Showing papers on "Herschel–Bulkley fluid published in 2007"
TL;DR: This work considers the simplest model of propulsion and transport in a complex fluid, a waving sheet of small amplitude free to move in a polymeric fluid with a single relaxation time, and shows that, compared to self-propulsion in a Newtonian fluid occurring at a velocity UN, the sheet swims or transports fluid with velocity U∕UN.
Abstract: Flagella beating in complex fluids are significantly influenced by viscoelastic stresses. Relevant examples include the ciliary transport of respiratory airway mucus and the motion of spermatozoa in the mucus-filled female reproductive tract. We consider the simplest model of such propulsion and transport in a complex fluid, a waving sheet of small amplitude free to move in a polymeric fluid with a single relaxation time. We show that, compared to self-propulsion in a Newtonian fluid occurring at a velocity UN, the sheet swims (or transports fluid) with velocity U∕UN=(1+De2ηs∕η)∕(1+De2), where ηs is the viscosity of the Newtonian solvent, η is the zero-shear-rate viscosity of the polymeric fluid, and De is the Deborah number for the wave motion, product of the wave frequency by the fluid relaxation time. Similar expressions are derived for the rate of work of the sheet and the mechanical efficiency of the motion. These results are shown to be independent of the particular nonlinear constitutive equations ...
329 citations
TL;DR: In this article, a two-dimensional boundary element model is used to investigate the propagation of fluid-driven or hydraulic fractures deflected at bedding interfaces in layered sedimentary rocks and subsequent fluid invasion.
268 citations
TL;DR: In this article, a smoothed particle hydrodynamics (SPH) method is presented to solve non-Newtonian fluid flow problems, where the governing equations are momentum equations along with the continuity equation which are described in a Lagrangian framework.
Abstract: Purpose – This paper sets out to present a fully explicit smoothed particle hydrodynamics (SPH) method to solve non‐Newtonian fluid flow problems.Design/methodology/approach – The governing equations are momentum equations along with the continuity equation which are described in a Lagrangian framework. A new treatment similar to that used in Eulerian formulations is applied to viscous terms, which facilitates the implementation of various inelastic non‐Newtonian models. This approach utilizes the exact forms of the shear strain rate tensor and its second principal invariant to calculate the shear stress tensor. Three constitutive laws including power‐law, Bingham‐plastic and Herschel‐Bulkley models are studied in this work. The imposition of the incompressibility is fulfilled using a penalty‐like formulation which creates a trade‐off between the pressure and density variations. Solid walls are simulated by the boundary particles whose positions are fixed but contribute to the field variables in the same ...
146 citations
TL;DR: In this article, the influence of pH between 7.5 and 10.0 M on the type of particle association of the montmorillonite particles was investigated, and the effect of pH and electrolyte concentration is significant, affecting the rheology, the three Herschel-Bulkley parameters and apparent viscosity.
137 citations
TL;DR: In this paper, a new numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method (LBM) is proposed, which is applied to two representative test case problems.
Abstract: A new numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method (LBM) is proposed. The essence of the present method lies in the determination of shear-dependent viscosity of the fluid by using a variable parameter related to the local shear rate. Also, the relaxation time in the BGK collision term is kept at unity taking account of numerical stability. The method is applied to two representative test case problems, power-law fluid flows in a reentrant corner geometry and non-Newtonian fluid flows in a three-dimensional porous structure. These simulations indicate that the method can be useful for practical non-Newtonian fluid flows, such as shear-thickening (dilatant) and shear-thinning (pseudoplastic) fluid flows.
120 citations
TL;DR: It is shown that the velocity decreases as the yield stress increases for given values of other parameters, whereas the frictional resistance increases and the wall shear stress decreases with increasing catheter radius ratio k (catheter radius to vessel radius).
111 citations
TL;DR: In this paper, the linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid.
Abstract: The linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid. A pair of coupled Orr-Sommerfeld eigenvalue equations are derived and solved using an efficient spectral collocation method for cases in which unyielded regions are absent. An asymptotic analysis is also carried out in the long-wave limit, the results of which are in excellent agreement with the numerical predictions. Our analytical and numerical results indicate that increasing the dimensionless yield stress, prior to the formation of unyielded plugs below the interface, is destabilizing. Increasing the shear-thinning tendency of the lower fluid is stabilizing.
