Viscosity Of non-Newtonian Fluid Research Articles

Characteristic scales and drag reduction evaluation in turbulent channel flow of nonconstant viscosity viscoelastic fluids

The polymer-induced drag reduction in turbulent viscoelastic channel flow is customarily investigated from first principles through direct numerical simulations. In contrast to Newtonian fluid mechanics, in viscoelastic fluid mechanics there are more parameters and those are typically referenced under standard, zero shear-rate conditions. For a nonconstant viscosity non-Newtonian fluid it is necessary to correlate the effective wall viscosity to the parameters of the model. This correlation can only be evaluated a posteriori based on the wall statistics. It is used here to relate the computational to the wall units. Furthermore, the relationship between the effective wall properties and the corresponding steady shear values is elucidated. Moreover, an accurate and robust procedure for evaluating the overall drag reduction is presented.

목분 충진 고분자 용융체의 압출다이 내 유동 및 열전달에 관한 수치해석

A three-dimensional numerical analysis of the flow and heat transfer characteristic of wood-flour-filled polypropylene melt in an extrusion die was carried out. Used for this analysis were Finite Concept Method based on FVM. unstructured grid and non-Newtonian fluid viscosity model. Temperature and flow fields are closely coupled through temperature dependent viscosity and viscous dissipation. With large Peclet, Nahme, Brinkman numbers, viscous heating caused high temperature belt near die housing. Changing taper plate thickness and examining some predefined parameters at die exit investigated the effect of taper plate on velocity and temperature uniformities. In the presence of taper plate、uniformity at die exit could be improved and there existed an optimum thickness to maximize it.<br/>

Blood viscosity measurements using a pressure-scanning capillary viscometer

A previously designed capillary viscometer with measuring differential pressure was modified to measure the viscosity of non-Newtonian fluids including unadulterated blood continuously over numerous shear rates in a single measurement. Because of unavoidable experimental noise and a limited number of data, the previous capillary viscometer experienced an inaccuracy and could not directly determine a viscosity without an iterative calculation. However, in the present measurement there are numerous data available near the point of interest so that the numeric-value of the derivative,d(lnQ)/dln τω), is no longer sensitive to the method of differentiation. In addition, relatively low and wide shear rate viscosity measurements were possible because of the present precision pressure-scanning method with respect to time. For aqueous polymer solutions, excellent agreement was found between the results from the pressure-scanning capillary viscometer and those from a commercially available rotating viscometer. In addition, the pressure-scanning capillary viscometer measured the viscosity of unadulterated whole blood without adding any anticoagulants.

Continuous viscosity measurement of non-Newtonian fluids over a range of shear rates using a mass-detecting capillary viscometer

A newly designed mass-detecting capillary viscometer uses a novel concept to continuously measure non-Newtonian fluids viscosity over a range of shear rates. A single measurement of liquid-mass variation with time replaces the flow rate and pressure drop measurements that are usually required by capillary tube viscometers. Using a load cell and a capillary, we measured change in the mass flow rate through a capillary tube with respect to the time,m(t), from which viscosity and shear rate were mathematically calculated. For aqueous polymer solutions, excellent agreement was found between the results from the mass-detecting capillary viscometer and those from a commercially available rotating viscometer. This new method overcomes the drawbacks of conventional capillary viscometers meassuring non-Newtonian fluid viscosity. First, the mass-detecting capillary viscometer can accurately and consistently measure non-Newtonian viscosity over a wide range of shear rate extending as low as 1 s−1. Second, this design provides simplicity (i. e., ease of operation, no moving parts), and low cost.

Determination of the pressure dependent viscosity of non-Newtonian fluid using a new rheometrical device

A new type of rheometer has been designed based on hydrodynamic principle. The pressure chamber (rheometer) consists of a rotating inner cylinder (shaft) in a fixed hollow outer cylinder. The complex geometry gap between the two cylinders is filled with a viscous non-Newtonian fluid. When the solid cylinder moves inside the hollow cylinder shearing takes place and hydrodynamic pressure develops. The magnitude of the pressure depends upon the shear rate, i.e. the speed with which the inner solid cylinder is rotated and the viscosity of the fluid. The rheometer has been developed to measure the rheological properties of viscous fluid at pressures up to 4 MPa. The rheometer has a shear rate range 1000–3000 s −1. A number of experiments have been carried out to determine the effects of shear rate and pressure on the viscosity of glycerine. This paper outlines the method for establishing the pressure dependent viscosity–shear rate relationship based on experimental results and theoretical analysis.

