Showing papers on "Herschel–Bulkley fluid published in 2011"

Stress overshoot in a simple yield stress fluid: An extensive study combining rheology and velocimetry

Abstract: We report a large amount of experimental data on the stress overshoot phenomenon which takes place during start-up shear flows in a simple yield stress fluid, namely a carbopol microgel. A combination of classical rheological measurements and ultrasonic velocimetry makes it possible to get physical insights on the transient dynamics of both the stress σ(t) and the velocity field across the gap of a rough cylindrical Couette cell during the start-up of shear under an applied shear rate . (i) At small strains (γ w. Finally, by changing the boundary conditions from rough to smooth, we show that there exists a critical shear rate s fixed by the wall surface roughness below which slip at both walls allows for faster stress relaxation and for stress fluctuations strongly reminiscent of stick-slip. Interestingly, the value of s is observed to coincide with the shear rate below which the flow curve displays a kink attributed to wall slip.

From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids

Abstract: Stress-induced fluidization of a simple yield stress fluid, namely a carbopol microgel, is addressed through extensive rheological measurements coupled to simultaneous temporally and spatially resolved velocimetry. These combined measurements allow us to rule out any bulk fracture-like scenario during the fluidization process such as that suggested in [Caton et al., Rheol Acta, 2008, 47, 601–607]. On the contrary, we observe that the transient regime from solid-like to liquid-like behaviour under a constant shear stress σ successively involves creep deformation, total wall slip, and shear banding before a homogeneous steady state is reached. Interestingly, the total duration τf of this fluidization process scales as τf ∝ 1/(σ − σc)β, where σc stands for the yield stress of the microgel, and β is an exponent which only depends on the microgel properties and not on the gap width or on the boundary conditions. Together with recent experiments under imposed shear rate [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301], this scaling law suggests a route to rationalize the phenomenological Herschel-Bulkley (HB) power-law classically used to describe the steady-state rheology of simple yield stress fluids. In particular, we show that the steady-state HB exponent appears as the ratio of the two fluidization exponents extracted separately from the transient fluidization processes respectively under controlled shear rate and under controlled shear stress.

Flows and heterogeneities with a vane tool: Magnetic resonance imaging measurements

Abstract: We study the local flow properties of various materials in a vane-in-cup geometry. We use magnetic resonance imaging techniques to measure velocities and particle concentrations in flowing Newtonian fluid, yield stress fluid, and in a concentrated suspension of noncolloidal particles in a yield stress fluid. In the Newtonian fluid, we observe that the θ-averaged strain rate component drθ decreases as the inverse squared radius in the gap, in agreement with a Couette analogy. This allows direct comparison (without end-effect corrections) of the resistances to shear in vane and Couette geometries. Here, the mean shear stress in the vane-in-cup geometry is slightly lower than in a Couette cell of same dimensions, and a little higher than when the vane is embedded in an infinite medium. We also observe that the flow enters deeply the region between the blades, leading to significant extensional flow. In the yield stress fluid, in contrast with the usually accepted picture based on simulation results from the ...

Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative

Abstract: This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid. The fractional calculus approach is used to establish the constitutive relationship model of a viscoelastic fluid. Exact analytic solutions for the velocity field and shear stress in terms of Fox H-function are obtained by means of the Laplace transform. The influence of the relaxation and retardation times, the orders of the time fractional derivative and the magnetic body force on the velocity and shear stress are analyzed. It is shown that the ordinary Oldroyd-B fluid, generalized second grade fluid and Maxwell fluid are the limiting cases of the presented results.

