Showing papers in "Journal of Non-newtonian Fluid Mechanics in 2006"
TL;DR: This work states thatKinetic theory models involving the Fokker-Planck equation can be accurately discretized using a mesh support using a reduced approximation basis within an adaptive procedure making use of an efficient separation of variables.
Abstract: Kinetic theory models involving the Fokker-Planck equation can be accurately discretized using a mesh support (finite elements, finite differences, finite volumes, spectral techniques, etc.). However, these techniques involve a high number of approximation functions. In the finite element framework, widely used in complex flow simulations, each approximation function is related to a node that defines the associated degree of freedom. When the model involves high dimensional spaces (including physical and conformation spaces and time), standard discretization techniques fail due to an excessive computation time required to perform accurate numerical simulations. One appealing strategy that allows circumventing this limitation is based on the use of reduced approximation basis within an adaptive procedure making use of an efficient separation of variables. (c) 2006 Elsevier B.V. All rights reserved.
546 citations
TL;DR: In this paper, a general structural kinetics model is presented to describe the flow behavior of thixotropic systems based on inelastic suspending media, where the total stress is divided in structure-dependent elastic and viscous contributions.
Abstract: A general structural kinetics model is presented to describe the flow behaviour of thixotropic systems based on inelastic suspending media. The total stress is divided in structure-dependent elastic and viscous contributions. The kinetic equation for the structure parameter takes into account the effect of shear on structure breakdown and build-up, as well as the effect of Brownian motion on build-up. The relaxation and deformation of the flocs is also included. Both the kinetic and the relaxation equations contain a distribution of time constants. The predictions of this model, as well as those of two representative models from the literature, are compared with experimental data using an objective method for parameter estimation. Model validation is based on stress transients resulting from sudden changes in shear rate, including both structure build-up and breakdown. The predictions of the viscous and elastic components are evaluated separately using stress jump experiments with steady and non-steady state starting conditions.
239 citations
TL;DR: In this paper, the effects of viscosity ratio and fluid elasticity on the mechanism of drop detachment and break-up, final drop size and frequency of drop formation were studied in a non-Newtonian-newtonian multiphase system.
Abstract: Polymeric microdrops of low viscosity, elastic fluids have been generated in T-shaped microfluidic devices using a cross-flow shear-induced drop generation process. Dilute (c/c* similar to 0.5) aqueous solutions of polyethylene oxide (PEO) of various molecular weights (3 x 10(5) -2 x 10(6) g/mol) were used as the drop phase fluids whilst silicone oils (5 mPa s <= eta <= 50 mPa s) were used as the continuous phase fluids. The effects of viscosity ratio and fluid elasticity on the mechanism of drop detachment and break-up, final drop size and frequency of drop formation were studied in this non-Newtonian-Newtonian multiphase system. The generation of thinning filaments between subsequent drops of these low viscosity fluids signifies the presence of elastic stresses in this low Reynold's number flow. Two distinct regions of filament thinning dynamics, a 'pre-stretch' region and an exponential self-thinning region, were observed for the highest molecular weight of PEO studied. The 'experimental' relaxation times extracted from the exponential self-thinning region were of the same order of magnitude as the calculated Zimm relaxation time but were shown to increase as the cross-flow shear was increased. This increase is associated with substantial pre-stretching of the polymer molecules within the forming neck prior to the onset of thread self-thinning. The presence of elasticity within these low viscosity fluids resulted in the production of secondary drops of varying sizes upon final breakup. The substantial threads between the primary drop and the nozzle display traditional bead-on-a-string morphologies, with the final drop size and polydispersity being a distinct function of cross-flow rate, dispersed flow rate and polymer molecular weight. (c) 2006 Elsevier B.V. All rights reserved.
204 citations
TL;DR: In this paper, the authors studied the axial development of a noncolloidal suspension flow in two-dimensional channel and axisymmetric circular pipe geometries at bulk solids fractions of 0.2 ≤ ϕ ≤ 0.5.
