Showing papers on "Herschel–Bulkley fluid published in 2012"

Slip effects on MHD flow of a generalized Oldroyd-B fluid with fractional derivative

Abstract: This paper presents an analysis for magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid inducing by an accelerating plate. Where the no-slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is introduced to establish the constitutive relationship of a viscoelastic fluid. Closed form solutions for velocity and shear stress are obtained in terms of Fox H-function by using the discrete Laplace transform of the sequential fractional derivatives. The solutions for no-slip condition and no magnetic field can be derived as the special cases. Furthermore, the effects of various parameters on the corresponding flow and shear stress characteristics are analyzed and discussed in detail.

Shear-induced sedimentation in yield stress fluids

Abstract: Stability of coarse particles against gravity is an important issue in dense suspensions (fresh concrete, foodstuff, etc.). On the one hand, it is known that they are stable at rest when the interstitial paste has a high enough yield stress; on the other hand, it is not yet possible to predict if a given material will remain homogeneous during a flow. Using MRI techniques, we study the time evolution of the particle volume fraction during the flows in a Couette geometry of model density-mismatched suspensions of noncolloidal particles in yield stress fluids. We observe that shear induces sedimentation of the particles in all systems, which are stable at rest. The sedimentation velocity is observed to increase with increasing shear rate and particle diameter, and to decrease with increasing yield stress of the interstitial fluid. At low shear rate (’plastic regime’), we show that this phenomenon can be modelled by considering that the interstitial fluid behaves like a viscous fluid–of viscosity equal to the apparent viscosity of the sheared fluid–in the direction orthogonal to shear. The behavior at higher shear rates, when viscous effects start to be important, is also discussed. We finally study the dependence of the sedimentation velocity on the particle volume fraction, and show that its modelling requires estimating the local shear rate in the interstitial fluid.

A study of the anisotropy of stress in a fluid confined in a nanochannel

Abstract: We present molecular dynamics simulations of planar Poiseuille flow of a Lennard-Jones fluid at various temperatures and body forces. Local thermostatting is used close to the walls to reach steady-state up to a limit body force. Macroscopic fields are obtained from microscopic data by time- and space-averaging and smoothing the data with a self-consistent coarse-graining method based on kernel interpolation. Two phenomena make the system interesting: (i) strongly confined fluids show layering, i.e., strong oscillations in density near the walls, and (ii) the stress deviates from the Newtonian fluid assumption, not only in the layered regime, but also much further away from the walls. Various scalar, vectorial, and tensorial fields are analyzed and related to each other in order to understand better the effects of both the inhomogeneous density and the anisotropy on the flow behavior and rheology. The eigenvalues and eigendirections of the stress tensor are used to quantify the anisotropy in stress and form the basis of a newly proposed objective, inherently anisotropic constitutive model that allows for non-collinear stress and strain gradient by construction.

Herschel-Bulkley rheological parameters of a novel environmentally friendly lightweight biopolymer drilling fluid from xanthan gum and starch

Abstract: This article summarizes a concise investigation on the effect of concentration of the four main components of a novel lightweight drilling fluid, i.e., glass bubbles, xanthan gum, starch, and clay, to the Herschel-Bulkley rheological model parameters. The three parameters of Herschel-Bulkley model, i.e., yield stress, fluid consistency, and fluid index were calculated by fitting the experimental data of shear stress as a function of rate of shear to the model. Results indicate that the increment of the amount of four main components increase the yield stress of the final fluid as the flow resistance is increased. Furthermore, the result also showed that the calculated fluid consistency of the drilling fluid appears to be strongly dependent on the presence of glass bubbles, xanthan gum, and clay. However, the fluid consistency appears not to be affected by the presence of starch. It is also concluded that the presence of glass bubbles, xanthan gum, and clay in the fluid tends to determine the final fluid to behave as pseudoplastic. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Rheo-PIV of a yield-stress fluid in a capillary with slip at the wall

Abstract: An analysis of the yielding and flow behavior of a model yield-stress fluid, 0.2 wt% Carbopol gel, in a capillary with slip at the wall has been carried out in the present work. For this, a study of the flow kinematics in a capillary rheometer was performed with a two-dimensional particle image velocimetry (PIV) system. Besides, a stress-controlled rotational rheometer with a vane rotor was used as an independent way to measure the yield stress. The results in this work show that in the limit of resolution of the PIV technique, the flow behavior agrees with the existence of a yield stress, but there is a smooth solid–liquid transition in the capillary flow curve, which complicates the determination of the yield stress from rheometrical data. This complication, however, is overcome by using the solely velocity profiles and the measured wall shear stresses, from which the yield-stress value is reliably determined. The main details of the kinematics in the presence of slip were all captured during the experiments, namely, a purely plug flow before yielding, the solid–liquid transition, as well as the behavior under flow, respectively. Finally, it was found that the slip velocity increases in a power-law way with the shear stress.