Introduction to the physics of landslides : lecture notes on the dynamics of mass wasting

Abstract: Preface.- 1. Introduction and problems.- 1.1 Landslides: an overview.- 1.1.1. What is a landslide?.- 1.1.2. Landslides as a geological hazard.- 1.1.3. Landslides as a geomorphic driving force.- 1.1.4. Physical aspects of landslides.- 1.2. Types of landslides.- 1.2.1. Geometrical characteristics of a landslide.- 1.2.2. Description of the seven types of movements.- 1.3. A physical classification of Gravity Mass Flows.- 2. Friction, cohesion, and slope stability.- 2.1. Friction and Cohesion.- 2.1.1. Normal and shear stresses.- 2.1.2. Friction.- 2.1.3. Cohesion.- 2.2. Slope Stability 2.2.1. A few words on slope stability.- 2.2.2. An example: layered slope. 2.2.3. A few basics concepts of soil mechanics and an application to slumps.- 2.2.4. Other factors contributing to instability.- 3. Introduction to fluid mechanics.- 3.1. Introduction.- 3.1.1. What is a fluid?.- 3.2.Fluid static.- 3.3. Simple treatment of some topics in fluid dynamics.- 3.3.1. Fluid flow (key concept: velocity field, streamlines, streamtubes).- 3.3.2. Fluid flow in a pipe with a constriction (key concepts: continuity, incompressibility).- 3.3.3. Lift force on a half-cylinder (key concept: energy conservation and the Bernoulli equation).- 3.3.4. Flow of a plate on a viscous fluid (key concepts: no-slip condition, viscosity, Newtonian fluids).- 3.3.5. Fluid pattern around a cylinder (key concepts: Reynolds number, turbulence).- 3.4. Microscopic model of a fluid and mass conservation.- 3.4.1. The pressure in a gas is due to the impact of molecules.- 3.4.2. Viscosity.- 3.5. Conservation of mass: the continuity equation.- 3.5.1. Flux.- 3.5.2. Continuity equation in Cartesian coordinates.- 3.6. A more rigorous approach to Fluid Mechanics: momentum and Navier-Stokes equation.- 3.6.1. Lagrangian and Eulerian viewpoints.- 3.6.2. Momentum equation.- 3.6.3. Analysis of the forces.- 3.6.4. Adding up the rheological properties: the Navier-Stokes equation.- 3.7. Some applications.- 3.7.1. Dimensionless numbers in fluid dynamics.- 3.7.2. Application to open flow of infinite width channel.- 4. Non-Newtonian fluids, mudflows, and debris flows: a rheological approach.- 4.1. Momentum equations, rheology, and fluid flow.- 4.2. Dirty water: the rheology of dilute suspensions.- 4.3. Very dirty water: rheology of clay slurries and muds.- 4.3.1. Clay mixtures.- 4.3.2. Interaction between clay particles.- 4.3.2. Rheology of clay mixtures and other fluids.- 4.3.4. Bingham and Herschel Bulkley.- 4.3.5. Shear strength as a function of the solid concentration.- 4.3.6. Relationship between soil properties and fluid dynamics properties.- 4.4. Behavior of a mudflow described by Bingham rheology: one-dimensional system.- 4.5. Flow of a Bingham fluid in a channel.- 4.6. Rheological flows: general properties.- 4.6.1. Introduction.- 4.6.2. Geological Materials of rheological flows.- 4.6.3. Structure of a debris flow chute and deposit.- 4.6.4. Examples of rheological flows.- 4.7. Debris flows: dynamics.- 4.7.1. Velocity.- 4.7.2. Dynamical description of a debris flow.- 4.7.3. Impact force of a debris flow against a barrier.- 4.7.4. Quasi-periodicity.- 4.7.5. Theoretical and semiempirical formulas to predict the velocity.- 5. A short introduction to the physics of granular media.- 5.1 Introduction to granular materials.- 5.1.1. Solid mechanics: Hooke's law, Poisson coefficients, elasticity.- 5.1.2. Granular media in the Earth Sciences. Angle of repose.- 5.1.3. Force between grains.- 5.2. Static of granular materials.- 5.2.1. Pressures inside a container filled with granular material.- 5.2.2. Force chains.- 5.3. Grain Collisions.- 5.3.1. Grain-wall collisions.- 5.3.2. Grain-grain collisions.- 5.4. Dynamics of granular materials avalanching.- 5.4.1. General.- 5.4.2. Dynamics of granular materials at high shear rate: granular gases and granular temperature.- 5.4.3. Haff's equation.- 5.4.4. Fluid dynamical model of a granular flow.- 5.5. Dispersive stresses and the Brazil nut effect.- 5.5.1. Dispersive pressure.- 5.5.2. Brazil nuts and inverse grading.- 6. Granular flows and rock avalanches.- 6.1. Rock avalanches: an introduction.- 6.1.1. Historical note.- 6.1.2. Examples of rock avalanches: a quick glance.- 6.1.3. The volumes of rock avalanches.