Abstract: Pressure-driven flow of a noncolloidal suspension is studied in two-dimensional channel and axisymmetric circular pipe geometries at bulk solids fractions of 0.2 ≤ ϕ ≤ 0.5 . Flows are modeled by the “suspension balance” approach, consisting of mass and momentum balances for the bulk suspension and particle phase. For particles in Newtonian fluid, cross-stream motion is driven by spatial variation of particle phase normal stresses. The particle phase stress model is based strictly upon the computed rate of strain, with a nonlocal contribution to the normal stress. Two solution procedures for the suspension flow equations are described. The first is a “solve–evolve” scheme based upon a full two-dimensional solution of the unsteady, axially varying behavior using a conservative finite volume method to solve the bulk mass and momentum conservation equations. The flow solution is coupled to an explicit update (evolve) step of the particle conservation equation. The second is a nonconservative but efficient marching solution for the asymptotically steady, but axially varying, problem. Predicted axial variation of the particle fraction, velocity and pressure gradient, as well as the fully developed profiles in channel and pipe flows are presented. The rate of axial development is strongly dependent upon the ratio of particle size to channel half-width (or pipe radius), ɛ ≡ a / B (or a / R ). The agreement of marching method and full model solutions is very close for the cases studied; both agree quantitatively well with available experimental results, including axial development in the pipe flow, where the model predicts the second normal stress difference to influence the migration. Migration in a 2:1 contraction flow provides an illustration of a flow where the full solution is required.
153 citations
TL;DR: In this article, the transient extensional rheology and the dynamics of elastocapillary thinning in aqueous solutions of polyethylene oxide (PEO) are studied with high-speed digital video microscopy.
Abstract: The transient extensional rheology and the dynamics of elastocapillary thinning in aqueous solutions of polyethylene oxide (PEO) are studied with high-speed digital video microscopy. At long times, the evolution of the thread radius deviates from self-similar exponential decay and competition between elastic, capillary and inertial forces leads to the formation of a periodic array of beads connected by axially uniform ligaments. This configuration is unstable and successive instabilities propagate from the necks connecting the beads and ligaments. This iterated process results in multiple generations of beads developing along the string in general agreement with predictions of Chang et al. [Phys. Fluids, 11 (1999) 1717] although the experiments yield a different recursion relation between the successive generations of beads. At long times, finite extensibility truncates the iterated instability, and slow axial translation of the bead arrays along the interconnecting threads leads to progressive coalescence before the ultimate rupture of the fluid column. Despite these dynamical complexities it is still possible to measure the steady growth in the transient extensional viscosity by monitoring the slow capillary-driven thinning in the cylindrical ligaments between beads.
150 citations
TL;DR: In this paper, the issue of whether extensional viscosity is a concept that causes more confusion than enlightenment is addressed, and the author's view is that misuse of the concept certainly has caused much confusion and, although it is in principle a simple and straightforward idea, it continues to be misused.
Abstract: The issue of whether extensional viscosity is a concept that causes more confusion than enlightenment is addressed. This author’s view is that misuse of the concept certainly has caused much confusion and, although it is in principle a simple and straightforward idea, it continues to be misused. What is straightforward is the formal definition of extensional viscosity, for steady uniform extensional flow. What gives rise to confusion is the careless use of measurements in flows which are not both steady and spatially uniform.
147 citations
TL;DR: In this paper, the authors examined the numerical simulation of isothermal transient flows for a weakly compressible viscoplastic fluid in an axisymmetric pipe geometry using the Bingham model.
Abstract: In this paper we examine the numerical simulation of isothermal transient flows for a weakly compressible viscoplastic fluid in an axisymmetric pipe geometry. We use the Bingham model to describe the viscoplastic feature of the fluid and the compressibility is introduced in the continuity equation using the isothermal compressibility coefficient. Particular attention is devoted to the velocity-pressure problem in which the "true" (without regularization procedure) viscoplastic model is accounted for by using Lagrange multipliers techniques and augmented Lagrangian/Uzawa methods. The mass, momentum and constitutive equations are discretized using a finite volume method on a staggered grid with a TVD (Total Variation Diminishing) scheme for the convective terms. The resulting numerical method highlights strong and robust convergence properties. Obtained results regarding the transient solution underline the influence of compressibility on the flow pattern, especially in terms of yielded/unyielded regions, pressure and time to restart the flow.
