Showing papers on "Herschel–Bulkley fluid published in 2004"

Peristaltic transport of a power-law fluid in a porous tube

Abstract: Peristaltic transport of a power-law fluid in an axisymmetric porous tube is studied under long wavelength and low Reynolds number assumptions The slip boundary conditions given by Beavers–Joseph and Saffman type are considered in obtaining solutions for the flow and resulting pumping characteristics are compared Trapping and reflux phenomena are discussed for various parameters of interest governing the flow like Da Darcy number, α Beavers–Joseph constant and n the fluid behavior index The novel feature arising in pumping due to a straight section dominated (SSD) wave form other than sinusoidal wave is discussed The time mean flow becomes negative in free pumping for a shear thickening fluid or shear thinning fluid for an expansion or contraction SSD wave, respectively The pressure rise increases for the increasing of Da against which the peristalsis acts as a pump and decreases for an increase in α Peristalsis works as a pump against a greater pressure rise for a shear thickening fluid and the opposite happens for a shear thinning fluid, compared with Newtonian fluid The trapped bolus volume for sinusoidal wave is observed to decrease as the fluid behavior index decreases from shear thickening to shear thinning fluid, whereas it increases for increasing Darcy number The rheological property of the fluid, wave shape and porous nature of the wall play an important role in peristaltic transport and may be useful in understanding transport of chyme in small intestines

Conditions for static bubbles in viscoplastic fluids

Abstract: We consider the slow motion of a gas bubble in a cylindrical column filled with a viscoplastic fluid, modeled here as a Herschel–Bulkley fluid. Because of the yield stress of the fluid, it is possible that a bubble will remain trapped in the fluid indefinitely. We adapt Prager’s two variational principles to our problem. From these variational principles we develop two general stopping conditions, i.e., for a given bubble we can calculate a critical Bingham number above which the bubble will not move. The first condition is derived by bounding the velocity field and the second condition by bounding the stress field. We illustrate these conditions by considering specific bubble shapes, e.g., axisymmetric bubbles. We also develop a condition for bubble motion.

Estimation of the parameters of Herschel-Bulkley fluid under wall slip using a combination of capillary and squeeze flow viscometers

Abstract: The determination of the parameters of viscoplastic fluids subject to wall slip is a special challenge and accurate results are generally obtained only when a number of viscometers are utilized concomitantly. Here the characterization of the parameters of the Herschel-Bulkley fluid and its non-linear wall slip behavior is formulated as an inverse problem which utilizes the data emanating from capillary and squeeze flow rheometers. A finite element method of the squeeze flow problem is employed in conjunction with the analytical solution of the capillary data collected following Mooney’s procedure, which uses dies with differing surface to volume ratios. The uniqueness of the solution is recognized as a major problem which limits the accuracy of the solution, suggesting that the search methodology should be carefully selected.

Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate

Abstract: The boundary layer flow of a viscoelastic fluid of the second-grade type over a rigid continuous plate moving through an otherwise quiescent fluid with constant velocity U is studied. Assuming the flow to be laminar and two-dimensional, local similarity solution is found with fluid's elasticity and plate's withdrawal speed as the main variables. Results are presented for velocity profiles, boundary layer thickness, wall skin friction coefficient and fluid entrainment in terms of the local Deborah number. A marked formation of boundary layer is predicted, even at low Reynolds numbers, provided the Deborah number is sufficiently large. The boundary layer thickness and the wall skin friction coefficient are found to scale with fluid's elasticity—both decreasing the higher the fluid's elasticity. The amount of fluid entrained is also predicted to decrease whenever a fluid exhibits elastic behavior.

Roll waves in mud

Abstract: The stability of a viscoplastic fluid film falling down an inclined plane is explored, with the aim of determining the critical Reynolds number for the onset of roll waves. The Herschel–Bulkley constitutive law is adopted and the fluid is assumed two-dimensional and incompressible. The linear stability problem is described for an equilibrium in the form of a uniform sheet flow, when perturbed by introducing an infinitesimal stress perturbation. This flow is stable for very high Reynolds numbers because the rigid plug riding atop the fluid layer cannot be deformed and the free surface remains flat. If the flow is perturbed by allowing arbitrarily small strain rates, on the other hand, the plug is immediately replaced by a weakly yielded ‘pseudo-plug’ that can deform and reshape the free surface. This situation is modelled by lubrication theory at zero Reynolds number, and it is shown how the fluid exhibits free-surface instabilities at order-one Reynolds numbers. Simpler models based on vertical averages of the fluid equations are evaluated, and one particular model is identified that correctly predicts the onset of instability. That model is used to describe nonlinear roll waves.