- 6.2. Rock avalanche scars and deposits.- 6.2.1. Rock avalanche deposits: large-scale features.- 6.2.2. Rock avalanche deposits: intermediate-scale features.- 6.3 Dynamical properties of rock avalanches and stages of their development.- 6.3.1. Velocity of a rock avalanche.- 6.3.2. Stages in the development of a rock avalanche.- 6.4. Simple lumped mass and slab models for rock avalanches.- 6.4.1. A simple model of landslide movement.- 6.4.2. Use of energy conservation (1): runout of a Coulomb frictional sliding body.- 6.4.3. Use of energy conservation (2): calculation of the velocity with arbitrary slope path.- 6.4.4. A slab model.- 6.5. Application of the models to real case studies.- 6.5.1. Elm.- 6.5.2. The landslides of Novaya Zemlia test site.- 6.6. The fahrboschung of a rock avalanche.- 6.6.1. The importance of the centre of mass of the landslide distribution.- 6.6.2. Fahrboschung of a rock avalanche.- 6.7. How does a rock avalanche travel?.- 6.8 The problem of the anomalous mobility of large rock avalanches.- 6.8.1. Statement of the problem.- 6.8.2. A list of possible explanations.- 6.8.3. Explanations than do not require liquid or gaseous phases.- 6.8.4. Explanation of the anomalous mobility of rock avalanches invoking exotic mechanisms and new phases.- 6.9. Frictionites, frictional gouge, thermal effects, and behavior of rocks at high shear rates fragmentation.- 6.9.1. Frictionite, melt lubrication, and the Kofels landslide.- 6.9.2. Vapor or gas at high pressure.- 7. Landslides in peculiar environments.- 7.1. Landslides falling into water reservoirs.- 7.1.1. General classification.- 7.1.2. Limit C landslide comparable to the water mass, C=1.- 7.2. Coastal landslides and landslides falling onto large water basins, C"1.- 7.2.1. General.- 7.2.3. Landslides propagating retrogressively from the sea to land.- 7.2.5. Generation and propagation of the tsunami in lakes and fjords.- 7.3. Landslides traveling on glaciers.- 7.3.1. General considerations.- 7.3.2. Dinamics of landslides traveling on glaciers.- 7.4. Landslides in the Solar System.- 7.4.1. Landslides on planets and satellites, except Mars.- 7.4.2. Landslides on Mars.- 8. Rockfalls, talus formation and hillslope evolution.- 8.1. Introduction to the problems and examples.- 8.1.1. General.- 8.1.2. Physical processes during a rock fall.- 8.2. Simple models of a simple object falling down a slope.- 8.2.1. Simple models of rolling, bouncing, gliding, and falling.- 8.3. Simple rockfall models.- 8.3.1. A simple lumped mass model.- 8.3.2. The CRSP model.- 8.3.3. Three-dimensional programs.- 8.4. The impact with the terrain.- 8.4.1. The physical process of impact against hard and soft ground.- 8.4.2. Coefficents of restitution and friction.- 8.4.3. Block disintegration and extremely energetic rockfalls.- 8.5. Talus formation and evolution.- 8.5.1. Kinds of talus and their structure.- 8.5.2. Physical processes on top of taluses.- 8.6. Topple.- 9. Subaqueous landslides.- 9.1. Introduction and examples.- 9.1.1. Some examples in brief.- 9.2. Peculiarities of subaqueous landslides.- 9.2.1. Types of subaqueous landslides.- 9.2.2. Differences between subaerial and subaqueous landslides.- 9.2.3. The H/R-volume diagram for submarine landslides.- 9.3. Triggering of subaqueous landslides (especially submarine).- 9.4. Forces on a body moving in a fluid.- 9.4.1. General considerations.- 9.4.2. Drag force.- 9.4.3. Skin friction.- 9.4.4. Added mass coefficient.- 9.5. Tsunamis.- 9.5.1. Introduction.- 9.5.2. Propagation of tsunami waves in the ocean.- 9.6. More dynamical problems.- 9.6.1. Outrunner blocks.- 9.6.2. Debris flows.- 9.6.2. Theories for the mobility of submarine landslides.- 10. Other forms of gravity mass flows with potentially hazardous effects.- 10.1. Lava streams.- 10.2. Ice avalanches.- 10.3. Catastrophic flood waves.- 10.4. Snow avalanches.- 10.5 Slow landslides and soil creep.- 10.5.1. Sackungs and lateral spreads.- 10.5.2. Soil creep and other superficial mass movements.- 10.6. Suspension flows: turbidites and turbidity currents, and relationship with submarine landslides.- 10.6.1. Turbiditic basins.- 10.1.2. Ancient turbidites.- 10.6.3. Flow of a turbidity current.- Appendix GeoApp (Geological and Geotechnical).- Appendix PhysApp (Physical).- Appendix MathApp (Mathematical).- References.-