146 citations
TL;DR: In this paper, a new constitutive equation for whole human blood is derived using ideas drawn from temporary polymer network theory to model the aggregation and disaggregation of erythrocytes in normal human blood at different shear rates.
Abstract: A new constitutive equation for whole human blood is derived using ideas drawn from temporary polymer network theory to model the aggregation and disaggregation of erythrocytes in normal human blood at different shear rates. Each erythrocyte is represented by a dumbbell. The use of a linear spring law in the dumbbells leads to a multi-mode generalized Maxwell equation for the elastic stress and both the relaxation times and viscosities are functions of a time-dependent structure variable. An approximate constitutive equation is derived by choosing a single mode corresponding to the cell aggregate size where the largest number of cells are to be found. This size is identified in the case of steady flows. The model exhibits shear-thinning, viscoelasticity and thixotropy and these are clearly related to the microstructural properties of the fluid. Agreement with the experimental data of Bureau et al. [M. Bureau, J.C. Healy, D. Bourgoin, M. Joly, Rheological hysteresis of blood at low shear rate, Biorheology 17 (1980) 191–203] in the case of a simple triangular step shear rate flow is convincing.
142 citations
TL;DR: In this article, the authors analyzed the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method and compared the numerical results with the good agreement between them.
Abstract: Flow of a power-law fluid film on an unsteady stretching surface is analyzed by means of homotopy analysis method (HAM [1] ). For real power-law index and the unsteadiness parameter in wide ranges, analytic series solutions are given and compared with the numerical results. The good agreement between them shows the effectiveness of HAM to this problem. Additionally, unlike previous studies, the value of the critical unsteadiness parameter S 0 , above which no solution exists, is determined analytically in this paper.
141 citations
TL;DR: In this paper, the authors investigated convective heat transfer of non-Newtonian fluids within a thin liquid film on an unsteady stretching sheet, taking into consideration the viscous dissipation effect.
Abstract: Convective heat transfer of non-Newtonian fluids within a thin liquid film on an unsteady stretching sheet is investigated, taking into consideration the viscous dissipation effect. Results for the temperature distribution, the free-surface temperature, and the wall temperature gradient are illustrated at selected values of the unsteadiness parameter, the power-law index, and Eckert number for a wide range of the generalized Prandtl number, ranging from 0.001 to 1000. Also, new results for the velocity profiles, the free-surface velocity, and the wall shear stress are presented. The deviation from Newtonian behavior on the variation of the horizontal velocity component across the liquid film is observed more significant than that reported in the previous investigation. As compared to the case where viscous dissipation is neglected, the dimensionless fluid temperature is found to increase when the fluid is being heated but to decrease when the fluid is being cooled. For the fluid heating case, the dimensionless fluid temperature decreases monotonically in the vertical direction; while for the fluid cooling case it decreases rapidly at first, reaches a minimum value, and then increases more gradually to its free-surface value. The wall temperature gradient takes a higher value for a negative Eckert number but a lower value for a positive Eckert number, as compared to the case without viscous dissipation. The effects of positive or negative Eckert numbers on heat transfer are found to be more pronounced for higher generalized Prandtl numbers.
138 citations
TL;DR: In this paper, the effects of surfactant (EHAC) and salt (NH4Cl) concentrations on the linear viscoelastic parameters are determined using small amplitude oscillatory shear experiments, and the steady and time-dependent shear rheology is determined in a double gap Couette cell, and transient extensional flow measurements are performed in a capillary breakup extensional rheometer.