The significant influence of internal stresses on the dynamics of bubbles in a yield stress fluid

Abstract: The shape and trajectory of bubbles in Carbopol gels were accurately observed over long periods. As the concentration increases, the trajectories are observed to evolve from vertical and rectilinear to three-dimensional shapes. Local strain and velocity fields have been determined. Bubble injection is quasi-static in order to obtain a separation governed by the equilibrium among surface tension, buoyancy and stresses applied to the bubble. Internal stresses in the fluid, of structural origin and induced by the mechanical history in the fluid volume, remain in the fluid for at least several months. They play a major role in bubble formation and propagation.

Fluid dynamics of dilatant fluids.

Abstract: A dense mixture of granules and liquid often shows a severe shear thickening and is called a dilatant fluid. We construct a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of dispersed particles. With simple assumptions for an equation of the state variable, we demonstrate that the model can describe basic features of the dilatant fluid such as the stress-shear rate curve that represents discontinuous severe shear thickening, hysteresis upon changing shear rate, and instantaneous hardening upon external impact. An analysis of the model reveals that the shear thickening fluid shows an instability in a shear flow for some regime and exhibits the shear thickening oscillation (i.e., the oscillatory shear flow alternating between the thickened and the relaxed states). The results of numerical simulations are presented for one- and two-dimensional systems.

Boundary layer in pastes—Displacement of a long object through a yield stress fluid

Abstract: When it moves through a yield stress fluid, a solid object continuously reaches and liquefies new solid regions, so that both flow in liquid regions and deformations in solid regions occur. In the present work, we focus on the displacement of a plate through simple yield stress fluids (non-thixotropic). Through force vs velocity and particle imaging velocimetry measurements with a detailed analysis of the deformation history, we are able to identify the solid and liquid regions and their respective role in the flow characteristics. It is shown that the displacement of a long object through a yield stress fluid gives rise to the formation of a liquid boundary layer (BL) of uniform thickness at short distance from the leading edge, while the rest of the material remains solid. The original result is that the thickness of this boundary layer, which is of the order of 10 mm, only slightly increases with velocity and does not tend to zero when the velocity tends to zero, in contrast with usual flows of yield s...

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., Phys. Rev. Lett., 2010, 104, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration τf decreases as a power law of the applied shear rate . 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 τf, different fluidization processes are observed depending on 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 or e, the transient shear band is seen to invade the whole gap in a much smoother way. Still, the power-law behaviour appears to be 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.

Phase-field simulations of dynamic wetting of viscoelastic fluids

Abstract: We use a phase-field model to simulate displacement flow between a Newtonian and a viscoelastic fluid in a two-dimensional channel. The viscoelastic fluid is described by the Oldroyd-B model and the stress singularity at the contact line is regularized by the Cahn–Hilliard diffusion. In a small region near the contact line, the flow field features a large shear rate that produces a high polymer stress even at relatively low wetting speed. This polymer stress pulls the interface toward the viscoelastic fluid. As a result, the viscous bending at the contact line is enhanced when the advancing fluid is viscoelastic and weakened when the receding fluid is viscoelastic. However, the overall effect is limited by the small size of this strong shear region. These results are consistent with experimental observations. By examining the flow and stress field in the neighborhood of the contact line, we find that viscoelastic stress growth within a finite residence time provides a plausible explanation of the curious experimental observation that the contact line is affected by the viscoelasticity of the oligomeric solvent rather than the high molecular-weight polymer solute.

Hydromagnetic rotating flows of an oldroyd-b fluid in a porous medium

Abstract: In this article we consider the unsteady rotating flow of a magnetohydrodynamic (MHD) Oldroyd-B fluid for both constant and variable accelerated flows in a porous half space. The modified Darcy's law for an Oldroyd-B fluid is employed to model the governing equations. The exact solutions for these governing equations are obtained by employing the Laplace transform technique. The graphs are plotted for different values of dimensionless parameters. It is observed that the velocity field is strongly influenced by the porosity of the medium, applied magnetic field, fluid parameters and angular frequency. As a special case the obtained solutions are reduced to those for a hydrodynamic fluid in a non-porous medium. The corresponding solutions for a hydromagnetic Newtonian fluid in a porous medium are also recovered.

