changing the yield number of the displaced fluid has more impact than changing the yield number of the displacing fluid. Besides that transition flow patterns of the viscoplastic-viscoplastic displacement can be very different from the ones obtained in the Newtonian–Newtonian displacement problem. Increasing the yield number of the displacing fluid or the displaced one induces a thinner film of mass attached to the wall. Finally, we found that when the capillary number changes, the yielded zones change in a complex manner, i.e. regions that were yielded turn to unyielded and vice versa. [Copyright &y& Elsevier]

Abstract: In this article, mixed approximations for inertial viscoplastic fluid flows are considered. The governing equations for incompressible flows, coupled with the Bingham model modified by the regularization, are approximated by a Galerkin-least-squares-type formulation. Numerical simulations of flows inside a lid-driven cavity and trough a sudden expansion are carried out to investigate the influence of inertia and yield limit on yield surfaces shapes, with Reynolds and Bingham numbers taken up to 1000. In all computations, a combination of equal-order bi-linear interpolations for the pair velocity–pressure is used – a choice a priori interdicted by the Babuška–Brezzi condition. [Copyright &y& Elsevier]

The paper develops a general scheme for viscoelastic materials, where the constitutive properties are described by means of measures of strain, stress, heat flux, and their time derivatives. The constitutive functions are required to be consistent with the second law of thermodynamics. Indeed, a new view is associated with the second law: the non-negative expression of the entropy production is set equal to a further constitutive function. The introduction of the entropy production as a constitutive function allows for a much wider range of models. Within this range, a scheme to obtain nonlinear models of thermo-viscoelastic materials subject to large deformations is established. Notably, the Kelvin–Voigt, Maxwell, Burgers, and Oldroyd-B viscoelastic models, along with the Maxwell–Cattaneo heat conduction, are obtained as special cases. The scheme allows also for modelling the visco-plastic materials, such as the Prandtl–Reuss work-hardening function and the Bingham–Norton fluid. [ABSTRACT FROM AUTHOR]

Abstract: In this work, the creeping flow of a viscoplastic fluid through a planar channel with an expansion followed by a contraction is analyzed numerically. The solution of the conservation equations of mass and momentum is obtained via the finite volume method. In order to model the non-Newtonian behavior of the fluid, it was used the generalized Newtonian fluid constitutive equation. The viscosity function was the one proposed by Souza Mendes and Dutra [Souza Mendes, P.R., Dutra, E.S.S., 2004. Viscosity function for yield-stress liquids. Appl. Rheol. 14, 296–302]. The yielded and unyielded regions are obtained for several combinations of rheological parameters. The influence of these parameters on pressure drop through the cavity is also obtained and analyzed. [Copyright &y& Elsevier]

Abstract: The Storegga slide, released about 8200 years ago off the western coast of Norway, is a complex system of debris flows which occurred on the remains of previous Pleistocenic slides materials. Following geological mapping and interpretation of data gathered with geological and geophysical methods, the Storegga slide has been interpreted as consisting of a giant slide (volume ≈3100km3 and runout of about 400km) followed by a swarm of progressively smaller events. The flow of the giant slide, object of the present, study, represents a dynamical enigma. Indeed, if one simulates the flow of the giant slide with simple non-Newtonian soil properties constant along the path, extremely small yield strength must be attributed to the material. This finding is incompatible with observations of the smaller slides, where the simplest non-Newtonian soil properties models work well with a yield strength more than one order of magnitude larger. A possible conclusion is that the material has charged its properties during the flow. Numerical simulations are conducted with a newly introduced model where in analogy with soil mechanical models, the material progressively loses strength during the flow. The model gives results comparable to field data if the shear strength decreases by at least a factor of 30 during flow. [Copyright &y& Elsevier]

Abstract: In this paper, slides and debris flows in overconsolidated clay materials are simulated numerically. As a case study, the models are applied to the Storegga slide in the Norwegian Sea and in particular to the sub-region called Ormen Lange, where the information available is the most precise for a subaqueous debris flow. Three different models for the rheology of clay are used: a viscoplastic (Bingham) fluid model, a viscoplastic fluid with interspersed solid blocks, and a viscoplastic model with yield strength increasing with depth. The small-scale debris flows in the Ormen Lange area can be reasonably well understood in terms of a pure Bingham model without granular effects and blocks. The presence of intact blocks in the region, however, indicates that at least the top layer of the sliding sediments was not destroyed by the flow. It suggests that the flow occurred mainly at high shear rate in a lubricating layer of mud deriving partly from the disintegration of the block''s own material, and possibly from the entrainment of hemipelagic sediments along the flow path while the top part was left unsheared. The failure of the model with blocks probably stems from the use of the Coulomb friction law to represent the interaction between the block and the seabed. The Bingham model works better because during the flow of such fluids an unsheared plug region is formed naturally, even in unconsolidated materials. Combining the simulations with these three models, a possible scenario for the Ormen Lange debris flows is deduced according to which the lubricating layer supporting the blocks has a yield strength of about 10–15 kPa. [Copyright &y& Elsevier]