Abstract: Nonlinear shear and extensional flow dynamics of a wormlike micellar solution based on erucyl bis(2-hydroxyethyl) methyl ammonium chloride (EHAC) are reported here. The influences of surfactant (EHAC) and salt (NH4Cl) concentrations on the linear viscoelastic parameters are determined using small amplitude oscillatory shear experiments. The steady and time-dependent shear rheology is determined in a double gap Couette cell, and transient extensional flow measurements are performed in a capillary breakup extensional rheometer (CABER). In the nonlinear shear flow experiments, the micellar fluid samples show strong hysteretic behavior upon increasing and decreasing the imposed shear stress due to the development of shear-banding instabilities. The non-monotone flow curves of stress versus shear rate can be successfully modeled in a macroscopic sense by using the single-mode Giesekus constitutive equation. The temporal evolution of the flow structure of the surfactant solutions in the Couette flow geometry is analyzed by instantaneous shear rate measurements for various values of controlled shear stress, along with FFT analysis. The results indicate that the steady flow bifurcates to a global time-dependent state as soon as the shear-banding/hysteresis regime is reached. Increasing the salt–surfactant ratio or the temperature is found to stabilize the flow, and corresponds to decreasing values of anisotropy factor in the Giesekus model. Finally, we have investigated the dynamics of capillary breakup of the micellar fluid samples in uniaxial extensional flow. The filament thinning behavior of the micellar fluid samples is also accurately predicted by the Giesekus constitutive equation. Indeed quantitative agreement between the experimental and numerical results can be obtained providing that the relaxation time of the wormlike micellar solutions in extensional flows is a factor of three lower than in shear flows.
TL;DR: In this paper, the authors performed direct numerical simulations of polymer induced drag reduction in turbulent channel flows up to the maximum drag reduction (MDR) limit using a fully spectral method in conjunction with kinetic theory based elastic dumbbell models for the description of polymer chain dynamics.
Abstract: Direct numerical simulations (DNS) of polymer induced drag reduction in turbulent channel flows up to the maximum drag reduction (MDR) limit have been performed using a fully spectral method in conjunction with kinetic theory based elastic dumbbell models for the description of polymer chain dynamics. It is shown that to obtain significant levels of drag reduction large polymer chain extensibility and high Weissenberg numbers are required. In addition, it is demonstrated that to capture flow dynamics in the high drag reduction (HDR) and MDR regimes, very long computational domain lengths of the order of 10 4 wall units are required. The simulation results in turn have been used to develop a scaling that describes the interplay between rheological parameters (i.e., maximum chain extension and relaxation time) and the extent of drag reduction as a function of Reynolds number. In addition, turbulence statistics are analyzed and correlations between the polymer body force and velocity fluctuations have been developed with particular emphasis on the HDR and MDR regimes. These observations have been used to decipher the effect of polymer additives on the dynamics of the flow and drag reduction.
TL;DR: In this paper, the smoothed particle hydrodynamics (SPH) method is extended and tested for the numerical simulation of transient viscoelastic free surface flows, and the basic equations governing the free surface flow of an Oldroyd-B fluid are considered and approximated by SPH.
Abstract: The smoothed particle hydrodynamics (SPH) method is extended and tested for the numerical simulation of transient viscoelastic free surface flows. The basic equations governing the free surface flow of an Oldroyd-B fluid are considered and approximated by SPH. In particular, a drop of an Oldroyd-B fluid impacting a rigid plate is simulated. Results for a Newtonian fluid are also presented for comparison. It is found that the original SPH method, which has been successfully applied to the simulation of transient viscoelastic flows in bounded domains (such as the start-up flow between parallel plates), is unable to simulate the viscoelastic free surface flow considered here because of the so-called tensile instability. This instability leads to unrealistic fracture and particle clustering in fluid stretching and may eventually result in complete blowup of the simulation. Recent works have shown that in simulations of elastic solids the tensile instability can be removed by an artificial stress. Here we show that the same idea also works for viscoelastic fluids provided that the constant parameter entering in the definition of the artificial stress is properly chosen. Numerical results obtained are in good agreement with those simulated by a finite difference technique.
TL;DR: In this article, the authors review viscoplastic flow over inclined surfaces, focusing on constant-flux extrusions from small vents and the slumping of a fixed volume of material.
Abstract: We review viscoplastic flow over inclined surfaces, focusing on constant-flux extrusions from small vents and the slumping of a fixed volume of material. Lubrication theory is used for shallow and slow flows to reduce the governing equations to a nonlinear diffusion-type equation for the local fluid depth; this model is used as the basis for exploration of the problem. Theory is compared to experiments. A number of complications and additional physical effects are discussed that enrich real situations.
