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Showing papers on "Herschel–Bulkley fluid published in 1994"


Journal ArticleDOI
TL;DR: In this article, the interparticle forces and resulting shear stresses in a magnetorheological fluid are calculated from a finite element analysis in which the nonlinearity and saturation of the particle magnetization are incorporated.
Abstract: The interparticle forces and resulting shear stresses in a magnetorheological fluid are calculated. The field due to a linear chain of particles in a fixed average magnetic induction Bave is determined from a finite element analysis in which the nonlinearity and saturation of the particle magnetization are incorporated. The shear stresses are then computed from the field using Maxwell’s stress tensor. The stresses obtained for all but the lowest magnetic inductions are controlled by the saturation of the magnetization in the contact regions of each particle. Identifying the maximum shear stress as a function of shear strain with the yield stress gives values in agreement with results reported for typical fluids. For high magnetic inductions the yield stress plateaus due to the complete saturation of the particle magnetization; the stress scales as the square of the saturation magnetization in this regime.

317 citations


Journal ArticleDOI
TL;DR: In this article, the authors analyzed the peristaltic pumping of a non-Newtonian fluid through an axisymmetric conduit, represented by the constitutive equation for a second-order fluid.
Abstract: We have analyzed the mechanics of peristaltic pumping of a non-Newtonian fluid through an axisymmetric conduit. The material was represented by the constitutive equation for a second-order fluid. A perturbation series (to second order) in dimensionless wavenumber of an infinite harmonic traveling wave was used to obtain explicit forms for the velocity field and a relation between the flow rate and the pressure gradient, in terms of the Reynolds number, the dimensionless non-Newtonian parameters, and the occlusion. Results were compared with other studies, in both Newtonian and non-Newtonian cases. Also, we have shown that the flow of a Newtonian fluid through a rigid, axisymmetric tube with an axial, sinusoidal variation of radius is a special case of this analysis.

182 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the lubrication theory in more detail by a comparison with equilibrium stress analysis for rigid-plastic solids, and the results were consistent with the theory, suggesting that it is a useful first approximation.
Abstract: Lubrication theory is commonly employed to analyse the squeeze-film flow of plastic fluids under no-slip wall boundary conditions. Solutions exist for both Bingham and Herschel-Bulkley fluids but they infer that there exists a rigid or unyielded core and flow zones adjacent to the platens; it has been recognised previously that such a velocity field is kinematically inconsistent. Furthermore, the pressure boundary condition at the edge of the platens is conventionally set to zero which is inconsistent with experimental data presented here for a model Herschel-Bulkley fluid (Plasticine). An attempt has been made to examine the lubrication theory in more detail by a comparison with equilibrium stress analysis for rigid-plastic solids. Squeeze-film measurements were carried out using a model Herschel-Bulkley fluid and the results were consistent with the theory, suggesting that it is a useful first approximation. Nevertheless, the approach does not resolve the kinematic inconsistency resulting in lubrication theory.

92 citations


Journal ArticleDOI
TL;DR: In this paper, a truncated Fourier representation of the conservation and constitutive equations for an Oldroyd-B fluid, leading to a four-dimensional system that constitutes a generalization of the classical Lorenz system for a Newtonian fluid.
Abstract: The onset of aperiodic or chaotic behaviour in viscoelastic fluids is examined in the context of the Rayleigh-Benard thermal convection setup. A truncated Fourier representation of the conservation and constitutive equations, for an Oldroyd-B fluid, leads to a four-dimensional system that constitutes a generalization of the classical Lorenz system for a Newtonian fluid. It is found that, to the order of the present truncation and below a critical Deborah number De c , the critical Rayleigh number Ra c , for the onset of steady thermal convection does not depend on fluid elasticity or retardation. For De > De c , it is shown that steady convection does not exist, with the fluid becoming overstable instead. Fluid overstability, namely when the convective cell structure is time periodic, and which is attributed to fluid elasticity, is found to set in at a Rayleigh number that depends on the Deborah number and fluid retardation, and may be much smaller than Ra c . It is also found that fluid elasticity tends to destabilize the convective cell structure, precipitating the onset of chaotic motion, at a Rayleigh number that may be well below that corresponding to Newtonian fluids.