Semiclassical law for the apparent viscosity of non-Newtonian fluids: An analogy between thixotropy of fluids and sintering of solids

A theory is presented to describe the apparent viscosity of thixotropic fluids as a function of the rate of shear. It represents the extension of a semiclassical approach that was previously formulated to deal with matter densification phenomena in solids starting from the state equation of the medium. In this context, the Debye expression for the Helmholtz free energy has been provided with a density of vibrational modes that accounts for atomic and microstructural changes occurring at the frequency scale of momentum transport (see diffusion). Working out the steady-state condition with respect to time gives an equation relating reduced apparent viscosity (η̃) and shear rate (γ̃) through the temperature value (θ*) that is energetically equivalent to the medium vibrations implied. Viscosity also turns out to depend on the Debye temperature θD (see φ∼θ*/θD) and an equivalent Gruneisen parameter (μ), defined with respect to viscosity variations. Increasing φ in pseudoplastic and dilatant media, respectively, increases and decreases η̃, which always increases with increasing μ. The analogy between dilatancy/sintering and pseudoplasticity/desintering is suggested, and a correspondence between matter and momentum transports is traced on the basis of the phononic spectrum properties. Application to experimental measurements are presented and discussed for aqueous monodispersions of polystyrene (PS) latex particles, aqueous glycerol solutions of partially hydrolyzed polyacrylamide (PHPAA) at different sodium chloride (NaCl) concentrations, polymethylmethacrylate (PMMA) suspensions in dioctylphthalate (DOP), and for a molecularly thin liquid film of octamethylciclotetrasiloxane (OMCTS). Best fit coefficients for φ and μ have been constrained to the Debye temperature and the effective low-shear viscosity (η0) according to their dependences upon the suspended volume fraction (φ), θD=θD(φ), and η0=η0(φ), and the agreement with experimental data is quite satisfactory in all cases here examined. It is then suggested that the viscous character of a liquid can be described in terms of a coupling between Brownian diffusion and phonon wave motion.

The Marsh Funnel and Drilling Fluid Viscosity: A New Equation for Field Use

Summary The flow behavior of a Marsh funnel was numerically simulated for power law fluids and was found to give good agreement with experimental measurements. As a result, the simulation provides a general picture of the meaning of the Marsh funnel time and a correlation enabling this to be converted into a value for effective viscosity of non-Newtonian fluids. For field use, the following equation relates the effective viscosity μe (cp) to the Marsh funnel (quart) time t (seconds) and the density ρ (g/cm−3) μe = ρ (t-25).

Pulmonary airway reopening: effects of non-Newtonian fluid viscosity.

This paper considers the effects of non-Newtonian lining-fluid viscosity, particularly shear thinning and yield stress, on the reopening of the airways. The airway was simulated by a very thin, circular polyethylene tube, which collapsed into a ribbon-like configuration. The non-Newtonian fluid viscosity was described by the power-law and Herschel-Buckley models. The speed of airway opening was determined under various opening pressures. These results were collapsed into dimensionless pressure-velocity relationships, based on an assumed shear rate gamma = U/(0.5 H), where U and H are the opening velocity and fluid film thickness, respectively. It was found that yield stress, like surface tension, increases the yield pressure and opening time. However, shear thinning reduces the opening time. An increased film thickness of the non-Newtonian lining fluid generally impedes airway reopening; a higher pressure is needed to initiate the airway reopening and a longer time is required to complete the opening process.

Use of nuclear magnetic resonance imaging as a viscometer for process monitoring

Nuclear magnetic resonance imaging (NMRI or MRI) flow measurements and fundamental principles of capillary flow are combined to determine the shear viscosity of non-Newtonian fluids. Shear viscosity data are obtained over the shear rates inferred from the velocity profile measured using MRI. A single, 3 minute measurement consisting of a MRI-determined velocity profile (also referred to as a dynamic displacement profile or positiondisplacement correlation) and the corresponding pressure drop produces multiple shear viscosity-shear rate data points. This technique was applied to obtain shear viscosity-shear rate data for an aqueous carboxymethyl cellulose (CMC) solution. Good agreement is found between these data and those measured by conventional rotational rheometry. The potential applications of this MRI-based technique include on-line and in-line monitoring of the shear viscosity of single and multiphase non-Newtonian fluids that can be either opaque or transparent.

A sensor for on-line measurement of the viscosity of non-Newtonian fluids using a neural network approach

Non-Newtonian fluids are characterized by a nonlinear relationship between viscosity and shear rate. Typical examples are some emulsions. The graph of viscosity as a function of the shear rate is known as the rheogram or the rheological chart. In this work, a very simple mechanical device with minimal moving parts has been used as a sensor for measuring both the viscosity and the shear rate. A mathematical model to measure the viscosity in Newtonian fluids has been confirmed. However, a mathematical model of the sensor for the case of non-Newtonian fluids is difficult because several variables defining the transducing properties are not independent and the measurement is made during transient dynamic conditions. In solving this problem, a neural network approach has been used. The input consists of two voltages representing the sensor response and the temperature. The outputs are the viscosity and the shear rate. The measurement system is made out of a sensor head, an electronic circuit for powering the sensor and signal conditioning, and a neural network software, based in the back propagation learning algorithm. The neural net has been trained using experimental data from a laboratory viscometer and a simplified mathematical correlation relating the viscosity and input voltages. The sensor has been tested by measurement of the viscosity and the shear rate for emulsions of heavy crude oil (bitumen) and water. Good correlation between experimental data and the system output was observed after the neural net training. On-line tests of the sensor are being conducted.