103 citations
TL;DR: In this article, the peristaltic mechanism of Jeffrey fluid in a circular tube is investigated and the modeled equations are solved using perturbation technique when the ratio of the wave amplitude to the radius of the pore is small.
Abstract: The peristaltic mechanism of a Jeffrey fluid in a circular tube is investigated. The rheological effects and compressibility of the fluid are taken into account. The modeled equations are solved using perturbation technique when the ratio of the wave amplitude to the radius of the pore is small. In the second order approximation, a net flow due to a travelling wave is obtained and effects of Reynolds number, relaxation and retardation times, compressibility of the fluid and tube radius are studied. It is noticed that for the Jeffrey fluid the back flow only occurs for large values of the relaxation time and small values of the retardation time (less than 10 in the present analysis). Another interesting observation is that oscillatory behavior of the net flow rate in the Jeffrey fluid is less than that of a Maxwell fluid. Several results of other fluid models can be deduced as the limiting cases of our situation.
78 citations
TL;DR: From magnetic resonance imaging rheometry, it is shown that a pure emulsion can be turned from a simple yield stress fluid to a thixotropic material by adding a small fraction of colloidal particles.
Abstract: From magnetic resonance imaging rheometry we show that a pure emulsion can be turned from a simple yield stress fluid to a thixotropic material by adding a small fraction of colloidal particles. The two fluids have the same behavior in the liquid regime but the loaded emulsion exhibits a critical shear rate below which no steady flows can be observed. For a stress below the yield stress, the pure emulsion abruptly stops flowing, whereas the viscosity of the loaded emulsion continuously increases in time, which leads to an apparent flow stoppage. This phenomenon can be very well represented by a model assuming a progressive increase of the number of droplet links via colloidal particles.
73 citations
TL;DR: In this paper, the energetic balance in the Rayleigh-Stokes problem for a Maxwell fluid is studied for several initial and/or boundary conditions, in comparison with the Newtonian fluid, and the power of the wall shear stress and the dissipation increase while the boundary layer thickness decreases.
71 citations
TL;DR: In this article, the effects of catheterization and non-Newtonian nature of blood on yield plane locations, velocity, flow rate, wall shear stress and longitudinal impedance of the artery are discussed.
TL;DR: In this paper, the steady flows of a non-Newtonian fluid are considered when the slippage between the plate and the fluid is valid and the constitutive equations of the fluid are modeled by those for an Oldroyd 6-constant fluid.
TL;DR: In this article, the effect of Hall current on the rotating flow of a non-Newtonian fluid in a porous medium taking into consideration the modified Darcy's law was analyzed.
Abstract: In this article, analysis is presented to study the effect of Hall current on the rotating flow of a non-Newtonian fluid in a porous medium taking into consideration the modified Darcy's law. The Oldroyd-B fluid model is used to characterize the non-Newtonian fluid behavior. The governing equations for unsteady rotating flow have been modeled in a porous medium. The analysis includes the flows induced by general periodic oscillations and elliptic harmonic oscillations of a plate. The effect of the various emerging parameters is discussed on the velocity distribution. The analytical results are confirmed mathematically by giving comparison with previous studies in the literature. It is observed that the velocity distribution increases with an increase of Hall parameter. The behavior of permeability is similar to that of the Hall parameter.
TL;DR: Dam break flows of viscoplastic fluids are studied theoretically using a Herschel-Bulkley constitutive law and a lubrication model of the motion in this paper, and the evolution of these flows from initiation to arrest is studied by integrating the equations of motion numerically.
Abstract: Dam break flows of viscoplastic fluids are studied theoretically using a Herschel–Bulkley constitutive law and a lubrication model of the motion. Following initiation these fluids are gravitationally driven out of the lock in which they had resided. Their motion is eventually arrested because they exhibit a yield stress and they attain a stationary state in which the gravitational forces are in equilibrium with the yield stress. We study the evolution of these flows from initiation to arrest by integrating the equations of motion numerically. We demonstrate that the final arrested state is approached asymptotically and find analytically that the perturbations to the final state decay algebraically with time as 1 / t n , where n is the power index of the Herschel–Bulkley model.
