Showing papers on "Herschel–Bulkley fluid published in 1993"

Design and construction of a linear shear stress flow chamber

Abstract: A new paralle plate flow chamber that has a linear variation of shear stress, starting from a predetermined maximum value at the entrance and falling to zero at the exit, has been designed and tested. This is in contrast to the usual rect-angular channel plan which produces a constant shear stress over the entire length. The new design is based on the theory of Hele-Shaw flow between parallel plates. To verify the efficacy of the flow channel, the effect of fluid shear stress on platelet adhesion to a fibrinogen-coated glass surface was tested. The percentage of attached platelets after 5 min of shear stress is shown to be a function of shear stress. With this new flow chamber, cell-cell interactions can be studied efficiently over a wide range of shear stress using a single run at constant discharge.

Flow of a generalized second grade fluid between heated plates

Abstract: We examine the fully developed flow of a generalized fluid of second grade between heated parallel plates, due to a pressure gradient along the plate. The constant coefficient of shear viscosity of a fluid of second grade is replaced by a shear dependent viscosity with an exponentm. If the normal stress coefficients are set equal to zero, this model reduces to the standard power-law model. We obtain the solution for the case when the temperature changes only in the direction normal to the plates for the two most commonly used viscosity models, i.e. (i) when the viscosity does not depend on temperature, and (ii) when the viscosity is an exponentially decaying function of temperature.

Peristaltic motion of a third-order fluid in a planar channel

Abstract: In order to determine the characteristics of the peristaltic transport of shear thinning non-Newtonian materials, the motion of a third-order fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength and negligibly small Reynolds number was analyzed using a perturbation expansion in terms of a variant of the Deborah number. Within the range of validity of this analysis, we found the pumping rate of a shear-thinning fluid is less than that for a Newtonian fluid having a shear viscosity the same as the lower-limiting viscosity of the nonNewtonian material. Also, the space of variables for which trapping of a bolus of fluid occurs is reduced for the shear-thinning fluid investigated here.

Free convection effects on the oscillatory flow of a couple stress fluid through a porous medium

Abstract: Effects of free convection currents on the oscillatory flow of a polar fluid through a porous medium, which is bounded by a vertical plane surface of constant temperature, have been studied. The surface absorbs the fluid with a constant suction and the free stream velocity oscillates about a constant mean value. Analytical expressions for the velocity and the angular velocity fields have been obtained, using the regular perturbation technique. The effects of Grashof numberG; material parameters α and β; Prandtl numberP; permeability parameterK and frequency parametern on the velocity and the angular velocity are discussed. The effects of cooling and heating of a polar fluid compared to a Newtonian fluid have also been discussed. The velocity of a polar fluid is found to decrease as compared to the Newtonian fluid.

Laminar, unidirectional flow of a thixotropic fluid in a circular pipe

Abstract: In this paper we study the unidirectional, axisymmetric flow of a bentonite mud in a circular pipe. Bentonite mud is an inelastic, thixotropic, generalised-Newtonian fluid. We use a rheological model that characterises this behaviour in terms of a single parameter Λ which is a measure of the amount of structure in the fluid. The behaviour of Λ is determined by a single rate equation which models the tendency of fluid structure to increase whilst being limited by the imposed shear rate. We find that, for certain parameter ranges, the model is not structurally stable, but that this problem can be eliminated by including diffusion of fluid structure. A graph of the equilibrium shear stress for a given shear rate (the rheogram) is not monotonic, yet no mechanical instability occurs in pipe flow. We contrast this with recent work on the pipe flow of a Johnson-Segalman-Oldroyd fluid which displays spurting and oscillatory behaviour. The difference lies in the relative magnitude of normal stress effects in the two fluids. There appear to be no grounds for discarding the constitutive model studied here simply because of the non-monotonicity of the equilibrium rheogram.