Yielding dynamics of a Herschel-Bulkley fluid: a critical-like fluidization behaviour

Abstract: The shear-induced fluidization of a carbopol microgel is investigated during long start-up experiments using combined rheology and velocimetry in Couette cells of varying gap widths and boundary conditions. As already described in [Divoux et al., {\it Phys. Rev. Lett.}, 2010, {\bf 104}, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration $\tau_f$ decreases as a power law of the applied shear rate $\gp$. Here we go one step further by an exhaustive investigation of the influence of the shearing geometry through the gap width $e$ and the boundary conditions. While slip conditions at the walls seem to have a negligible influence on the fluidization time $\tau_f$, different fluidization processes are observed depending on $\gp$ and $e$: the shear band remains almost stationary for several hours at low shear rates or small gap widths before strong fluctuations lead to a homogeneous flow, whereas at larger values of $\gp$ or $e$, the transient shear band is seen to invade the whole gap in a much smoother way. Still, the power-law behaviour appears as very robust and hints to critical-like dynamics. To further discuss these results, we propose (i) a qualitative scenario to explain the induction-like period that precedes full fluidization and (ii) an analogy with critical phenomena that naturally leads to the observed power laws if one assumes that the yield point is the critical point of an underlying out-of-equilibrium phase transition.

Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

Abstract: The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t 1 and t 2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

RETRACTED ARTICLE: Flow of fractional Maxwell fluid between coaxial cylinders

Abstract: This paper deals with the study of unsteady flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial circular cylinders, using Laplace and finite Hankel transforms. The motion of the fluid is produced by the inner cylinder that, at time t = 0+, is subject to a time-dependent longitudinal shear stress. Velocity field and the adequate shear stress are presented under series form in terms of the generalized G and R functions. The solutions that have been obtained satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases of general solutions. Finally, the influence of the pertinent parameters on the fluid motion as well as a comparison between the three models is underlined by graphical illustrations.

Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow

Abstract: The characteristics of flow and heat transfer of a fluid in a channel with oscillatory stretching walls in the presence of an externally applied magnetic field are investigated. The fluid considered is a second-grade viscoelastic electrically conducting fluid. The partial differential equations that govern the flow are solved by developing a suitable numerical technique. The computational results for the velocity, temperature and the wall shear stress are presented graphically. The study reveals that flow reversal takes place near the central line of the channel. This flow reversal can be reduced to a considerable extent by applying a strong external magnetic field. The results are found to be in good agreement with those of earlier investigations.