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Abstract: Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper. The Jeffrey fluid has two parameters, the relaxation time λ1 and retardation time λ2. The governing equations are simplified using the case of mild stenosis. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature profile, wall shear stress, shearing stress at the stenotsis throat and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

Pinch-off dynamics in foams, emulsions and suspensions

Abstract: The break up of a non-Newtonian yield stress fluid bridge (acrylic paint, mayonnaise, hair gel, foam, and bentonite) was investigated. The minimum neck radius, hmin, was measured as a function of time and fit to a power law with exponent n1. A rotational rheometer was used to measure the shear stress-rate of strain curve which was fit to a Herschel–Bulkley model with exponent n2. For the pure, as purchased fluids, the exponent from the time dependence of hmin (n1) and the rheology power law index (n2) were quantitatively the same. These results provide the first experimental confirmation of this relationship predicted by Suryo and Basaran. In the pure fluids, the pinch-off did not produce a satellite drop. In contrast, when the non-Newtonian fluids were diluted with a Newtonian fluid, the relationship between n1 and n2 was more complicated even though the diluted fluids were still Herschel–Bulkley, and the pinch-off produced satellite drops whose size was a continuous function of dilution.

Axial laminar flow of viscoplastic fluids in a concentric annulus subject to wall slip

Abstract: The flow of non-Newtonian fluids in annular geometries is an important problem, especially for the extrusion of polymeric melts and suspensions and for oil and gas exploration. Here, an analytical solution of the equation of motion for the axial flow of an incompressible viscoplastic fluid (represented by the Hershel–Bulkley equation) in a long concentric annulus under isothermal, fully developed, and creeping conditions and subject to true or apparent wall slip is provided. The simplifications of the analytical model for Hershel–Bulkley fluid subject to wall slip also provide the analytical solutions for the axial annular flows of Bingham plastic, power-law, and Newtonian fluids with and without wall slip at one or both surfaces of the annulus.

Cell models for micropolar flow past a viscous fluid sphere

Abstract: The Stokes axisymmetrical flow of an incompressible micropolar fluid past a viscous fluid sphere and the flow of a viscous fluid past a micropolar fluid sphere are investigated. The appropriate boundary conditions are taken on the surface of the sphere, while the proper conditions applied on the fictitious boundary of the fluid envelope vary depending on the kind of cell-model. These problems are solved separately in an analytical fashion, and the velocity profile and the pressure distribution inside and outside of the droplet are shown in several graphs for different values of the parameters. Numerical results for the normalized hydrodynamic drag force acting, in each case, on the spherical droplet-in-cell are obtained for various values of the parameters representing volume fraction, the classical relative viscosity, the micropolarity and spin parameters are presented both in tabular and graphical forms. Results of the drag force are compared with the previous particular cases.

MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermophysical properties

Abstract: In this paper we investigate the effects of temperature-dependent viscosity, thermal conductivity and internal heat generation/absorption on the MHD flow and heat transfer of a non-Newtonian UCM fluid over a stretching sheet. The governing partial differential equations are first transformed into coupled non-linear ordinary differential equation using a similarity transformation. The resulting intricate coupled non-linear boundary value problem is solved numerically by a second order finite difference scheme known as Keller-Box method for various values of the pertinent parameters. Numerical computations are performed for two different cases namely, zero and non-zero values of the fluid viscosity parameter. That is, 1/θ r →0 and 1/θ r ≠0 to get the effects of the magnetic field and the Maxwell parameter on the velocity and temperature fields, for several physical situations. Comparisons with previously published works are presented as special cases. Numerical results for the skin-friction co-efficient and the Nusselt number with changes in the Maxwell parameter and the fluid viscosity parameter are tabulated for different values of the pertinent parameters. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid phenomena, especially the UCM fluid phenomena. Maxwell fluid reduces the wall-shear stress.