TL;DR: This work focuses on power-law fluids with index n, and uses the lattice Boltzmann method to simulate the flow of non-Newtonian fluids through complex random porous media in both two and three dimensions.
Abstract: The lattice Boltzmann (LB) method has been used to simulate, at the pore scale, the flow of non-Newtonian fluids through complex random porous media in both two and three dimensions We focus our work on power-law fluids with index n
TL;DR: In this paper, the impact of a solid sphere on the free surface of a viscoelastic wormlike micellar fluid was studied, where spheres of various densities and diameters were dropped from different heights above the fluid surface, reaching it with a nonzero velocity which determines the subsequent dynamics.
Abstract: We present an experimental study of the impact of a solid sphere on the free surface of a viscoelastic wormlike micellar fluid. Spheres of various densities and diameters are dropped from different heights above the fluid surface, reaching it with a nonzero velocity which determines the subsequent dynamics. Measurements of the initial sphere penetration are found to scale with the ratio of the kinetic energy of the sphere at impact to the elastic modulus of the fluid. The cavity formed in the wake of the sphere, observed with high-speed video imaging, also undergoes transitions from a smooth to fractured surface texture, dependent on both the Deborah number and the ratio of the gravitational force to elasticity.
TL;DR: In this paper, a new finite-difference formulation was proposed to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor and prevents over-extension for finite-extensible models.
Abstract: We present a new finite-difference formulation to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor (i.e., the tensor remains positive definite) and prevents over-extension for finite-extensible models. The formulation is a generalization of the second-order, central difference scheme developed by Kurganov and Tadmor [A. Kurganov, E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations, J. Comput. Phys. 160 (2000) 241–282] that guarantees a scalar field remains everywhere positive. We have extended the algorithm to guarantee a tensor field remains everywhere positive definite following an update. Extensive testing of the algorithm shows that the volume average of the conformation tensor is conserved. Furthermore, volume averages of the conformation tensor in homogeneous turbulent shear flow made over the Eulerian grid are in quantitative agreement with Lagrangian averages made over fluid particles moving throughout the domain, highlighting the accuracy of the treatment of the convective terms.
TL;DR: In this paper, the aggregation of particles settling in a shear-thinning fluid is numerically investigated with the distributed-Lagrange-multiplier based fictitious domain (DLM/FD) method.
Abstract: In this study, the aggregation of particles settling in a shear-thinning fluid is numerically investigated with the distributed-Lagrange-multiplier based fictitious domain (DLM/FD) method. The collocation-element method and a fractional-step scheme based on keeping the Lagrange multiplier at the previous time level in the momentum equations are adopted to discretize the Lagrange multiplier. The lubrication force correction is implemented in the code as a collision strategy. We employ a thixotropic model to account for the time effect of shear-thinning. The results confirm that the memory of shear-thinning is responsible for the aggregation of two end-to-end settling particles, and indicate that the elasticity of the fluid, though may be very weak, seems necessary for the randomly distributed particles to aggregate into stable clusters or columns.
TL;DR: In this article, the effect of high molecular weight polymer on the low-flow limit of slot coating was examined by visualization experiments and theoretical analysis using an algebraic non-Newtonian model that takes into account the extensional thickening behavior of polymer solutions.
Abstract: The region of acceptable quality in the space of operating parameters of a coating process is usually bounded by various coating defects An important limit of the slot coating process is the low-flow limit It is the maximum web speed at a given film thickness and distance between coating die and web (coating gap); equivalently, the minimum film thickness at a given web speed and coating gap; again equivalently, the maximum gap at a given film thickness and web speed at which the coating bead remains stable The condition that defines this limit is a force balance at the downstream meniscus of the coating bead, where the coated layer is carried away by the web translating past the die Although most of the liquids coated industrially are polymeric solutions, dispersions, or both, that are not Newtonian, most previous investigations of the low-flow limit in slot coating dealt with Newtonian liquids Recently, the effect of high molecular weight polymer on the low-flow limit of slot coating was examined by visualization experiments and theoretical analysis using an algebraic non-Newtonian model that takes into account the extensional thickening behavior of polymer solutions Although Generalized Newtonian Models of this class may capture the different ways that dilute polymer molecules behave in extension- and shear-dominated flow zones and the reported predictions display the same trends that are observed experimentally, algebraic models cannot represent viscoelastic stresses In the present work, the low-flow limit of slot coating of mildly viscoelastic liquids is examined by solving the conservation equations for two-dimensional flow, coupled with either of two differential viscoelastic models that describe the mechanical behavior of dilute polymer solutions (namely the Oldroyd-B and FENE-CR models) The results show how the different rheological properties affect the flow and the critical conditions at the onset of the low-flow limit
TL;DR: In this article, a reduced approximation basis is constructed for the Fokker-Planck equation with a mesh support, which reduces the number of realizations required for describing accurately the microstructural state due to Brownian effects.