TL;DR: In this paper, it was shown that the stress at time zero on the stationary boundary for the flows generated by impulsive motion of a boundary or two boundaries is finite for a fluid of second grade and infinite for a Newtonian fluid.
01 Jan 2007
TL;DR: A body as a fluid is regarded, if in the time scale of observation of interest, it undergoes a flow that is discernible to the naked eye because of the application of a shear stress that can be measured with the aid of reasonably unsophisticated instruments.
Abstract: A meaningful discussion of the mathematical properties of the equations governing the flow of fluids requires a proper understanding of what is meant by a fluid as well as a clear understanding of the nature of the specific fluid. It is impossible to provide a definition of fluid, without the definition's inadequacy being laid bare with an easy counterexample. Many of the definitions, including those in renowned dictionaries are circular; a fluid being defined as a material that flows and flow being defined as an innate property of the fluid. For the purposes of this chapter a body as a fluid is regarded, if in the time scale of observation of interest, it undergoes a flow that is discernible to the naked eye because of the application of a shear stress (that can be measured with the aid of reasonably unsophisticated instruments; i.e., the forces in question are robust, not mere picoNewtons). Based on how they are constituted, different fluids respond differently to the application of external stimuli. Many mathematical models have been developed to describe the diverse response exhibited by fluids, but Navier–Stokes fluid model enjoys a central place amongst them.
TL;DR: In this article, Frigaard et al. provided an experimental demonstration that axisymmetric flows can be established and persist stably over many hundreds of diameters, using Xanthan and Carbopol solutions.
Abstract: In a core-annular pipe flow, if the outer lubricating fluid has a yield stress, it is possible for the flow to be both linearly and nonlinearly stable; see Frigaard [I.A. Frigaard, Super-stable parallel flows of multiple visco-plastic fluids, J. Non Newtonian Fluid Mech. 100 (2001) 49–76] or Moyers-Gonzalez et al. [M.A. Moyers-Gonzalez, I.A. Frigaard, C. Nouar, Nonlinear stability of a visco-plastically lubricated viscous shear flow, J. Fluid Mech. 506 (2004) 117–146]. In this paper we provide an experimental demonstration that such flows can be observed in a laboratory setting. Approximately 120 experiments using Xanthan and Carbopol solutions have been carried out and show that stable axisymmetric flows can be established and persist stably over many hundreds of diameters. Via control of the individual fluid flow rates, it is also possible to vary the inner fluid radius over a significant range, which suggests utility for various industrial processes.
TL;DR: In this paper, the influence of pre-stress on the propagation of interfacial waves along the boundary of an incompressible hyperelastic half-space that is in contact with a viscous fluid extending to infinity in the adjoining halfspace was analyzed.
Abstract: We analyse the influence of pre-stress on the propagation of interfacial waves along the boundary of an incompressible hyperelastic half-space that is in contact with a viscous fluid extending to infinity in the adjoining half-space.
One aim is to derive rigorously the incremental boundary conditions at the interface; this derivation is delicate because of the interplay between the Lagrangian and the Eulerian descriptions but is crucial for numerous problems concerned with the interaction between a compliant wall and a viscous fluid. A second aim of this work is to model the ultrasonic waves used in the assessment of aortic aneurysms, and here we find that for this purpose the half-space idealization is justified at high frequencies. A third goal is to shed some light on the stability behaviour in compression of the solid half-space, as compared with the situation in the absence of fluid; we find that the usual technique of seeking standing waves solutions is not appropriate when the half-space is in contact with a fluid; in fact, a correct analysis reveals that the presence of a viscous fluid makes a compressed neo-Hookean half-space slightly more stable.
For a wave travelling in a direction of principal strain, we obtain results for the case of a general (incompressible isotropic) strain-energy function. For a wave travelling parallel to the interface and in an arbitrary direction in a plane of principal strain, we specialize the analysis to the neo-Hookean strain-energy function.