Pressure transmission in Bingham fluids compressed within a closed pipe

Abstract: This study presents a mathematical model to simulate the pressure transmission that takes place when a Bingham fluid is pressurized at one pipe end and the other is maintained closed. The fluid motion inside the pipe is assumed to be one-dimensional, isothermal, weakly compressible and laminar. The model is based on the continuity and momentum equations which are iteratively solved by the method of characteristics. In contrast with Newtonian fluids, the results point out that Bingham fluids cannot transmit pressure because of the yield stress. In other words, as soon as the pressure gradient along the pipe is not enough to overcome the yield stress the fluid stops moving. A sensitivity analysis also shows that the final pressure gradient along the pipe depends not only on the Bingham number, i.e. yield stress, but also on the relationship between the pipe aspect ratio, the Reynolds and Mach numbers.

Mathematical model of pulsatile flow of non-Newtonian fluid in tubes of varying cross-sections and its implications to blood flow

Abstract: The effects of rheological behavior of blood and pulsatility on flow through an artery with stenosis have been investigated. Blood has been represented by a non-Newtonian fluid obeying Herschel–Bulkley equation. Using the Reynolds number as the perturbation parameter, a perturbation technique is adopted to solve the resulting quasi-steady non-linear coupled implicit system of differential equations. Analytical expressions for velocity distribution, wall shear stress, volumetric flow rate and the mean flow resistance have been obtained. It is observed that the wall shear stress and flow resistance increase for increasing value of yield stress with other parameters held fixed. One of the remarkable results of the present analysis is not only to bring out the effect of the size of the stenosis but also to study the influence of the shape of the stenosis. The change in the shape of the stenosis brings out a significant change in the value of flow resistance but it has no effect on the variation of wall shear stress except shifting the point (where it attains its maximum value) towards downstream. It is pertinent to point out that pulsatile flow of Newtonian fluid, Bingham plastic fluid and Power-law fluid become particular cases of the present model. The present approach has general validity in comparison with many mathematical models developed by others and may be applied to any mathematical model by taking into account of any type of rheological property of blood. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel–Bulkley fluid rather than Power-law and Bingham fluids. Finally, some biorheological applications of the present model have briefly been discussed.

Non-newtonian power-law fluid flow past a shrinking sheet with suction

Abstract: The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a shrinking sheet is investigated. The transformed boundary-layer equation is solved numerically for some values of the power-law index n and suction parameter s. The effects of these parameters on the skin friction coefficient are analyzed and discussed. Different from those of a stretching sheet, the solutions are not unique and exist only if adequate suction on the boundary is imposed.

Measurement of Magnetorheological Fluid Properties at Shear Rates of up to 25 000 s $^{-1}$

Abstract: Magnetorheological energy absorbers (MREAs) have been successfully deployed in occupant protection systems to protect against potentially injurious shock, crash and blast loads. These MREAs operate at shear rates upwards of 25 000 s-1, but magnetorheological fluids (MRFs) are typically characterized for shear rates up to 1000 s-1 in commercially available parallel counter-rotating disk rheometers. Because of the lack of availability of data at the required high shear rates, a Searle-type magnetorheometer (essentially a concentric cylinder rotating in a cup) was designed and fabricated at the University of Maryland. Using this magnetorheometer, two commercial MRFs were characterized over the shear rate range of 0-25 000 s-1 . It is shown that the rheometer was successful in replicating available characterization data at low shear rate, as well as quantifying high shear rate behavior as a function of applied field. In addition, it was shown that the Herschel-Bulkley constitutive model is appropriate and successfully characterized the apparent viscosity vs. shear rate behavior of the MRFs over this shear rate range. Experimental data demonstrate that an increase in field dependent yield stress can be realized over this entire shear rate range, so that MREAs can be designed using data taken with the magnetorheometer. Finally, the Mason number, which has been shown to be a useful non-dimensional number at low shear rates, also provides a useful physical interpretation at high shear rates.

Nonlinear stability of a visco-plastically lubricated viscoelastic fluid flow

Abstract: A core-annular flow of an Oldroyd-B fluid surrounded by a lubricating Bingham fluid is studied using energy stability methods. We consider base flows for which the lubricating fluid is unyielded close to the interface. For small finite restrictions on the size of shear stress and elastic stress perturbations we are able to demonstrate the exponential decay of a suitable energy functional for sufficiently small Reynolds number and Weissenberg number. These results extend those of [1] where only inelastic fluids were considered.

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

Abstract: The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.

