Non-Newtonian flow in microporous structures under the electroviscous effect

Single phase non-Newtonian microporous flow combined with the electroviscous effect is investigated in the pore-scale under conditions of various rheological properties and electrokinetic parameters. The lattice Boltzmann method is employed to solve both the electric potential field and flow velocity field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends on both the fluid rheological behavior and pore surface area ratio significantly. For the shear thinning fluid with power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electrovicous effect plays a more important role compared to the Newtonian fluid and shear thickening fluid. The high pore surface area ratio in the porous structure increases the electroviscous force and the induced flow resistance becomes important even to the flow of Newtonian and shear thickening fluids.     

Particle manipulation via integration of electroosmotic flow of power-law fluids with standing surface acoustic waves (SSAW)

Standing surface acoustic wave (SSAW) based microfluidic devices have shown great promise toward fluid and particle manipulation applications in medicine, chemistry, and biotechnology. In this article, we present an analytical model for investigating continuous manipulation of particles (both synthetic and biological) within electroosmotic flow of non-Newtonian bio-fluids in a microfluidic channel under the influence of standing surface acoustic waves (SSAW). The particles are injected along the center of channel into the electroosmotically driven flow of power-law fluids, wherein their transport through the SSAW region is dictated by the hydrodynamic, electrophoretic, and acoustic forces. We first present a mathematical model to analyze the characteristics of electroosmotic flow of non-Newtonian power-law fluids in a hydrophobic slit microchannel. Next, we investigate the trajectories of particles in the flow field due to the combined effect of electroosmotic, electrophoretic, and acoustophoretic forcing mechanisms. The effect of key parameters such as particle size, their physical properties, input power, flow rate, and flow behavior index on the particle trajectories is examined while including the effect of the channel walls. The presented model delineates the methodologies of improving SSAW-based particle separation technology by considering the fluid rheology as well as the surface properties of the channel walls. Therefore, we believe that this model can serve as an efficient tool for device design and quick optimizations to explore novel applications concerning the integration of electroosmotic flows with acoustofluidic technologies.     

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.     

基于舌/上颚微间隙下流体流动行为研究

为探讨口腔环境下流体的流动行为,采用数值方法与流变试验深入研究舌/上颚微间隙下流体流量的影响因素. 建立舌/上颚微间隙的简化模型及Reynolds方程,通过数值方法获取微间隙下流量变化;在DHR-2流变仪上研究非牛顿流体的黏度与剪切率的变化,探讨牛顿流体和非牛顿流体的流量影响. 结果表明:牛顿流体流量平方的倒数同载荷和黏度比值和时间均呈线性函数关系;所制备的非牛顿流体近似为幂律流体,其黏度随脂肪含量的增加而增大,而非牛顿流体流量率先高于后低于等效牛顿流体,其研究结果将为特定人群功能产品的研发提供技术支持.      

Electroviscous effect on non-Newtonian fluid flow in microchannels

Understanding non-Newtonian flow in microchannels is of both fundamental and practical significance for various microfluidic devices. A numerical study of non-Newtonian flow in microchannels combined with electroviscous effect has been conducted. The electric potential in the electroviscous force term is calculated by solving a lattice Boltzmann equation. And another lattice Boltzmann equation without derivations of the velocity when calculating the shear is employed to obtain flow field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends significantly on the fluid rheological behavior. For the shear thinning fluid of the power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electroviscous effect plays a more important role. And its effect on the flow increases as the ratio of the Debye length to the channel height increases and the exponent n decreases. While the shear thickening fluid of n > 1 is less affected by the electroviscous force, it can be neglected in practical applications.     