55 citations


Journal ArticleDOI
TL;DR: This paper considers the immiscible displacement of a non-Newtonian fluid in a radial Hele-Shaw cell, and presents a detailed analysis of the flow, thus exposing features which until now have not been reported.
Abstract: The displacement of a high-viscosity non-Newtonian fluid by a low-viscosity Newtonian fluid in a Hele-Shaw cell is capable of producing ramified viscous-fingering patterns exhibiting fractal characteristics. Recently, it was established that interfacial tension has little influence on the formation of these fractal patterns. However, the precise mechanism behind their formation is not as yet fully understood. In this paper, we consider the immiscible displacement of a non-Newtonian fluid in a radial Hele-Shaw cell, and present a detailed analysis of the flow, thus exposing features which until now have not been reported. In particular, we find an effective length compression for the formation of viscous-fingering patterns and accelerated growth rates, which upon consideration of recent experimental results, are consistent with the formation of fractal viscous-fingering patterns.

47 citations


Journal ArticleDOI
V. K. Garg1
TL;DR: In this article, heat transfer analysis for steady, laminar flow of an incompressible, homogeneous, non-Newtonian fluid of second grade at a stagnation point is presented.
Abstract: Heat transfer analysis for steady, laminar flow of an incompressible, homogeneous, non-Newtonian fluid of second grade at a stagnation point is presented. A pseudosimilarity solution is used that enables computation of the flow characteristics for any value of the dimensionless normal stress modulus,K, of the fluid. The energy equation is discretized using central differences, and solved using the Thomas algorithm. A powerlaw variation for the wall temperature is assumed. Results provide the effect of non-Newtonian nature of the fluid on the heat transfer characteristics for different values of Prandtl and Eckert numbers, and wall-temperature variation. Results match exactly with those from an earlier perturbation analysis for smallK. For largeK as well as for the effect of viscous dissipation, no results are available heretofore. Amongst other applications, the analysis is relevant to the impingement of a non-Newtonian jet on a flat surface.

37 citations


Journal ArticleDOI
TL;DR: In this article, the authors used molecular scale simulations of the evolution of the separating interface of two immiscible fluids of equal viscosity driven by solid rollers, and found that high curvature interfaces do not reach a steady state, but instead drops of the fluid above the free surface are detached.
Abstract: Recent experiments and calculations have exhibited apparent steady cusps in certain fluid free surfaces driven by a converging subsurface flow Molecular dynamics simulations are used to elucidate some of the issues raised by this phenomenon, with emphasis on the behavior of the fluid on very small scales The similar but different situation of two immiscible fluids of equal viscosity driven by solid rollers is considered Molecular scale simulations of the evolution of the separating interface exhibit a gradual increase of curvature with rotation rate However, high curvature interfaces do not reach a steady state, but instead drops of the fluid above the free surface are detached In no case does a true cusp form, and the stress tensor is never unusually large in the near‐cusp region

10 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived yield shear stresses and shear rates at a valve wall from experimental results on a series of concentric cylinder valves, where the fluid constitutive equation used for this purpose is that of a Bingham Plastic.
Abstract: Yield shear stresses and shear rates at a valve wall are derived from experimental results on a series of concentric cylinder valves. The fluid constitutive equation used for this purpose is that of a Bingham Plastic. Valve plates (which are such that the radial gap is small compared to its mean pitch) are taken to be parallel so far as the derivation of the flow ν's pressure ν's geometry model is concerned. A range of electrode separations from 0.5 to 1.0mm are used with flow velocities being limited to the region where the viscous pressure drop component is below that caused by the electro stress. Results show that (away from the region of low shear rates and high voltages) the wall stresses for equivalent conditions are comparable for different valves, for a range of applied field strengths and mean flow velocities. Thus, provided the hysteretic region is avoided the fluid can be treated as a Bingham continuum with some stated reservations. However, this is only applied with precision for the truly corresponding situations defined in the paper.

9 citations


Journal ArticleDOI
TL;DR: In this article, a non-orthogonal stagnation flow of an Oldroyd-B fluid between two parallel plates is considered and the problem is reduced to a set of ODEs, which are then solved with finite differences using a parameter continuation method.
Abstract: This paper is concerned with a non-orthogonal stagnation flow of an Oldroyd-B fluid between two parallel plates. We reduce the problem to a set of ordinary differential equations (ODE's), which is then solved with finite differences using a parameter continuation method. Perturbation analyses are also carried out for small Reynolds numbers and small Weissenberg numbers respectively. The solution of the set of ODE's is discussed. It is known that for a Newtonian fluid, the stagnation point shifts from the potential flow case in the opposite direction of the tangential velocity. The effect of the fluid elasticity is to reduce this shift. It is also shown that the Oldroyd-B model has a limiting Weissenbeg number, depending on the angle of the injected flow.