Flow of a generalized second grade non-Newtonian fluid with variable viscosity

Abstract: A modified constitutive equation for a second grade fluid is proposed so that the model would be suitable for studies where shear-thinning (or shear-thickening) may occur. In addition, the dependence of viscosity on the temperature follows the Reynolds equation. In this paper, we propose a constitutive relation, (18), which has the basic structure of a second grade fluid, where the viscosity is now a function of temperature, shear rate, and concentration. As a special case, we solve the fully developed flow of a non-Newtonian fluid given by (11), where the effects of concentration are neglected.

Rheological Properties of Banana Puree at High Temperatures

Abstract: The rheological behavior of banana puree was determined using a dynamic stress rheometer with a pressure couette fixture, which allowed experiments to be conducted at high temperature. The pressure couette was pressurized with compressed air to 206.8 kPa (gage pressure) and experiments were carried out at temperatures ranging from 30 to 120°C. The shear stress values ranged from 10 to 170 Pa and the shear rate values from 10−5 to 103 s−1. The model that best fitted the experimental data at all temperatures was the Herschel-Bulkley model. There was a usual tendency for the apparent viscosity to decrease with increasing temperature but an increase in apparent viscosity with increasing from 50 to 60°C and from 110 to 120°C was found. This could be due to interaction of polysaccharides present in banana puree. There was a slight difference between the apparent viscosity values for increasing shear stress sweeps and those for the decreasing shear stress sweeps suggesting time dependency of the rheolog...

Theory and applications of viscous fluid flows

Abstract: 1 Navier-Stokes-Fourier Exact Model.- 2 Some Features and Various Forms of NSF Equations.- 3 Some Simple Examples of Navier, NS and NSF Viscous Fluid Flows.- 4 The Limit of Very Large Reynolds Numbers.- 5 The Limit of Very Low Reynolds Numbers.- 6 Incompressible Limit: Low Mach Number Asymptotics.- 7 Some Viscous Fluid Motions and Problems.- 8 Some Aspects of a Mathematically Rigorous Theory.- 9 Linear and Nonlinear Stability of Fluid Motion.- 10 A Finite-Dimensional Dynamical System Approach to Turbulence.- References.

Squeeze flow of soft solids between rough surfaces

Abstract: Newtonian liquids and non-Newtonian soft solids were squeezed between parallel glass plates by a constant force F applied at time t=0. The plate separation h(t) and the squeeze-rate % MathType!MTEF!2!1!+- % feaafaart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiabg2 % da9iabgkHiTiqadIgagaGaaaaa!39AF! $$ V = - \dot h $$ were measured for different amplitudes of plate roughness in the range 0.3–31 μm. Newtonian liquids obeyed the relation V∝h 3 of Stephan (1874) for large plate separations. Departures from this relation that occurred when h approached the roughness amplitude were attributed to radial liquid permeation through the rough region. Most non-Newtonian materials showed boundary-slip that varied with roughness amplitude. Some showed slip that varied strongly during the squeezing process. Perfect slip (zero boundary shear stress) was not approached by any material, even when squeezed by optically-polished plates. If the plates had sufficient roughness amplitude (e.g. about 30 μm), boundary slip was practically absent, and the dependence of V on h was close to that predicted by no-slip theory of a Herschel-Bulkley fluid in squeeze flow (Covey and Stanmore 1981, Adams et al. 1994).

Nonlinear stability of a visco-plastically lubricated viscous shear flow

Abstract: A common problem in multi-layer shear flows, especially from the perspective of process engineering, is the occurrence of interfacial instabilities. Here we show how multi-layer duct flows can in fact be made nonlinearly stable, by using a suitable lubricating fluid. First we show how interfacial instabilities may be eliminated through the introduction of a yield stress fluid as the lubricant and by preserving an unyielded layer adjacent to the interface. Second we show how to treat the nonlinear stability of a two-layer flow, allowing finite motion of the domains. We focus on the simplest practically interesting case of visco-plastically lubricated viscous shear flow: a core–annular pipe flow consisting of a central core of Newtonian fluid surrounded by a Bingham fluid. We demonstrate that this flow can be nonlinearly stable at significant Reynolds numbers and produce stability bounds. Our analysis can be straightforwardly generalized to other flows in this class.