Flow characteristics and mixing performance of electrokinetically driven non-Newtonian fluid in contraction–expansion microchannel

A numerical investigation is performed into the flow characteristics and mixing performance of electrokinetically driven non-Newtonian fluid in a contraction–expansion microchannel. In the study, the rheological behavior of the fluid is characterized using a power-law model. The results show that the volumetric flow rate reduces as the flow behavior index increases, and thus an improved mixing performance is obtained. Furthermore, it is shown that for all considered values of the flow behavior index, the mixing performance can be enhanced by increasing the ratio of the main channel width to the contraction channel width, extending the length of the contraction channel, assigning a smaller value to the nondimensional Debye–Hückel parameter, and applying an appropriate electric field strength. Finally, it is shown that although the mixing efficiency reduces with a reducing flow behavior index, an acceptable mixing performance can still be obtained given an appropriate specification of the flow conditions and geometry parameters.     

活性流体流变行为的布朗动力学模拟研究

活性流体在用于开发新材料方面具有巨大潜力, 满足这一需求就要定量掌握活性流体所表现的特殊力学行为, 特别是流变行为. 扩展布朗运动方程, 建立自驱动活性粒子的运动模型, 基于反向非平衡法确定活性流体的黏度, 考察活性粒子体积分数、直行速度和转向扩散系数对活性流体流变行为的影响规律, 确定活性流体特殊流变行为的形成机理. 结果表明, 活性流体的流变曲线可被划分为黏度下降区、过渡区和牛顿区; 活性粒子体积分数越高, 活性流体的非牛顿特性越显著, 活性粒子的直行运动引起活性流体在低剪切速率区域黏度下降, 直行运动和转向运动的耦合作用导致中剪切速率区域流变曲线非单调变化, 活性粒子频繁发生转向运动会导致活性流体非牛顿特性受到抑制; 活性流体的宏观流变学特性和粒子的涨落直接相关, 活性粒子体积分数越高、直行速度越快和转向扩散系数越小, 活性流体中活性粒子越容易产生显著的涨落; 低剪切速率区域内活性粒子涨落明显, 随着剪切速率增大, 活性粒子的涨落逐渐被削弱, 粒子的聚集结构不断被破坏, 最终体系的流变行为类似一般被动流体.      

Anomalous predictions of pressure drop and heat transfer in ducts of arbitrary cross-section with modified power law fluids

 The apparent viscosities of purely viscous non-Newtonian fluids are shear rate dependent. At low shear rates, many of such fluids exhibit Newtonian behaviour while at higher shear rates non-Newtonian, power law characteristics exist. Between these two ranges, the fluid's viscous properties are neither Newtonian or power law. Utilizing an apparent viscosity constitutive equation called the “Modified Power Law” which accounts for the above behavior, solutions have been obtained for forced convection flows. A shear rate similarity parameter is identified which specifies both the shear rate range for a given fluid and set of operating conditions and the appropriate solution for that range. The results of numerical solutions for the friction factor–Reynolds number product and for the Nusselt number as a function of a dimensionless shear rate parameter have been presented for forced fully developed laminer duct flows of different cross-sections with modified power law fluids. Experimental data is also presented showing the suitability of the “Modified Power Law” constitutive equation to represent the apparent viscosity of various polymer solutions. Received on 21 August 2000     

A Lattice Boltzmann study of non-newtonian flow in digitally reconstructed porous domains

In the present study, the Lattice Boltzmann Method (LBM) is applied to simulate the flow of non-Newtonian shear-thinning fluids in three-dimensional digitally reconstructed porous domains. The non-Newtonian behavior is embedded in the LBM through a dynamical change of the local relaxation time. The relaxation time is related to the local shear rate in such a way that the power law rheology is recovered. The proposed LBM is applied to the study of power-law fluids in ordered sphere packings and stochastically reconstructed porous domains. A linear relation is found between the logarithm of the average velocity and the logarithm of the body force with a curve slope approximately equal to the inverse power-law index. The validity of the LBM for the flow of shear thinning fluids in porous media is also tested by comparing the average velocity with the well known semi-empirical Christopher–Middleman correlation. Good agreement is observed between the numerical results and the Christopher–Middleman correlation, indicating that the LBM combined with digital reconstruction constitutes a powerful tool for the study of non-Newtonian flow in porous media.     

Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes

The results of direct numerical simulation of turbulent flows of non-Newtonian pseudoplastic fluids in a straight pipe are presented. The data on the distributions of the turbulent stress tensor components and the shear stress and turbulent kinetic energy balances are obtained for steady turbulent flows at the Reynolds numbers of 10⁴ and 2×10⁴. As distinct from Newtonian fluid flows, the viscous shear stresses turn out to be significant even far from the wall. In power-law fluid flows the mechanism of the energy transport from axial to transverse component fluctuations is suppressed. It is shown that with decrease in the fluid index the turbulent transfer of the momentum and the velocity fluctuations between the wall layer and the flow core reduces, while the turbulent energy flux toward the wall increases. The earlier-proposed models for the average viscosity and the non-Newtonian one-point correlations are in good agreement with the data of direct numerical simulation.     

Non-Newtonian effect on natural convection flow over cylinder of elliptic cross section

The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convectionflows, the surface of the cylinder is maintained by the uniform surface temperature(UST)or the uniform heat flux(UHF) condition. The governing equations corresponding to theflow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids(n > 1) than the other fluids(n≤1).The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.     

Dynamic scaling of unsteady shear-thinning non-Newtonian fluid flows in a large-scale model of a distal anastomosis

Dimensional analysis has been applied to an unsteady pulsatile flow of a shear-thinning power-law non-Newtonian liquid. An experiment was then designed in which both Newtonian and non-Newtonian liquids were used to model blood flow through a large-scale (38.5 mm dia.), simplified, rigid arterial junction (a distal anastomosis of a femorodistal bypass). The flow field within the junction was obtained by Particle Imaging Velocimetry and near-wall velocities were used to calculate the wall shear stresses. Dimensionless wall shear stresses were obtained at different points in the cardiac cycle for two different but dynamically similar non-Newtonian fluids; the good agreement between the measured dimensionless wall shear stresses confirm the validity of the dimensional analysis. However, blood exhibits a constant viscosity at high-shear rates and to obtain complete dynamic similarity between large-scale experiments and life-scale flows, the high-shear viscosity also needs to be included in the analysis. How this might be done is discussed in the paper.     

A cell model theory of the shear viscosity of a concentrated suspension of interacting spheres in a non-Newtonian fluid

A theoretical approach to the shear viscosity of concentrated suspensions of small particles in a non-Newtonian fluid has been developed using a cell theory model involving particle-particle interaction. The cell theory of Frankel and Acrivos was first generalized to power-law fluid matrices without particle interaction. Particle-particle interaction was then taken into consideration. The theory suggests that the flow behavior of such systems at low shear rates is chiefly dependent upon non-hydrodynamics interparticle interaction such as van der Waals—London and electrostatic forces which induce flocculation and yield stresses. The flow properties at high shear rates are determined by hydrodynamics interaction essentially dependent upon particle concentration and shape.     

A smoothed particle hydrodynamics-based fluid model with a spatially dependent viscosity: application to flow of a suspension with a non-Newtonian fluid matrix

A smoothed particle hydrodynamics approach is utilized to model a non-Newtonian fluid with a spatially varying viscosity. In the limit of constant viscosity, this approach recovers an earlier model for Newtonian fluids of Español and Revenga (Phys Rev E 67:026705, 2003). Results are compared with numerical solutions of the general Navier–Strokes equation using the “regularized” Bingham model of Papanastasiou (J Rheol 31:385–404, 1987) that has a shear-rate-dependent viscosity. As an application of this model, the effect of having a non-Newtonian fluid matrix, with a shear-rate-dependent viscosity in a moderately dense suspension, is examined. Simulation results are then compared with experiments on mono-size silica spheres in a shear-thinning fluid and for sand in a calcium carbonate paste. Excellent agreement is found between simulation and experiment. These results indicate that measurements of the shear viscosity of simple shear-rate-dependent non-Newtonian fluids may be used in simulation to predict the viscosity of concentrated suspensions having the same matrix fluid.     