8 citations


Journal ArticleDOI
TL;DR: In this paper, a slightly misaligned cone-and-plate rheometer where the cone is spinning and the plate is stationary is used to calculate velocity and stress profiles in a slightly mismatched cone and plate, and results for a Newtonian fluid, a Criminale-Ericksen-Filbey fluid, an upper-convected Maxwell fluid, and a White-Metzner fluid are presented.
Abstract: The method of domain perturbation developed by Joseph is used to calculate velocity and stress profiles in a slightly misaligned cone-and-plate rheometer where the cone is spinning and the plate is stationary. Results for a Newtonian fluid, a Criminale-Ericksen-Filbey fluid, an upper-convected Maxwell fluid, and a White-Metzner fluid are presented and compared with earlier results in which the cone is stationary and the plate is spinning (Dudgeon and Wedgewood, 1993). Streamlines calculated for the Newtonian fluid show a very small recirculation region near the stationary plate. Velocity and stress contours are symmetric around the plane of largest gap width. For the elastic fluids studied, streamlines are asymmetric. The fluid response lags where the fluid is dominated by memory effects. Much larger recirculation regions are calculated for fluids dominated by shear thinning. These recirculation regions contain a large fraction of the fluid in the apparatus and have the effect of changing the shape of the flow domain for the remaining fluid that rotates around the cone's axis. Elasticity also has a pronounced effect on the stress profile, indicating that the accuracy of the cone and plate may be compromised even for small mis-alignments.

7 citations


Journal ArticleDOI
Fan Chun1
TL;DR: In this article, the stability of a generalized Newtonian fluid flowing down an inclined plane under gravity is studied, and the critical Reynolds number is given as a function of dimensionless steady flow velocityU(y) and the slope of the plane.
Abstract: The analogue of Orr-Sommerfeld equation is derived for a generalized Newtonian fluid. Based on this equation, the stability of such fluid flowing down an inclined plane under gravity is studied. The critical Reynolds number is given as a function of dimensionless steady flow velocityU(y) and the slope of the plane, and is computed for several fluids.

Journal ArticleDOI
TL;DR: In this paper, the authors evaluated the pressure of mud-debris flow acting on an obstacle for cases in which the mud debris flow was regarded as a non-compressible, then as a compressible fluid.
Abstract: The pressure of mud-debris flow acting on an obstacle was evaluated for cases in which the mud-debris flow was regarded as a non-compressible, then as a compressible fluid. In a non-compressible fluid, an equation of the fluid motion describes an equilibrium between pressure and potential rate. For a compressible fluid, the force is calculated by the density, impact velocity, and propagation velocity of pressure in the fluid. Analytical results showed that in a very few times, the force acting on a structure was some times the expected momentum value (per second)

Journal ArticleDOI
01 Sep 1994
TL;DR: In this paper, a rotary shear viscometer was used to measure the effect of test parameters on the performance of a journal bearing lubricated with different types of non-Newtonian fluids.
Abstract: Viscosity index improvers cause the lubricants to exhibit non-Newtonian flow behaviour and display shear thinning and normal stress differences. Shear thinning behaviour is studied by using a rotary shear viscometer. Owing to the non-availability of a rheogoniometer (for the measurement of normal stress differences), the first normal stress difference is calculated from the viscometric data using the Carreau viscosity function. The influence of the first normal stress difference on the hydrodynamic lubrication is analysed and shows that most of the commercial oils are inelasticoviscous in nature. Regression analysis shows that a large number of commercial lubricants follow the inelasticoviscous cubic law fluid model. Hence the cubic law fluid model is considered for the theoretical analysis.An experimental programme is developed to measure the effect of test parameters on the performance of a journal bearing lubricated with different types of non-Newtonian fluids. The experiments mainly include the measur...

Journal ArticleDOI
范椿1, Fan Chun1
TL;DR: In this paper, the equations describing the flow of a viscoplastic fluid on a rotating disk are derived and are solved by perturbation technique and numerical computation respectively for 2 cases, which makes it possible to calculate the thickness distribution of film.
Abstract: The equations describing the flow of a viscoplastic fluid on a rotating disk are derived and are solved by perturbation technique and numerical computation respectively for 2 cases. This makes it possible to calculate the thickness distribution of film. Two kinds of distribution of thickness have been found. For the viscoplastic fluid for which both viscosity and yield stress are independent of radial coordinate r, the thickness h decreases with increasing r. For a Bingham fluid for which both viscosity and yield stress are function of time and r, the thickness h increases with increasing r.