A model for wave propagation in a composite solid matrix saturated by a single-phase fluid

Abstract: This paper presents a theory to describe wave propagation in a porous medium composed of two solids saturated by a single-phase fluid for spatially variable porosity. This problem has been previously solved for constant porosity when one of the solids is ice or clay, but that model is not useful for most realistic situations. The equations for variable porosity are derived from the virtual work principle, where the generalized coordinates are identified as the displacements of the two solid phases and a new variable associated with the relative fluid flow, whose divergence is the change in fluid content. The generalized forces are the fluid pressure and combinations of the stress tensor of each solid phase and the fluid pressure. The Lagrangian equations of motion are derived for the isotropic case and a theorem on the existence and uniqueness of their solution is given. The plane wave analysis reveals the existence of three compressional and two shear waves. The theory is applied to wave propagation in s...

One‐dimensional fluid diffusion induced by constant‐rate flow injection: Theoretical analysis and application to the determination of fluid permeability and specific storage of a cored rock sample

Abstract: [1] We describe the conceptual design and first application of a new method for simultaneously measuring the fluid permeability and specific storage of a rock sample. In our laboratory tests, a constant flow rate single-stroke piston pump injects fluid into a cored rock specimen placed between two reservoirs in which fluid pressure is recorded. For this geometry we have derived a new analytic solution of the governing diffusion equation describing the one-dimensional fluid flow. This new analytic solution in the time domain consists of two parts: an asymptotic linear function of time, and a transient part which decays to zero as time increases. The model predicts that the fluid pressures of the upstream and downstream reservoirs both increase linearly with time after the initial transient vanishes. The slope of the linear pressure variation depends on the specific storage of the rock sample for a given test condition, and the differential pressure between the two reservoirs is related to the permeability. If the downstream pressure is not recorded, the permeability can be calculated from the zero intercept of the linear upstream fluid pressure variation. This calculation is quite straightforward and no tedious history curve matching is required. We applied our new method to measure fluid permeability and specific storage of Westerly granite. The measured values of the permeability are consistent with those published in the literature. The main advantages of our method are the reliability of the testing method, its economy of time, and the flexibility in adapting the system parameters to tests at different conditions.

A Study of Dam Break Wave of Thixotropic Fluid: Bentonite Surges down an Inclined plane

Abstract: Thixotropic fluids are commonly used in the construction industry (e.g. liquid cements, liquid concrete, drilling fluids), industrial applications (e.g. muds, paints) and the food industry (e.g. liquid dairy products, ketchup). Related applications include some forms of mud flows and debris flows, pasty sewage sludges and some wastewater treatment residues. Thixotropy is the characteristic of a fluid to form a gelled structure over time when it is not subjected to shearing and to liquefy when agitated. A thixotropic fluid is a non-Newtonian fluid with a viscosity that is a function of both shear rate y and instantaneous state(s) of structure of the material. Such a fluid exhibits a reversible time-dependent decrease in apparent viscosity under shear rate and a gradual recovery when the shear stress is removed. This report describes a basic study of dam break wave with thixotropic fluid. A dam break wave is a sudden release of a mass of fluid in a channel. This type of flows has not been studied to date with thixotropic fluid, despite its practical applications : e.g., mudflow release, concrete tests including L-Box and J-Ring for self-consolidating concrete testing, paint applications. Theoretical considerations were developed based upon a kinematic wave approximation of the Saint-Venant equations for a thixotropic fluid down a prismatic sloping channel. The thixotropic fluid model of COUSSOT et al. (2002a) was used since it describes the instantaneous state of fluid structure by a single parameter. The analytical solution of the basic flow motion and rheology equations predict three basic flow regimes depending upon the fluid properties and flow conditions, including the initial degree of jamming of the fluid : (1) a short motion with relatively-rapid flow stoppage for relatively small mass of fluid, (2) a fast flow motion for a large mass of fluid, or (3) an intermediate motion initially rapid before final fluid stoppage for intermediate mass of fluid and intermediate initial rest period To. Physical experiments were performed with bentonite suspensions. Systematic experiments showed four types of flows. For small bentonite mass concentrations and short relaxation times To, the fluid flowed rapidly down the slope and spilled into the overflow container (Flow Type I). For intermediate concentrations and rest periods, the suspension flowed rapidly initially, decelerated relatively suddenly, continued to flow slowly for sometimes before complete stoppage (Flow Type II). For large mass concentrations and long rest periods, the mass of fluid stretched down the slope, until the head separated from the tail (Flow Type III). The last flow pattern (Type IV) corresponded to an absence of flow for large bentonite concentrations and long rest times. Quantitative informations were documented in terms of the final fluid thickness, wave front position, wave front curvature, side profile of the wave front during motion and after stoppage, as well as the flow motion immediately after gate opening. Some freesurface instabilities are also discussed and illustrated. It is believed that the present study is the first theoretical analysis combining successfully the basic principles of unsteady flow motion (i.e. Saint-Venant equations) with a thixotropic fluid model, which was validated with large-size systematic laboratory experiments. It is the belief of the writers that, for such complex systems this kind of approach, combining both rheology and fluid dynamics, is necessary to gain new insights of these complicated flow motions.