Determination of the blood viscosity and yield stress with a pressure- scanning capillary hemorheometer using constitutive models

Abstract: We investigated the applicability of two non-Newtonian constitutive models (Casson and Herschel-Bulkley models) in the determination of the blood viscosity and yield stress using a pressure-scanning microfluidic hemorheometer. The present results were compared with the measurements through a precision rheometer (ARES2). For a Newtonian fluid (standard oil), the two constitutive models showed excellent agreement with a reference value and the measurement of ARES2. For human blood as a non-Newtonian fluid, both the Casson and Herschel-Bulkley models exhibited similar viscosity results over a range of shear rates and showed excellent agreement with the ARES2 results. The Herschel-Bulkley model yielded a slightly higher value than other results at low shear rates ( $$ \dot \gamma $$ < 10), which may be due to the relatively high value of the yield stress. The yield stress values for whole blood were 14.4 mPa for the Casson model and 32.5 mPa for the Herschel-Bulkley model, respectively. Thus, the present study showed that the Casson model would be better than the Herschel-Bulkley model for representing the non-Newtonian characteristics of blood viscosity.

Translational flows of an Oldroyd-B fluid with fractional derivatives

Abstract: The objective of this paper is to study the unsteady flow of an Oldroyd-B fluid with fractional derivative model, between two infinite coaxial circular cylinders, using Laplace and finite Hankel transforms. The motion of the fluid is produced by the inner cylinder that, at time t=0^+, applies a time dependent longitudinal shear stress to the fluid. Velocity field and the adequate shear stress are presented in series form in terms of the generalized G and R functions. The solutions that have been obtained satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional Maxwell, ordinary Maxwell, fractional second grade, ordinary second grade and Newtonian fluids performing the same motion are obtained as limiting cases of general solutions. In particular, the existing solutions for ordinary Oldroyd-B and second grade fluids are compared with the present solutions. Finally, the influence of the pertinent parameters on the fluid motion as well as a comparison between models is underlined by graphical illustrations.

Controllable adhesion using field-activated fluids

Abstract: We demonstrate that field-responsive magnetorheological fluids can be used for variable-strength controllable adhesion. The adhesive performance is measured experimentally in tensile tests (a.k.a. probe-tack experiments) in which the magnetic field is provided by a cylindrical permanent magnet. Increasing the magnetic field strength induces higher peak adhesive forces. We hypothesize that the adhesion mechanism arises from the shear resistance of a yield stress fluid in a thin gap. This hypothesis is supported by comparing the experimentally measured adhesive performance to the response predicted by a lubrication model for a non-Newtonian fluid with a field-dependent yield stress. The model predictions are in agreement with experimental data up to moderate field strengths. Above a critical magnetic field strength the model over-predicts the experimentally measured values indicating non-ideal conditions such as local fluid dewetting from the surface.

Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid

Abstract: The velocity field corresponding to the unsteady motion of a viscous fluid between two side walls perpendicular to a plate is determined by means of the Fourier transforms. The motion of the fluid is produced by the plate which after the time t = 0, applies an oscillating shear stress to the fluid. The solutions that have been obtained, presented as a sum of the steady-state and transient solutions satisfy the governing equation and all imposed initial and boundary conditions. In the absence of the side walls they are reduced to the similar solutions corresponding to the motion over an infinite plate. Finally, the influence of the side walls on the fluid motion, the required time to reach the steady-state, as well as the distance between the walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence, are established by means of graphical illustrations.

Peristaltic Pumping of Solid Particles Immersed in a Viscoelastic Fluid

Abstract: Peristaltic pumping of fluid is a fundamental method of transport in many biological processes. In some instances, particles of appreciable size are transported along with the fluid, such as ovum transport in the oviduct or kidney stones in the ureter. In some of these biological settings, the fluid may be viscoelastic. In such a case, a nonlinear constitutive equation to describe the evolution of the viscoelastic contribution to the stress tensor must be included in the govern- ing equations. Here we use an immersed boundary framework to study peristaltic transport of a macroscopic solid particle in a viscoelastic fluid governed by a Navier-Stokes/Oldroyd-B model. Numerical simulations of peristaltic pumping as a function of Weissenberg number are presented. We examine the spatial and temporal evolution of the polymer stress field, and also find that the viscoelasticity of the fluid does hamper the overall transport of the particle in the direction of the wave.