Abstract: Stochastic simulation for finitely extensible non-linear elastic (FENE) dumbbells has been successfully applied (seethe review paper of Keunings [R. Keunings, Micro-macro methods for the multiscale simulation viscoelastic flow using molecular models of kinetic theory, in: D.M. Binding, K. Walters (Eds.), Rheology Reviews, British Society of Rheology, 2004, pp. 67-98] and the references therein). The main difficulty in these simulations is related to the high number of realizations required for describing accurately the microstructural state due to Brownian effects. The discretisation of the Fokker-Planck equation with a mesh support (finite elements, finite differences, finite volumes, spectral techniques,...) allows to go beyond the difficulty related to Brownian effects. However, kinetic theory models involve physical and conformation spaces. Thus, the molecular distribution depends on time, space as well as on the molecular orientation and extension (conformation coordinates). In this form the resulting Fokker-Planck equation is defined in a space of dimension 7. In the reduction technique proposed in this paper, a reduced approximation basis is constructed. The new shape functions are defined in the whole domain in an appropriate manner. Thus, the number of degrees of freedom involved in the solution of the Fokker-Planck equation is significantly reduced. The construction of those new approximation functions is done with an 'a priori' approach, which combines a basis reduction (using the Karhunen-Loeve decomposition) with a basis enrichment based on the use of some Krylov subspaces. This numerical technique is applied for solving the FENE model of viscoelastic flows. (c) 2006 Elsevier B.V. All rights reserved.
TL;DR: In this paper, the authors investigated the generation and structure of roll waves developing on the surface of a power-law fluid layer flowing down a porous incline, where the unsteady equations of motion were integrated according to the von Karman momentum integral method accounting for the variation of the velocity distribution with depth.
Abstract: In this paper we investigate the generation and structure of roll waves developing on the surface of a power-law fluid layer flowing down a porous incline. The unsteady equations of motion for the power-law fluid layer are depth integrated according to the von Karman momentum integral method accounting for the variation of the velocity distribution with depth. The slip boundary condition at the interface between the fluid layer and the porous plane is based on the assumption that the flow through the porous medium is governed by the modified Darcy’s law, and that the characteristic length scale of the pore space is much smaller than the depth of the fluid layer above. An analytical theory of permanent roll waves is employed to determine under what flow conditions roll waves can exist and to calculate the wavelength, wave height, and speed of the roll waves. The nonlinear stability analysis is also carried out by numerically solving the time dependent governing equations and calculating the nonlinear evolution of infinitesimal disturbances imposed on the uniform and steady flow. Conclusions are drawn regarding the effect of the permeability of the porous medium and flow conditions on the development and characteristics of roll waves arising from the instability of the uniform flow.
TL;DR: In this paper, a convergent series solution for the viscous flow of non-Newtonian fluids near the forward stagnation point of a two-dimensional body is obtained, which is valid for all dimensionless time in the whole spatial region 0 ≤ η ∞.
Abstract: In this paper, the unsteady viscous flow of non-Newtonian fluids near the forward stagnation point of a two-dimensional body is studied analytically. By using the homotopy analysis method, a convergent series solution is obtained, which is uniformly valid for all dimensionless time in the whole spatial region 0 ≤ η ∞ . Besides, the effects of integral power-law index of the non-Newtonian fluids on the flow are investigated. To the best of our knowledge, such kind of series solutions have never been reported for this problem.