The laminar axial flow of non-Newtonian fluids obeying Robertson–Stiff model in concentric annuli is analysed. Fluid flow is produced by the inner cylinder moving along its axis and by the pressure gradient imposed in the axial direction. Both cases (where pressure gradient either assists the moving cylinder or opposes the moving cylinder) are considered. All possible cases with respect to the positions of the plug flow regions are uniquely diversified by the derived semi-analytical criteria using the entry (geometric, kinematic, and rheologic) parameters. The explicit semi-analytical expression is derived for each possible case of the volumetric flow rate. [Copyright &y& Elsevier]

Heat transfer in the entrance-region laminar axial flow of viscoplastic materials inside concentric annular spaces is analyzed. The material is assumed to behave as a generalized Newtonian liquid, with a modified Herschel–Bulkley viscosity function. The governing equations are solved numerically via a finite volume method. Two different thermal boundary conditions at the inner wall are considered, namely, uniform wall heat flux and uniform wall temperature. The outer wall is considered to be adiabatic. The effect of yield stress and power-law exponent on the Nusselt number is investigated. It is shown that the entrance length decreases as the material behavior departs from Newtonian. Also, it is observed that the effect of rheological parameters on the inner-wall Nusselt number is rather small. [Copyright &y& Elsevier]

In this paper, we address the numerical aspects and implementation of a nonlinear viscoplastic model of the mechanical behaviour of brain tissue to simulate the dynamic responses related to impact loads which may cause traumatic injury. Among the various viscoelastic models available, we deliberately considered modifying the Norton-Hoff model in order to introduce non-typical viscoplastic softening behaviour that imitates a brain's response just several milliseconds after a rapid impact. We describe the discretisation and three dimensional implementation of the model, with the aim of obtaining accurate numerical results in a reasonable computational time. Due to the large scale and complexity of the problem, a parallel computation technique, using a space-time finite element method, was used to facilitate the computation boost. It is proven that, after calibrating, the introduced viscoplastic-softening model is better suited for modelling brain tissue behaviour for the specific case of rapid impact loading rather than the commonly used viscoelastic models.

• Comparison of the slender filament model and 2D simulations. • 2D simulations performed with the PAL method. • Study of the effect of inertia in the pinching process of viscoplastic filaments. We use numerical simulations to study the stretching and pinching of a viscoplastic material that is confined by two coaxial disks when they are pulled apart. The material initially forms a cylindrical bridge between the disks, follows the Heschel-Bulkley model and yields according to the von Mises criterion. We solve the governing equations numerically in their 2D, axisymmetric form using the PAL algorithm (Dimakopoulos et al. (2018)) and the slender filament approximation using the Bercovier and Engelman (1980) regularization. This approximation is valid when the disk radius to the initial length of the bridge, ε = R ˜ / L ˜ o , is small, but it is often used even when this aspect ratio is O (1). The results from the 2D solution agree with the experiments of Balmforth et al. (2010) for both a Carbopol gel and a Kaolin suspension, which can be classified as materials of medium and high viscoplasticity, respectively. Depending on the values of the aspect ratio and the yield stress of the material, we show that stretching can or cannot be accurately described by the slender filament approximation. By varying the yield stress and the pulling velocity, we find that discrepancies arise when the viscoplastic character of the flow increases, even though R ˜ / L ˜ o < 1. The inaccuracy of the slender filament approximation stems from the omission of the shear component of the rate of strain tensor from the calculation of its magnitude in the von Mises criterion. This causes a significant overestimation of the effective viscosity, since this component can be comparable to or greater than the normal components outside the filament neck. Thus, larger unyielded regions are predicted by this approximation and the remaining yielded ones carry the burden of the deformation leading to much shorter pinching times. Our results for the pinching process of viscoplastic filaments show the minor role of the yield stress, in agreement with Balmforth et al. (2010). In particular, the process is almost the same as that of power-law fluids with the same value of the shear-thinning exponent n. Our simulations include cases with n < 0.54, where the slender filament approximation is known to fail, and also a case where inertia is accounted for. Still, we confirm that the behavior is similar to that of power-law fluids. [ABSTRACT FROM AUTHOR]