Mixing of a viscoelastic fluid in a time-periodic flow

Abstract: We present an experimental and computational investigation of mixing of a viscoelastic fluid in two-dimensional time-periodic flows generated in an eccentric cylindrical geometry. The objective of the study is to investigate the impact of fluid elasticity on the morphological structures produced by the advection of passive tracers in chaotic flows. The relevant dimensionless numbers that quantify the rheological differences with respect to the Newtonian fluid are the Deborah number (De), defined as the ratio of the fluid timescale to the flow timescale, and the Weissenberg number (We), defined as the product of the fluid timescale and the mean shear rate. The effects of elasticity are investigated in the limit of slow flows, De ≈ 0 and We < 0.1. The experimental window of We is limited to Newtonian behaviour on the low end and the transition to three-dimensional flow on the high end; experiments show that this window is small, 0.02 < We < 0.1. Typical values of the Reynolds number and the Strouhal number are O(0.001) and O(0.1), respectively.Results from experiments with a constant-viscosity elastic fluid and computations using the upper-convected Maxwell constitutive equation are presented. Even though the streamlines for the elastic flow are nearly indistinguishable from the Newtonian flow, small deviations in the velocity field produce large effects on chaotically advected patterns. Elasticity affects both the asymptotic coverage of a dyed passive tracer and the rate at which the tracer is stretched. In all cases the tracer undergoes exponential stretching, but on a longer timescale as the elasticity increases. According to flow conditions, elasticity might increase or decrease the degree of regularity; however, island symmetry does not seem to be affected. Similar phenomena are observed in both the experiments and computations; therefore, an analysis of the chaotic dynamics of the periodic flow using numerical techniques is possible.

Behavior of a Squeeze Film Damper with an Electrorheological Fluid

Abstract: The flow properties of electrorheological (ER) fluids change with the application of an electric field. These materials have been proposed as smart lubricants. Existing ER fluids are best described by the Bingham model. The Bingham material is described by two parameters, yield shear stress and viscosity. When the shear stress magnitude exceeds the yield shear stress, quasi-Newtonian flow results; otherwise, the material is rigid. For many ER fluids, the yield shear stress is proportional to the square of the applied electric field. In the present study, the Bingham model is applied to the one-dimensional squeeze film damper. A rigid core forms midway across the film, the core thickness being proportional to the yield shear stress. A modified Reynolds equation is obtained, from which the bearing behavior can be predicted. The damper forces are predicted as a function of the eccentricity ratio, and a dimensionless parameter which depends on the yield shear stress. Calculations are performed for a simple ro...

Observations of granular-fluid mixture under an oscillatory sheet flow

Abstract: Sediment transport due to wave action has been classified into three modes; bed load over a practically flat bed under small tractive force, suspended load over a rippled bed under moderate shear stress, and sheet flow under high shear stress where ripples are washed out. Studies of the sheet flow have recently received much attention because a large amount of sand is transported under this mode. However, sheet flow is a grain-fluid mixture flow of high concentration, thus the mechanism is more complex than that of the other two modes. In the sheet flow region where several layers of grains are mobilized, grain to grain collision performs a main role in the momentum exchange. The relationship between the applied stress and the bulk deformation is not a Newtonian, and depends on the grain concentration and the rate of deformation. Hanes - Bowen(1985) have proposed a granular - fluid model to describe intense bed - load transport in an uni-directional flow. In their model, the flow is divided into two regions; grain collision dominated granular fluid region, and fluid stress dominated fluid shear region. They have derived a relation mathematically between the grain transport rate and applied shear stress. Shibata - Mei(1986) have proposed another granular - fluid model in socalled macro viscous region where the shear rate is low and granular friction is as important as granular collision. Mathematical expressions to describe velocity profiles and granular discharge have been deduced. These studies provide physical insight into the mechanism of sheet flow, however, the results are not able to be applied directly because the oscillatory sheet flow is a dynamic process under an unsteady flow.

Secondary flow of a Casson fluid in a slightly curved tube

Abstract: The fully developed, steady flow of a Casson fluid through a slightly curved tube of circular cross-section has been analysed. The solution is developed by successive approximation from the perturbation of flow of a Casson fluid in a straight tube. The resulting differential equations have been solved by a finite difference method followed by an iterative procedure. Velocity distribution, pressure and nature of the streamlines have been obtained for different values of yield number and Reynolds number. For specific values of the yield number, the results have been compared with those for a Bingham fluid. Comparing the results with a Newtonian fluid, the effect of yield number has been determined.

A new approach to modelling viscoelastic flow

Abstract: By adapting the free Lagrangian approach (M.J. Fritts and J.P. Boris, J. Comput. Phys, 31 (1979) 173), a new numerical simulation technique for modelling viscoelastic fluid flow has been developed. Using a comoving Voronoi mesh, the method is able to track the details of fluid behaviours, e.g. deformation and stream line. The primary results include a Johnson-Segalman fluid and a single-integral Doi-Edwards fluid in a simple planar channel, and a Giesekus-Leonov fluid and an Oldroyd-B fluid in a planar 4:1 abrupt contraction at modestly high Weissenberg number. A free-surface flow is also considered.