Use of an optical meter to measure the flow rate and apparent viscosity of non-Newtonian fluids

An optical flow rate meter, based on laser Doppler anemometry, is presented. It measures the centreline velocity in pipe flow and converts this information to yield the corresponding volumetric flow rate. This conversion requires knowledge of the dependence of shear viscosity on shear rate and shear stress, respectively. The instrument needs no calibration.

Self-excited and stochastic oscillations in the hydrodynamics of non-Newtonian fluids

An approach is developed in accordance with which the Theological behaviour of non-Newtonian fluids is governed by the non-linear kinetics of processes involving the restoration and disruption of bonds between the structural elements of the medium. The corresponding kinetic equations are used as closing relationships in describing the unsteady motions of such fluids in the gap between the cylinders of a rotational viscosimeter. It is shown, by a numerical analysis of the method proposed, that the self-excited and stochastic oscillations when measuring the viscosity of non-Newtonian fluids may be the result of the joint action of the non-linear kinetics of structural changes in the fluid and the inertial properties of the viscosimeter.

A New Method for Predicting Friction Pressures and Rheology of Proppant-Laden Fracturing Fluids

Summary The prediction of friction pressures for proppant-laden fracturing fluids requires estimations of both the base-gel friction factor and the effect of proppant on fluid rheology. This paper introduces two new expressions, each theoretically based with constants determined from data, that address these two issues for hydroxypropyl guar (HPG)-based fracturing fluids in laminar and turbulent flow. The paper first introduces a new expression for the turbulent friction factor of HPG base gels. This implicit expression for the friction factor is more theoretically correct and requires one less empirical constant than explicit forms currently used. The effect of proppant on the effective viscosity of non-Newtonian fluids is then discussed and a new expression, which includes shear rate, temperature, gel concentration, and proppant volume fraction as parameters, is derived. Developed from laboratory data and existing slurry rheology theories, this expression is shown to provide excellent predictions of laboratory and field data for both tubing and annulus injection.

Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium

This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.

Heat transfer and power consumption of non-Newtonian fluids in agitated vessels

A new shear rate model is proposed for determining the apparent viscosity of non-Newtonian fluids: ▪ where f is defined as the flow regime coefficient. This model is based on the assumption that the torque offered by the rotating impeller is proportional to the average shear stress exerted on the wall surface of the agitated vessel. Under investigation were MIG impellers, flat-blade disc turbines, Pfaudler impellers, plate paddles, anchors and a semi-elliptical board impeller. The agitated vessel was equipped with three types of cooling tubes: inner helical coil, external helical coil and vertical tubes, the vertical tubes acting as a heat-exchanging surface as well. Heat transfer coefficients of non-Newtonian fluids in agitated vessels were correlated in the present model by using a generalized Reynolds number Re * and the dimensionless group εD 4/v 3 a , where ε is the power per unit mass. These heat transfer correlations for both the jacket and the colling tube can be used in the design and scale-up of industrial agitated vessels. Computation results indicated that the present shear rate model permits a good correlation of film coefficients for both the jacket and the cooling tube under different conditions and with different geometrical configurations for different types of impellers and cooling tubes, baffled or unbaffled, including the transition and turbulent regimes. The precision of the present model was compared with that of previous models.

Application of Hildebrand's fluidity model to non-Newtonian solutions

The fluidity model ofHildebrand has been applied to dilute aqueous polymer solutions exhibiting non-Newtonian behaviour. As for Newtonian fluids, it is found that the temperature dependence of apparent viscosity of non-Newtonian fluids is determined entirely by the temperature dependence of fluid density. However, whereas the parameters ofHildebrand's equation are constants, independent of the conditions of shear for Newtonian fluids, these parameters become shear-rate dependent for non-Newtonian fluids. The magnitude of the parameters and their variation with shear rate can be explained qualitatively in terms of interactions of polymer molecules and their behaviour in a shear field.

Reports on Progress in Physics

THIS the latest annual volume of progress reports sponsored by the Physical Society, is larger than any of its predecessors, and the editors' nets have been spread even more widely than heretofore. There are nineteen separate chapters, and of these general physics is divided into four sections (R. C. Brown on surface tension and Brownian motion, Cox on elasticity, and Good-eve on the viscosity of non-Newtonian fluids), and optics and spectroscopy have five sections each, specially edited by L. C. Martin and W. Jevons respectively. Atomic physics is represented by two sections, single scattering of elementary particles (Champion) and cosmic rays (Heitler). Skinner contributes a long article on the soft X-ray spectroscopy of the solid state, which might also be classified as atomic physics.