TL;DR: In this paper, the authors modeled the tube-to-casing annulus as vertical and large parallel plates and developed dimensionless numbers for the Bingham fluid in order to use the available linear viscous correlation equations.
TL;DR: In this article, the effect of a prescribed superficial shear stress on the generation and structure of roll waves developing from infinitesimal disturbances on the surface of a power-law fluid layer flowing down an incline was investigated.
TL;DR: In this paper, a simple analytic expression for the fluid reaction is obtained for high values of the dimensionless parameter β, which is the frequency times the length of the plate squared divided by the kinematic viscosity.
TL;DR: The steady flow of blood through tapered tube has been analyzed assuming blood as Casson fluid and Herschel–Bulkley fluid, and the expressions for pressure drop, wall shear stress and resistance to flow have been obtained.
TL;DR: In this paper, the stability of the plane Couette flow of a viscoelastic fluid adjacent to a flexible surface is analyzed with the help of linear and weakly nonlinear stability theory in the limit of zero Reynolds number.
Abstract: The stability of the plane Couette flow of a viscoelastic fluid adjacent to a flexible surface is analyzed with the help of linear and weakly nonlinear stability theory in the limit of zero Reynolds number. The fluid is described by an Oldroyd-B model, which is parametrized by the viscosity \eta, the relaxation time \lambda, and the parameter \beta, which is the ratio of solvent-to-solution viscosity; beta=0 for a Maxwell fluid and \beta=1 for a Newtonian fluid. The wall is modeled as an incompressible neo-Hookean solid of finite thickness and is grafted to a rigid plate at the bottom. The neo-Hookean constitutive model parametrized by the shear modulus G, augmented to include the viscous dissipation, is used for the solid medium. Previous studies for the Newtonian flow past a compliant wall predict an instability as the dimensionless shear rate \Gamma= $(\eta^{V/GR})$ is increased beyond the critical value $\Gamma_c$. The present analysis investigates the effect of fluid elasticity, in terms of the Weissenberg number W=$\lambda {G/\eta}$, on the critical value of the imposed shear rate $\Gamma_c$ for various parameters. The fluid elasticity is found to increase $\Gamma_c$, indicating the stabilizing influence of the polymer addition on the viscous instability. For dilute polymeric solutions with \beta \geq 0.5, the flow is stable when the Weissenberg number is increased beyond a maximum value Wmax, and Wmax increases proportional to the ratio of solid-to-fluid thickness H. For concentrated polymer solutions and melts with \beta \le0.5, the flow becomes unstable when the strain rate increases beyond a critical value for any large Weissenberg number. The weakly nonlinear analysis reveals that the bifurcation of the linear instability is subcritical when there is no dissipation in the solid. The nature of bifurcation, however, changes to supercritical when the viscous effects in the solid are taken into account and the relative solid viscosity \etar is large such that sqrt( \eta_r)/H \ge1. The equilibrium amplitude and the threshold strain energy for the solid have been calculated, and the effect of parameters H, \beta, \etar, and interfacial tension on these quantities is analyzed.
TL;DR: In this article, a numerical solution for the steady flow of an electrically conducting non-Newtonian incompressible fluid past a plate is obtained under condition where the no-slip assumption between the plate and the fluid is no longer valid.
Abstract: A numerical solution is obtained for the steady flow of an electrically conducting non-Newtonian incompressible fluid past a plate. The flow is analysed under condition where the no-slip assumption between the plate and the fluid is no longer valid. The fluid under consideration obeys the rheological equations of state due to a third-grade fluid. The fluid is conducting in the presence of a uniform magnetic field under a small magnetic Reynolds number. The solution of the nonlinear equations of motion is obtained using MATLAB®. The effects of the slip, third-grade parameter and magnetic field on the velocity distribution are presented graphically and discussed.
TL;DR: In this paper, the authors analyzed the flow of an Eyring fluid in a nanotube by using continuum mechanics and found that it flows like a Newtonian fluid at small pressure gradient and a pluglike fluid at high pressure gradient.