TL;DR: In this paper, a review of the literature on extensional flow is presented, starting with extracts from the seminal papers of Trouton [Proc Roy. Soc. A 77 (1906) 426-440] and Fano [Archivio di fisiologio, 5 (1908) 365-370].
Abstract: This historical review takes a few selected issues from the rheological studies of extensional flow that fill the literature, starting with extracts from the seminal papers of Trouton [Proc. Roy. Soc. A 77 (1906) 426–440] and Fano [Archivio di fisiologio, 5 (1908) 365–370]. Work in the first half of the 20th century on spinnability and extensional viscosity measurement is highlighted, followed by a discussion of the blossoming of studies on extensional flow. As a case study, a project on anti-misting additives in aviation fuel is taken; whether the rheology or the politics is the more interesting is an open question. Finally some current issues surrounding spinnability and other extensional flow phenomena are discussed.
TL;DR: In this paper, a strain-induced anisotropic flow law for polycrystalline ice and the associated equations describing the evolution of its fabric were formulated at polycrystal scale and tabulated using a micro-macro model.
Abstract: As fibers or other crystalline materials exhibiting hexagonal symmetry, the crystal of ice can be orientated by using only one single vector, i.e. its c-axis. Such a characteristic allows to apply specific methods to deal with the properties of the polycrystalline aggregate. Among others, the fabric (texture) of the ice polycrystal can be described by an ODF, i.e. a scalar function of two angles that gives the distribution of the orientation of all the constituents (grains). This paper presents a strain-induced anisotropic flow law for polycrystalline ice and the associated equations describing the evolution of its fabric. This constitutive law is formulated at the polycrystal scale and tabulated using a micro–macro model. The fabric is defined by the second- and fourth-order orientation tensors for the c-axes, assuming the so-called “invariant-based optimal fitting closure approximation”. Both the anisotropic constitutive law and the fabric evolution equations have been implemented in a finite element code in order to solve large scale ice flow problem. As an application, the flow of an idealized ice sheet over a bumpy bed is studied. © 2005 Elsevier B.V. All rights reserved.
TL;DR: In this article, the authors studied the 2D and 1D stretch-off dynamics of liquid threads of power law fluids surrounded by a passive ambient fluid and showed that the interface overturns first before the thread transitions from the PF to the IVP regime.
Abstract: Pinch-off dynamics of liquid threads of power law fluids surrounded by a passive ambient fluid are studied theoretically by fully two-dimensional (2-D) computations and one-dimensional (1-D) ones based on the slender-jet approximation for 0 1Oh>1, the 2-D computations reveal that a thinning thread transitions from the VP to the IVP regime when n>2/3n>2/3 in accordance with the 1-D results but a thinning thread transitions from the VP to the PF regime when 0.54 2/3n>2/3 in accordance with the 1-D results but a thinning thread remains in the PF regime until breakup when n 2/3n>2/3, the 2-D computations show that the interface overturns first before the thread transitions from the PF to the IVP regime. When Oh 2/3n>2/3, the transition between the PF and the IVP regimes is shown to occur when the minimum thread radius hmin∼Oh2/(3n−2)hmin∼Oh2/(3n−2). Scaling exponents and self-similar thread shapes and axial velocity profiles obtained from the 2-D computations are shown to be in excellent agreement with the 1-D results when thread shapes at breakup are slender.
TL;DR: In this paper, the drag force on two spheres moving at very low controlled velocity in a viscoplastic fluid was studied as a function of the distance separating them and the influence of the surface roughness of the spheres governing fluid adherence and slip at the wall was quantified.
Abstract: The drag force on two spheres moving at very low controlled velocity in a viscoplastic fluid was studied as a function of the distance separating them. Two configurations were studied, namely two spheres with their centre lines along or perpendicular to the flow. The influence of the surface roughness of the spheres governing fluid adherence and slip at the wall was quantified. The drag force on an isolated sphere was also measured and used as a reference. Correlations for predicting the drag coefficient and stability criterion, with respect to sedimentation, are proposed. These results show that viscoplasticity reduces the extent of the interactions in comparison with the case of a Newtonian fluid.