Velocity and stress fields of polymeric liquids flowing in a periodically constricted channel: Part 2. Observations of non-Newtonian behavior

Abstract: The apparatus described in the preceding Part 1 of this work has been used to investigate the flow behavior of a 20% polystyrene solution in a periodically constricted channel Local velocity and stress measurements made over a range of flow rates, corresponding to creeping flow and shear-rate based Weissenberg numbers as large as 15, exhibited clear departures from Newtonian behavior These departures included normal stress growth delay, local maxima and sign reversal in the shear stress near the flow cell surfaces, and significant deviation of the axial velocity profile from Newtonian predictions Finite element simulations for creeping flow of the generalized Newtonian, upper convected Maxwell and White-Metzner fluids predict all of these features to some extent, but in general fail to describe the overall behavior of the fluid A simplified analysis, using the Maxwell model with a shear-thinning velocity profile, indicates that the most striking non-Newtonian effect, the shear stress sign reversal, is associated with elastic recoil as fluid elements near the wall move from a region of high shear rate into a region of low shear rate That this can occur only if the shear rates along the wall exceed the Newtonian predictions is consistent with our observations

An experimental investigation of the flow of an electro-rheological fluid in a Rayleigh step bearing

Abstract: The transport properties of unexcited and excited electro-rheological (ER) fluid in combined Couette and Poiseuille flow are investigated. In particular the question of whether the fluid can be considered as a continuum with Bingham plastic constitutive properties, even though it is a two-phase solid-liquid mixture, is addressed. The hydrodynamic pressures generated using ER fluid in a Rayleigh step bearing at the limiting condition of zero net flow rate were measured. The properties exhibited by the fluid are compared with independently obtained data showing the continuum principle to be applicable to the flows examined.

Nonlinear stability and asymptotic behavior of shearing motions of a non-Newtonian fluid

Abstract: The goal is to establish the nonlinear stability of discontinuous steady states, and study the asymptotic behavior of solutions, for the initial-boundary value problem in one space dimension governing incompressible, isothermal shear flow of a non-Newtonian fluid driven by a constant pressure gradient. The fluid is assumed to be highly elastic and viscous; the non-Newtonian contribution to the shear stress satisfies a differential constitutive law characterized by a nonmonotone relation between the total steady shear stress and shear strain-rate that results in steady states having, in general, discontinuities in the strain rate. In a regime where Reynolds number is small compared to Deborah number, it is shown that every solution tends to a steady state as $t \to \infty $, and steady states that are nonlinearly stable, in a precise sense, are identified.

On the rectilinear flow of a second-order fluid and the role of the second normal stress difference in edge fracture in rheometry

Abstract: Assuming that a rectilinear flow is possible in an incompressible simple fluid, the vanishing of the shear stress on a free surface in the flow is shown to lead to one of three restrictions: the second normal stress is zero, or either the velocity gradient is orthogonal to the external, unit normal to the surface, or it is parallel to the unit normal. The consequences of the last two are investigated when the fluid is the second-order fluid and the flow occurs between two parallel plates and the free surface has a small semi-circular indentation in it and when the edge crack in the free surface is almost parallel to the plates. It is found that when there is a small semi-circular indentation, the normal stress at the midway point is tensile, causing the free surface to move into the fluid. The proof depends on obtaining a lower bound to the shear rate at this point and is based on an application of the maximum principle to harmonic functions. Hence, the Tanner-Keentok calculation of the stress at this point is in accord with the present proof; indeed, the magnitude found by them is the lower bound to the true tensile stress and equals the true tensile stress if the ratio of the radius of the indentation to the semi-gap between the parallel plates vanishes. When the edge fracture has moved into the fluid, driven by the above tensile stress and has become almost flat, it is shown that the velocity gradient is parallel to the unit normal to the surface and that the normal stress is compressive, forcing the edges together and preventing the crack from moving further into the fluid.

Motion of the yield surface in a Bingham fluid with a simple-shear flow geometry

Abstract: Non-steady flow of a Bingham fluid is analyzed for a simple-shear flow geometry. It is asserted that when a yield surface undergoes a lateral motion, the spatial gradient of shear stress in the lateral direction is continuous across the yield surface. Using this property, the equation of motion of a Bingham fluid was transformed into a form of the moving boundary problem in which appropriate boundary conditions are supplemented at the yield surface. This problem is compared with the co-called Stefan problem of crystallization. We find that, in a Bingham fluid, the lateral motion of the yield surface is determined by a spatio-temporally non-local mechanism, while, in the Stefan problem, the motion of the crystallization front is determined merely by a spatially non-local mechanism.