MHD free-convective flow of micropolar and Newtonian fluids through porous medium in a vertical channel

Abstract: We have studied the fully-developed free-convective flow of an electrically conducting fluid in a vertical channel occupied by porous medium under the influence of transverse magnetic field. The internal prefecture of the channel is divided into two regions; one region filled with micropolar fluid and the other region with a Newtonian fluid or both the regions filled by Newtonian fluids. Analytical solutions of the governing equations of fluid flow are found to be in excellent agreement with analytical prediction. Analytical results for the details of the velocity, micro-rotation velocity and temperature fields are shown through graphs for various values of physical parameters. It is noticed that Newtonian fluids prop up the linear velocity of the fluid in contrast to micropolar fluid. Also the skin friction coefficient at both the walls is derived and its numerical values are offered through tables.

Squeeze flow behavior of (soft glassy) thixotropic material

Abstract: We study the flow behavior of a model soft glassy material − an aqueous suspension of Laponite − when it is squeezed between two circular parallel plates of different roughness. Aqueous suspension of Laponite shows a time dependent aging behavior as reflected in increased elastic modulus as well as yield stress, both of which however also decrease with an increase in the strength of deformation field thereby demonstrating typical thixotropic character. In a squeeze flow situation, under both force as well as velocity controlled modes; we find the behavior to be independent of the initial gap between the plates. In a constant force mode, the gap between the plates decreases until it reaches a finite limiting value, which is found to increase with an increase in age of the material as well as with a decrease in the applied force. In constant velocity experiments, at large gaps between the plates, normal force varies inversely with plate separation. The normal force is higher for a sample aged for a longer time as well as for a larger velocity of the top plate. We observe that the experimental behavior follows prediction of Herschel–Bulkley model solved for the squeeze flow (with different friction coefficients at the two plates) reasonably well under weak deformation fields. However, under strong deformation fields, experimental behavior deviates significantly from the prediction of Herschel–Bulkley model. This deviation arises due to melting or partial yielding of Laponite suspension under large deformation fields causing decrease in the viscosity, elastic modulus and the yield stress.

Estimation of Flow Properties of Gelled Fuels with Regard to Propulsion Systems

Abstract: Gelled fuels and propellants are shear-thinning non-Newtonian fluids. Their dependency of the shear viscosity from the shear rate can be described with sufficient accuracy by an extended version of the Herschel-Bulkley equation in the whole rocket and ramjet propulsion-relevant shear-rate range. Additionally to the analytically determined generalized Reynolds number for fluids, which follow the extended Herschel-Bulkley equation, a method for the estimation of critical Reynolds numbers (as a phenomenological approach) is presented. Both dimensionless numbers are useful for the characterization of the flow and partially also of the spray processes of gel fluids. The results show furthermore that both the shear-thinning property and the yield stress tend to stabilize the laminar flow and thus shift the critical Reynolds number to higher values when compared to Newtonian liquids.

Numerical study of the parameters governing the impact dynamics of yield-stress fluid droplets on a solid surface

Abstract: The impact dynamics of a droplet onto a solid surface are important in a variety of applications, such as inkjet printing and spray coating. Many fluids encountered in practical industrial applications exhibit non-Newtonian behavior, and therefore more research associated with non-Newtonian fluids is necessary. This paper reports on a numerical study of the impact dynamics of yield-stress fluid droplets. The numerical simulation is performed using a computational fluid dynamics package, Fluent 6.3, with a volume of fluid model. The numerical simulation models the presence of yield-stress and shear-rate dependent viscosity using the Herschel–Bulkley rheological model. The numerical results are found to be in qualitative agreement with experimental data in the literature. By performing extensive numerical simulations varying the impact velocity, rheological parameters, and surface tension, the influence of these parameters on the impact dynamics are evaluated, and the dominant effects that govern the spreading and relaxation phases are determined. The results show that while the spreading behavior is determined by the power-law index n, the non-Newtonian Reynolds number Ren, and the Weber number We, the retraction behavior is determined by the non-Newtonian capillary Can and the Bingham-capillary number B ^ . In addition, the scaling law that predicts the maximum spreading diameter is presented.

Creeping flow of Micropolar fluid past a fluid sphere with non-zero spin boundary condition

Abstract: This paper concerns the problem of creeping flow of an incompressible micropolar fluid past a fluid sphere with non-homogeneous boundary condition for micro rotation vector i.e. the micro rotation on the boundary of the fluid sphere is assumed to be proportional to the rotation rate of the velocity field on the boundary. The stream functions are determined by matching the solution of micropolar field equation for flow outside the fluid sphere with that of the Stokes equation for the flow inside the fluid sphere. The drag force experienced by a fluid sphere is evaluated and its variation is studied with respect to the material parameters. Some well-known results are then deduced.