Stress-controlled localization of deformation and fluid flow in fractured rocks

Abstract: The discrete-element method (UDEC — Universal Distinct Element Code) was used to numerically model the deformation and fluid flow in fracture networks under a range of loading conditions. A series of simulated fracture networks were generated to evaluate the effects of a range of geometrical parameters, such as fracture density, fracture length and anisotropy. Deformation and fluid flow do not change progressively with increasing stress. Instability occurs at a critical stress and is charzacterized by the localization of deformation and fluid flow usually within intensively deformed zones that develop by shearing and opening along some of the fractures. The critical stress state may be described in terms of a driving stress ratio, R = (fluid pressure — mean stress)/1/2 (differential stress). Instability occurs where the R ratio exceeds some critical value, RC, in the range – 1 to –2. At the critical stress state, the vertical flow rates are characterized by a large increase in both their overal magnitude and degree of localization. This localization of deformation and fluid flow develops just prior to the critical stress state and may be characterized by means of multifractals. The stress-induced criticality and localization displayed by the models is an important phenomenon, which may help in the understanding of deformation-enhanced fluid flow in fractured rock masses

Characterization of the physical parameters in a process of magnetic separation and pressure-driven flow of a magnetic fluid

Abstract: The equations governing the motion of a magnetic fluid are presented. These equations are non-linear and give rise to non-Newtonian effects attributable to the magnetization of the fluid. The equations are made dimensionless and the physical parameters of the coupled hydrodynamic–magnetic problem identified. The study is first applied to describe the motion of a magnetic droplet freely suspended in a viscous fluid undergoing a permanent magnetic field. A first-order theory is developed for the regime of small drop deformation in which viscous forces dominate inertial hydrodynamic force. At this regime, it is shown that the drift velocity of a magnetic drop scales with the square of the applied magnetic field and the deformation of the drop scales linearly with the applied field. Experiments are carried out and the range of validity of the small deformation analysis determined. The pressure-driven flow of a magnetic fluid is solved by a regular asymptotic expansion for two cases: a Poiseuille flow of a single magnetic fluid and a core pipe flow with a magnetic fluid adjacent to the tube wall. The theory is used to predict the volume rate of a viscous magnetic fluid separated from a non-magnetic viscous fluid by the action of a magnetic field. The apparent viscosity of a magnetic fluid as a function of magnetic parameters is also examined from our theory. A possible application of the present theoretical studies is on the remediation technology addressed to oil spills in natural environments.

Model for large strain consolidation with compressible pore fluid

Abstract: A numerical model, called CCPF1 (Consolidation with Compressible Pore Fluid 1), is presented for one-dimensional large strain consolidation of a saturated porous medium with compressible pore fluid. The algorithm includes all the capabilities of a previous large strain consolidation code, CS2, written for incompressible pore fluid. In addition, fluid density and fluid viscosity are functions of fluid pressure in CCPF1. Generalization of the numerical approach to accommodate these functions requires several modifications to the CS2 method, including phase relationships, intrinsic permeability, pore pressure, fluid potential, and mass flux. Inertial forces are neglected and isothermal conditions are assumed. The development of CCPF1 is first presented, followed by an example that illustrates the effects of pore fluid compressibility on the mechanics of consolidation of saturated porous media. Copyright © 2004 John Wiley & Sons, Ltd.

An application of Bingham model to viscous fluid modeling of solid flow in moving bed

Abstract: Solid flow plays important roles in a moving bed reactor, for example, it determines the path and the residence time of the solid reactants as well as the stress distribution. The continuum models are useful for the kinetic based process analysis since their simplicity and computation load, although the discrete element approach is capable of estimating not only the particle motion but also the stress distribution in the bed. One of the continuum approaches is viscous fluid model. It is able to estimate solid flow pattern although it needs to appropriately determine the shape of stagnant region and viscosity before the simulation. In this study the Bingham model, which is the simplest shear rate-shear stress model of plastic fluid, is applied to the viscous fluid model of bulk solid flow within packed bed. This model successfully reproduce solid flow pattern in packed bed without setting stagnant zone, and the rheological properties can be obtained from simple preliminary experiments. Therefore, the viscous fluid model with the Bingham model is considered as a useful solid flow model for process analysis of moving bed reactors.