Suction-Injection Control of Shear Banding in Non-Isothermal and Exothermic Channel Flow of Johnson-Segalman Liquids

Abstract: For certain values of the material parameters, certain viscoelastic fluid models allow for a nonmonotonic relationship between the shear stress and shear rate in simple flows. We consider channel flow of such a fluid, the Johnson-Segalman liquid, subjected to exothermic reactions. A numerical algorithm based on the finite difference method is implemented in time and space for the solution process of the highly nonlinear governing equations. The phenomenon of shear banding is observed and explained in terms of the jump discontinuities in shear rates. We demonstrate that for a reacting Johnson-Segalman fluid, the shear banding can be catastrophic as it leads to large temperature buildup within the fluid and hence makes it easily susceptible, say, to thermal runaway. We also demonstrate that the shear banding can be eliminated by making the walls porous and hence allowing for suction and injection. The suction/injection flow is shown to significantly decrease fluid temperatures for the nonmonotonic viscoelastic Johnson-Segalman model but leads to significant temperature increases for the monotonic viscoelastic Oldroyd-B model.

Bingham fluid simulation with the incompressible lattice Boltzmann model

Abstract: The Bingham fluid flow is numerically studied using the lattice Boltzmann method by incorporating the Papanastasiou exponential modification approach. The He–Luo incompressible lattice Boltzmann model is employed to avoid numerical instability usually encountered in non-Newtonian fluid simulations due to a strong non-linear relationship between the shear rate tensor and the rate-of-strain tensor. First, the value of the regularization parameter in Bingham fluid mimicking is analyzed and a method to determine the value is proposed. Then, the model is validated by pressure-driven planar channel flow and planar sudden expansion flow. The velocity profiles for the pressure-driven planar channel flow are in good agreement with analytical solutions. The calculated reattachment lengths for a 2:1 planar sudden expansion flow also agree well with the available data. Finally, the Bingham flow over a cavity is studied, and the streamlines and yielded/unyielded regions are discussed.

Stable core-annular flows of viscoelastic fluids using the visco-plastic lubrication technique

Abstract: We give an experimental demonstration that stable core-annular flows can be achieved when lubricating a viscoelastic core fluid with a yield stress fluid. We use Carbopol as the lubricating yield stress fluid and Polyethylene Oxide (PEO) as the core fluid. The yield stress in the lubricating fluid preserves a ring of unyielded material around the interface, restricting the growth of instabilities. When the inlet radius is smaller than that of the established flow the core fluid stream expands, resulting in a net relaxation of the elastic normal stresses as the flow becomes fully developed. At low flow rates ( Q 1 ) of the core fluid this relaxation does not break the surrounding plug. At larger Q 1 secondary flows and then instabilities are observed. The secondary flows are interesting in that the elastic instability is frozen into the yield stress fluid at the interface, as the stresses drop below the yield stress in the developing flow. At still larger Q 1 the surrounding plug is broken and the interface may deform. In this case elasticity appears to retard the degree of interfacial mixing, in comparison to Newtonian core fluids. When the inlet radius is larger than that of the established flow a stabilizing effect is observed. The study shows that the visco-plastic lubrication technique is feasible for multi-layer flows with elasticity.

Moving wedge and flat plate in a power-law fluid

Abstract: The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a moving wedge in a moving fluid is studied in this paper. The transformed boundary-layer equation is solved numerically for some values of the involved parameters. The effects of these parameters on the skin friction coefficient are analyzed and discussed. It is found that multiple solutions exist when the wedge and the fluid move in the opposite directions, near the region of separation. It is also found that the drag force is reduced for dilatant fluids compared to pseudo-plastic fluids.