TL;DR: In this article, an extensional flow oscillatory rheometer has been proposed for measuring extensional viscosity and non-ideal Trouton ratios, following the evolution of molecular strain, assessing molecular flexibility and deriving the molecular weight distribution of high polymers.
Abstract: The measurement of extensional viscosity, particularly for low viscosity complex fluids, has long been recognised as both an essential and challenging rheological task. Many of the techniques currently available have drawbacks that either preclude the use of low viscosity fluids or provide varying levels of applied fluid strain. By combining oscillatory flow with a stagnation point extensional flow field, conditions of steady-state stretching using only tiny volume displacements can be achieved. This extensional flow oscillatory rheometer has four electronically controlled micro-pumps positioned at the end of each channel of a cross-slots flow cell, creating planar extension, a differential pressure transducer records flow resistance measurements. The geometry permits the shear and extensional rheological components to be separately determined. An optical probe records simultaneous flow field stability, microstructure and molecular orientation data. Results are presented for dilute (10–100 ppm) polystyrene and hyaluronan polymer solutions, showing the capability of the technique for measuring the extensional viscosity and non-ideal Trouton ratios, controlling the fluid strain, following the evolution of molecular strain, assessing molecular flexibility and deriving the molecular weight distribution of high polymers.
TL;DR: In this paper, a numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed and the results have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Reτ, and Weissenberg number, Weτ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile.
Abstract: Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Reτ, and Weissenberg number, Weτ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; 0 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 74) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.
TL;DR: In this paper, a time-dependent simulation of axisymmetric squeezing of viscoplastic materials under creeping flow conditions is examined, and the authors use the mixed finite element method with a quasi-elliptic mesh generation scheme to solve the governing equations.
Abstract: The transient, axisymmetric squeezing of viscoplastic materials under creeping flow conditions is examined. The flow of the material even outside the disks is followed. Both cases of the disks moving with constant velocity or under constant force are studied. This time-dependent simulation of squeeze flow is performed for such materials in order to determine very accurately the evolution of the force or the velocity, respectively, and the distinct differences between these two experiments, the highly deforming shape and position of all the interfaces, the effect of possible slip on the disk surface, especially when the slip coefficient is not constant, and the effect of gravity. All these are impossible under the quasi-steady state condition used up to now. The exponential constitutive model, suggested by Papanastasiou, is employed. The governing equations are solved numerically by coupling the mixed finite element method with a quasi-elliptic mesh generation scheme in order to follow the large deformations of the free surface of the fluid. As the Bingham number increases, large departures from the corresponding Newtonian solution are found. When the disks are moving with constant velocity, unyielded material arises only around the two centers of the disks verifying previous works in which quasi-steady state conditions were assumed. The size of the unyielded region increases with the Bingham number, but decreases as time passes and the two disks approach each other. Their size also decreases as the slip velocity or the slip length along the disk wall increase. The force that must be applied on the disks in order to maintain their constant velocity increases significantly with the Bingham number and time and provides a first method to calculate the yield stress. On the other hand, when a constant force is applied on the disks, they slow down until they finally stop, because all the material between them becomes unyielded. The final location of the disk and the time when it stops provide another, probably easier, method to deduce the yield stress of the fluid.
TL;DR: In this article, the authors focused on the numerical prediction of the pressure field associated with the flow of an Oldroyd-B fluid through 4:1 contractions, 1:4 expansions and combined 4: 1/4 contraction/expansions.
Abstract: This paper is concerned primarily with the numerical prediction of the pressure field associated with the flow of an Oldroyd-B fluid through 4:1 contractions, 1:4 expansions and combined 4:1:4 contraction/expansions. Particular interest lies in the effect of the ratio of solvent to total viscosity parameter on the profile of the pressure gradient and on the entry and exit development lengths. Although most of the results refer to planar (2D) flows, some results are presented to illustrate how the 3D case convergences towards two-dimensional flow as the relevant aspect ratio of the geometries becomes large. Some results are presented for certain aspects related to the flow kinematics, in order to illustrate the link between the pressure field and the resulting flow field.