Abstract: The flow of an Eyring fluid in a nanotube is analyzed by using continuum mechanics. The results reveal that the Eyring fluid flows like a Newtonian fluid at small pressure gradient and a pluglike fluid at high pressure gradient. The flow rate of the Eyring fluid in the nanotube at high pressure gradient with the Navier slip condition is several orders of magnitude higher than the Hagen-Poiseuille result for the flow of Newtonian fluids in the nanotube. This trend is similar to the experimental results reported in literature, suggesting that the Eyring fluid can be used to model nanoscale fluid flow.
TL;DR: In this paper, the normal stress at the surface of a sphere is calculated and the viscoelastic effects on the normal stresses for different separation distances are analyzed for small separation distances, when the particle is moving away from the wall, a tensile normal stress exists at the trailing edge if the fluid is Newtonian, while for a second-order fluid a larger tensile stress is observed.
Abstract: The motion of a sphere normal to a wall is investigated. The normal stress at the surface of the sphere is calculated and the viscoelastic effects on the normal stress for different separation distances are analysed. For small separation distances, when the particle is moving away from the wall, a tensile normal stress exists at the trailing edge if the fluid is Newtonian, while for a second-order fluid a larger tensile stress is observed. When the particle is moving towards the wall, the stress is compressive at the leading edge for a Newtonian fluid whereas a large tensile stress is observed for a second-order fluid. The contribution of the second-order fluid to the overall force applied to the particle is towards the wall in both situations. Results are obtained using Stokes equations when α 1 + α 2 = 0. In addition, a perturbation method has been utilized for a sphere very close to a wall and the effect of non-zero α 1 + α 2 is discussed. Finally, viscoelastic potential flow is used and the results are compared with the other methods.
TL;DR: It is shown that, by driving the fluid with a dynamic pressure gradient at the frequency that maximizes the dynamic permeability of the obstructed system, the magnitude of the flow can partially be recovered without the removal of the obstruction.
Abstract: We study the flow of a viscoelastic fluid flowing in an occluded tube due to either central or peripheral obstructions. We show that, by driving the fluid with a dynamic pressure gradient at the frequency that maximizes the dynamic permeability of the obstructed system, the magnitude of the flow can partially be recovered without the removal of the obstruction. We compare the results obtained for the two types of occlusions studied and find that flow recovering is larger in the case of central occlusions.
TL;DR: Torralba et al. as mentioned in this paper studied the dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, for both a Newtonian and a viscoelastic shear-thinning fluid.
Abstract: The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from 0.8 to 2.5 mm and of driving frequencies from 2.0 to 11.5 Hz. The Newtonian fluid exhibits a laminar flow regime, independent of the axial position, in the whole range of drivings. For the complex fluid, instead, the parallel shear flow regime exhibited at low amplitudes [Torralba, Phys. Rev. E 72, 016308 (2005)] becomes unstable at higher drivings against the formation of symmetric vortices, equally spaced along the tube. At even higher drivings the vortex structure itself becomes unstable, and complex nonsymmetric structures develop. Given that inertial effects remain negligible even at the hardest drivings (Re < 10(-1)), it is the complex rheology of the fluid that is responsible for the instabilities observed. The system studied represents an interesting example of the development of shear-induced instabilities in nonlinear complex fluids in purely parallel shear flow.
TL;DR: Results obtained by using a finite difference approach show significantly higher values of OSI when blood is assumed to be a viscoelastic fluid compared with those of simplified Newtonian fluid model.
TL;DR: In this article, the flow of a viscous compressible fluid about a sphere suddenly set in motion by an applied impulse is studied on the basis of linearized hydrodynamic equations.
Abstract: The flow of a viscous compressible fluid about a sphere suddenly set in motion by an applied impulse is studied on the basis of linearized hydrodynamic equations. Mixed slip-stick boundary conditions are assumed to hold at the surface of the sphere. An analytic expression for the flow pattern is presented for an idealized fluid in which the damping of sound waves is neglected. The time dependence of the pressure part and the viscous part of the fluid momentum is investigated. It is shown that at long times, one-third of the imparted momentum resides in the pressure part.