3D flow of a generalized Oldroyd-B fluid induced by a constant pressure gradient between two side walls perpendicular to a plate

Abstract: This paper deals with the 3D flow of a generalized Oldroyd-B fluid due to a constant pressure gradient between two side walls perpendicular to a plate. The fractional calculus approach is used to establish the constitutive relationship of the non-Newtonian fluid model. Exact analytic solutions for the velocity and stress fields, in terms of the Fox H-function, are established by means of the finite Fourier sine transform and the Laplace transform. Solutions similar to those for ordinary Oldroyd-B fluid as well as those for Maxwell and second-grade fluids are also obtained as limiting cases of the results presented. Furthermore, 3D figures for velocity and shear stress fields are presented for the first time for certain values of the parameters, and the associated transport characteristics are analyzed and discussed.

The angular velocity of a freely rotating sphere in a weakly viscoelastic matrix fluid

Abstract: This letter reports on the angular velocity of a freely rotating rigid sphere in a weakly viscoelastic matrix fluid subject to simple shear flow imposed at infinity. The three-dimensional creeping flow around the sphere is assumed steady and isothermal. The solution for the angular velocity, which is derived here is the first available analytical result in the literature and is in accordance with the few existing experimental data and simulation results for non-Newtonian ambient fluids. We show that the rotation of the sphere is slower than in the Newtonian case, and that this phenomenon is at least a third-order fluid effect.

Flow due to a plate that applies an accelerated shear to a second grade fluid between two parallel walls perpendicular to the plate

Abstract: The velocity field and the shear stresses corresponding to the motion of a second grade fluid between two side walls, induced by an infinite plate that applies an accelerated shear stress to the fluid, are determined by means of the integral transforms. The obtained solutions, presented under integral form in term of the solutions corresponding to the flow due to a constant shear on the boundary, satisfy all imposed initial and boundary conditions. In the absence of the side walls, they reduce to the similar solutions over an infinite plate. The Newtonian solutions are obtained as limiting cases of the general solutions. The influence of the side walls on the fluid motion as well as a comparison between the two models is shown by graphical illustrations.

The optimal solution for the flow of a fourth-grade fluid with partial slip

Abstract: The steady flow of a non-Newtonian fluid when slippage between the plate and the fluid occurs is considered. The constitutive equations of the fluid are modeled for a fourth-grade non-Newtonian fluid with partial slip; they give rise to nonlinear boundary value problems. Analytical solutions are obtained using powerful analytic techniques for solving nonlinear problems, homotopy perturbation and optimal homotopy asymptotic methods. The results obtained are compared with the numerical results and it is shown that solutions exist for all values of the non-Newtonian parameters. The solutions valid for the no-slip condition for all values of the non-Newtonian parameters can be derived as special cases of the present analysis. Finally the solutions are discussed using a graphical approach.

Transient Flow of A Generalized Second Grade Fluid Due to a Constant Surface Shear Stress: an approximate Integral-Balance Solution

Abstract: Integral balance solution to start-up problem of a second grade viscoelastic fluid caused by a constant surface stress at the surface has been developed by an entire-domain parabolic profile with an unspecified exponent. The closed form solution explicitly defines two dimensionless similarity variables y t ξ ν = and 2 0 D p t β χ ν = = , responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed, as well comparison with the existing exact solutions have been performed. Numerical test with variable exponent of the approximate profile have been performed as a step improving the approximate solution. Copyright © 2011 Praise Worthy Prize S.r.l. All rights reserved.

Exact analytic solutions of the lubrication equations for squeeze-flow of a biviscous fluid between two parallel disks

Abstract: Based on lubrication approximation, the squeezing flow of biviscous fluids between two parallel disks with partial slip boundary condition was investigated. In addition to the solution of the kinematics in the bi-viscosity region leading to a cubic equation of the yield surface, the full explicit expressions of radial pressure gradient, pressure and squeeze force are given in the exact relationships. According to three dimensionless numbers, different behaviors are covered including Bingham fluid as a limiting case of bi-viscosity model. Besides, a critical force separating the Newtonian and biviscous regions of the flow is provided. However, for a flow of a Bingham fluid without wall slip, the expression of the applied force may be expressed or not according to the yield stress. This depends on the ratio value of the characteristic time of the fluid to the time scale of observation if it is very lower or higher than unity.