Non-Newtonian Behavior of Ballistic Gelatin at High Shear Rates

A coordinated modeling and experimental effort to investigate the shear stress-shear strain rate response of ballistic gelatin is presented. A power-law constitutive model that captures non-Newtonian shear-thickening behavior, the evolution of viscosity, and the momentum diffusion at high shear rates is adopted. A simple asymptotic relationship between the maximum wall shear stress and the maximum striking wall velocity is derived in the high diffusion rate regime for a shear flow between two parallel plates. Experimental investigation is conducted on double lap-shear test fixture with gelatin specimens of different thicknesses subjected to high strain rate input on the inner surface, generated by a polymer split Hopkinson pressure bar. This test fixture allows measurement of transmitted shear stress as well as visualization of momentum diffusion through gelatin when imaged by a high speed camera. Gelatin specimens of various thicknesses were used for extracting the power-law model parameters. It is found that ballistic gelatin behaves as a shear-thickening fluid at high shear rates with a power-law exponent of 2.22.     

Computational Modelling of Non-Newtonian Effects on Flow in Channels with Moving Wall Indentations

Non-Newtonian effects in a channel with moving wall indentations are assessed numerically by a finite volume method for solving the unsteady incompressible Navier-Stokes equations and using a power-law model exhibiting shear thinning viscosity and Casson's model as the constitutive equations for the non-Newtonian fluid. The computations show that for a non-Newtonian fluid, there are differences in the velocity profiles and in the structure and size of the reversed flow regions as compared with the corresponding Newtonian fluid. The comparison of non-Newtonian and Newtonian wall shear stress reveals a slight decrease in the magnitude on the average for the non-Newtonian case, eventually resulting in the strength of the “wave train” being slightly weaker than those corresponding to a Newtonian fluid.     

Non-Darcy Free Convection of Power-Law Fluids Over a Two-Dimensional Body Embedded in a Porous Medium

A boundary layer analysis was presented to study the non-Darcy-free convection of a power-law fluid over a non-isothermal two-dimensional body embedded in a porous medium. The Ostwald-de Waele power-law model was used to characterize the non-Newtonian fluid behavior. Similarity solutions were obtained with variations in surface temperature or surface heat flux. In view of the fact that most of the non-Newtonian fluids have large Prandtl numbers, this study was directed toward such fluids. The effects of the porous medium parameters, k ₁ and k ₂, body shape parameter, m, and surface thermal variations parameter, p, as well as the power-law index, n, were examined.     

The end correction for power-law fluids in the capillary rheometer

The finite element scheme developed by Nickell, Tanner and Caswell is used to compute the entry and exit losses for creeping flow of power-law fluids in a capillary rheometer. The predicted entry losses for a Newtonian fluid agree well with available experimental and theoretical results. The entry losses for inelastic power-law fluids increased with decreasing flow behaviour index and show an increasing deviation from available upper bound results as the flow behaviour index in the power-law decreases.The exit losses are found to be finite for inelastic power-law fluids and increase as the flow behaviour index decreases. The predicted die swell for Newtonian fluids agrees well with the available experimental data while the influence of shear thinning is to reduce the die swell.The end correction which is the sum of the entry and exit losses relative to twice the viscometric wall shear stress varies from 0.834 for n = 1 to 2.917 for n = 1/6. This figure reaches a very high value as n tends to zero. The experimental variation in the Couette correction factor in capillary rheometry is explained in terms of the shear thinning characteristics of the fluid. It is concluded that the exit flow is not viscometric, contrary to a common assumption.     

The Falkner–Skan Wedge Flows of Power-Law Fluids Embedded in a Porous Medium

The non-Darcy flow characteristics of power-law non-Newtonian fluids past a wedge embedded in a porous medium have been studied. The governing equations are converted to a system of first-order ordinary differential equations by means of a local similarity transformation and have been solved numerically, for a number of parameter combinations of wedge angle parameter m, power-law index of the non-Newtonian fluids n, first-order resistance A and second-order resistance B, using a fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting method. Velocity and shear stress at the body surface are presented for a range of the above parameters. These results are also compared with the corresponding flow problems for a Newtonian fluid. Numerical results show that for the case of the constant wedge angle and material parameter A, the local skin friction coefficient is lower for a dilatant fluid as compared with the pseudo-plastic or Newtonian fluids.