The influence of viscometer dynamics on the characterization of an electrorheological fluid under sinusoidal electric excitation

Abstract: The dynamic response of a controlled‐strain, Couette viscometer employed for the characterization of the frequency response of an electrorheological (ER) fluid is studied both numerically and experimentally. In the numerical model, the ER fluid flow between the cup and bob elements of the viscometer is coupled with the mechanical response of the cup–torque sensor system. The Bingham model is used for describing the ER fluid, with various functional forms for relating the electric field strength to the Bingham stress. Variation in the shear‐rate dependency of the Bingham stress response is also represented. Dynamic resonance tends to dominate the cup rotation response and the shear rate of the fluid. The Bingham stress response contains higher harmonic components whenever it does not follow a second power‐law relationship exactly with the electric field strength. Higher harmonics induce their own resonances at relatively lower values of excitation frequency. Experimental results obtained with zeolite‐based ER fluids generally agree with those predicted through the numerical analysis. The characterization of an ER fluid will be reasonably accurate only if the excitation frequency of the electric field is low, say less than 0.1 times the natural frequency of the cup–torque sensor assembly.

Flow in the misaligned cone-and-plate rheometer

Abstract: The effects of small misalignment in the cone-and-plate rheometer on the flow of a Newtonian fluid, an upper-convected Maxwell fluid, and a White-Metzner fluid are examined in detail. The method of domain perturbation and the lubrication approximation are employed to calculate velocity and stress profiles to first order in the misalignment parameter ϵ. Results for the Newtonian fluid show symmetric velocity and stress profiles around the plane at the widest gap. The two elastic fluids studied exhibit asymmetry in their velocity and stress profiles caused by fluid memory effects. Misalignment effects on torque and thrust measurements in the cone and plate are also discussed, and results are compared with a similar calculation made for flow in the journal bearing.

Erfの降伏応力に関する理論的実験的検討 (小特集 電磁力関連流体工学)

Abstract: The static yield stress of Electrorheological Fluid(ERF) was calculated. The result is in good accordance with the experiment. Using a particle chain model to estimate the interactions of particles, we solved Maxwell equation by the finite differential method, and calculated Maxwell stress directly. In this method, both multipole and manybody effects between particles, which were not included or were treated inappropriately before, were treated exactly. The relationship of the static yield stress to the electric field strength and the particle size is also derived from our model.

Numerical solution for the dilation of a fluid-saturated porous elastic sphere due to a point source of fluid at the centre of the sphere

Abstract: Mathematical modelling of the ascent of free fluid through relatively strong rock, deep in the Earth's mantle, presents a challenge in geomechanics. Here the medium is considered as fluid-saturated, porous, elastic and bounded, and the fluid enters at a point source. An explicit finite difference method is developed for the numerical solution to the problem of the dilatation of a fluid-saturated porous elastic sphere due to a point fluid source of constant strength at the centre of the sphere. A cubic spline interpolant is used to evaluate a definite integral which occurs in the boundary condition for the pore fluid pressure at the surface of the sphere. The numerical solutions for the dilatation and pore fluid pressure are compared with analytical solutions and the absolute and relative errors of the numerical solutions are calculated. When the fluid source is switched on, the pore fluid pressure starts to decrease, reaches a minimum value and then steadily increases. The initial time rate of decrease of the pore fluid pressure is independent of the radial distance from the source. It decreases as the radius of the sphere increases and vanishes for a point fluid source in an infinite porous elastic medium.

The Lattice Boltzmann Equation Method for the Simulation of Compressible Fluid Flow

Abstract: We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a modified equilibrium distribution in Maxwell-Boltzmann type. With the use of the rest particles and the particle reservoir, we were able to add one degree of freedom into the sound speed of the modeled fluid. When the sound speed is tuned small enough, the compressible region of fluid flow can be reached. An example 2-D model is presented, together with the numerical verification for its transport coefficients.

Modelling of fluid expulsion and deformation behaviour of dewatering sediments

Abstract: A finite element model is developed for modelling coupled fluid expulsion/deformation behaviour of dewatering sediments subjected to external loadings under isothermal conditions. The non-linear deformation behaviour of the sediment (soil) skeleton is based on the force equilibrium equation in which the constitutive relationship of stress and strain is implemented by the modified Cam-Clay model in soil plasticity. The fluid flow behaviour in the model is described by the generalized porous media flow equation. The model allows temporal and spatial variations of porosity and permeability. The fluid viscosity and density are assumed to be temperature-dependent. The model also allows the development of single and multiple faults, depending upon the material (sediment and fluid) properties, loading and boundary conditions. Procedures are implemented for (1) updating the material properties such as porosity, permeability, fluid density and viscosity and (2) the development of faults which allow the formation of high-permeability conduits for fluid flow. The solution algorithm for displacements of the sediments and the excess pore (fluid) pressure is based on a residual load technique to handle the non-linear (elastic-plastic) deformation behaviour of the sediment skeleton. The model can be applied to one- and two-dimensional problems. Examples of a plane strain saturated sediment layer subjected to stepwise horizontal tractions versus time are given.