Journal ArticleDOI
TL;DR: In this paper, the stability of the large Reynolds number flow of a Newtonian fluid over a much more viscous viscoelastic fluid was studied via a linear analysis, where the two fluids are confined within a channel and the flow is driven by the motion of the plate bounding the Newton fluid.
Abstract: The stability of the large Reynolds number flow of a Newtonian fluid over a much more viscous viscoelastic fluid is studied via a linear analysis. The two fluids are confined within a channel and the flow is driven by the motion of the plate bounding the Newtonian fluid. Matched asymptotic expansions are used to derive the dispersion relation, and the flow is found to be always unstable to an interfacial mode due to the discontinuity in the fluid viscosities. It is shown that even a small amount of elasticity of the viscoelastic fluid can change the stability characteristics considerably.

01 Jan 1994
TL;DR: In this article, the bubble issuing from an orifice at the bottom of the boundary evolution in a finite non-Newtonian fluid (such as Maxwell fluid, Cararreu fluid) is numerically simulated and the effects of the rheological behavior,physical parameters and circumstantial conditions are discussed in detail.
Abstract: In this paper the bubble issuing from an orifice at the bottom of the boundary evolution in a finite Non-Newtonian fluid(such as Maxwell fluid,Carreu fluid)is numerically simulated The effects of the rheological behavior,physical parameters and circumstantial conditions are discussed in detail

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the behavior of a magnetic field in a viscous fluid cosmological model where the expansion θ in the model is proportional toσ11, the component of shear tensorσij, which leads to A=(Bc)n.
Abstract: We investigate the behavior of a magnetic field in a viscous fluid cosmological model where the expansionθ in the model is proportional toσ11, the component of shear tensorσij, which leads to A=(Bc)n. We also assume that the shear viscosity is proportional to the rate of expansion in the model. The behavior of the model in the absence of a magnetic field and viscosity is discussed as are some other physical and geometrical aspects.

Journal ArticleDOI
TL;DR: In this article, a new method for testing the strength of cells against fluid shear stress by using a long capillary column was proposed and the trajectories of cells in the column were simulated by introducing the Brownian motion model.
Abstract: A new method for testing the strength of cells against fluid shear stress by using a long capillary column was proposed The trajectories of cells in the column were simulated by introducing the Brownian motion model The Brownian motion was performed by the generation of random numbers The mean exposure time to shear stress and the mean shear stress acting on the surface of cells were discussed by the result of computer simulation The mean shear stress acting on the surface of cells flowing in the capillary column was estimated as 4/3-fold of the shear stress at the column wall provided that the ratio of the cell radius to the column radius does not exceed 008 The effectiveness of this new method for testing the strength of cells against fluid shear stress was shown

Dissertation
01 Jul 1994

Journal ArticleDOI
TL;DR: In this paper, the influence of radiation forces on two spheres in a viscous fluid during the transmission of an acoustic wave was investigated, based on the mutual disturbance of the flow fields around them as a result of interference between the primary and secondary waves reflected from the spheres.
Abstract: In this article we formulate and solve the problem of the influence of radiation forces (forces created by the radiation pressure) on two spheres in a viscous fluid during the transmission of an acoustic wave. On the basis of these forces we investigate the nature of the interaction between the spheres as determined by the mutual disturbance of the flow fields around them as a result of interference between the primary and secondary waves reflected from the spheres. A previously proposed [2] approach is used in the investigations. The radiation force acting on one of the spheres is filtered by averaging the convolution of the stress tensor in the fluid with the unit normal to the surface of the sphere over a time interval and over the surface of the sphere. The stresses in the fluid are represented, to within second-order quantities in the parameters of the wave field, in terms of the velocity potentials obtained from the solution of the linear problem of the diffraction of the primary wave by the free spheres. The diffraction problem is formulated and solved within the framework of the theory of linear viscoelastic solids [6]. The case of an ideal fluid has been studied previously [3–5, 7]. Radiation forces are one of the causes of the relative drift of solid particles situated in a fluid in an acoustic field.