On kinematic conditions affecting the existence and non-existence of a moving yield surface in unsteady unidirectional flows of Bingham fluids

Abstract: If a Bingham fluid at rest undergoes a unidirectional flow through the sudden motion of one of its boundaries and the diffusion equation applies in the yielded region, it is shown that the yield surface cannot move with a finite speed into the unyielded material if both the velocity and its gradient are zero at the interface. Conversely, if the velocity is non-zero at the yield surface it can move with a finite speed. Applications of this result to the Rayleigh problem and a few shearing flows are made to show when the Bingham fluid behaves like a Newtonian fluid throughout the flow region or when the yield stress effects are important.

Microstructural Analysis and Control of Magneto-Rheological Fluid

Abstract: Characteristic phenomenological behavior of MR fluids is typically modeled by Bingham’s equation, which has no fundamental connection to the microstructure of MR fluid and the fully coupled mechanical-electrical-magnetic equations. In this paper microstructurally, kinetic theory-based model of MR fluids (consisting of micro-sized ferrous particles suspended in a Newtonian fluid) are developed. For modeling these composite systems, dumbbell models in which two beads joined by an elastic connector are investigated. In these models the distributed forces from the carrier fluid and from the magnetic field on the suspended particle are idealized as being localized on beads. Microscale constitutive equations relating flow, stress, and particle orientation are produced by integrating the coupled equations governing forces, flow, and orientation over a representative volume of particles and carrier fluid. Coefficients in the constitutive equations are specified not by a fit to macroscale experimental flow measurement but rather in terms of primitive measurements of particle microstructure, carrier fluid, viscosity and density, and temperature. These new models for MR fluids are three dimensional and applicable to any flow geometry, while the Bingham plastic model is in general applicable only to shear flow. The models in this paper reduce to forms similar to Bingham’s model in a simple shear flow, but with coefficients which arise from fundamental electromagnetic considerations and microstructural features such as geometrical, magnetic and mechanical characterization of the particles, quantities measured primitively from the carrier fluid, magnetic field and temperature.Copyright © 2004 by ASME

Start-up of channel-flow of a Bingham fluid initially at rest

Abstract: — We present an analytical solution of plane motion for a Bingham fluid initially at rest subjected to a suddenly applied constant pressure gradient. Using the Laplace transform we obtain expressions which allow a direct easy calculation of the velocity, of the plug thickness and of the rate of flow as function of time.

Resistance to uniaxial extensional flow of fibre suspensions

Abstract: The tensile stress due to resistance to uniaxial extensional flow of fibre suspensions in Newtonian and non-Newtonian fluids has been measured using the filament stretching technique. It has been found that addition of fibres to a Newtonian fluid increases the extensional viscosity. The steady state results agree with Bachelor’s theory and the stress growth behaviour is qualitatively predicted by the theory of Dinh and Armstrong. Experimental results from this work have also shown that the behaviour of a fibre suspension in viscoelastic fluid is qualitatively described by Fan’s equation. The added fibres increase the extensional stress growth coefficient of the viscoelastic fluid at low strain but have marginal effect on the fluid after the onset of strain-hardening.

The Importance of Online Viscosity Measurement for Leak Detection and Other Simulation Applications

Abstract: Knowledge of viscosity is an important property in fluid dynamics because it is a key factor in determining the amount of fluid that can be transported in a pipeline during a specific period of time. Dynamic viscosity, defined as the viscosity measured under force induced flow, not only describes the nature of the fluid but is also useful in predicting the behavior of the shear stress with respect to the rate of the angular deformation of the fluid. The addition of the viscous deceleration component in the linear momentum equation is important in describing the real fluid flow in the pipeline. The two factors producing viscosity are cohension and the rate of transfer of molecular momentum. The Reynolds number, which is based on the viscosity, is an important quantity which engineers use to determine if a flow is laminar or turbulent. Hence viscosity plays a major role in the generation of turbulence. Knowing the viscosity is also essential to improving system performance (volumetric efficiency and mechanical efficiency). Because viscosity typically varies among the different fluids transported in petroleum pipelines, it is widely considered that online measurement can be beneficial to pipeline operations. This is particularly true for complex applications that depend on a real-time fluid mechanics model for leak detection, batch tracking, and power optimization, among others.Copyright © 2004 by ASME