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.     

Laminar,transitional and turbulent annular flow of drag-reducing polymer solutions

Mean and rms axial velocity-profile data obtained using laser Doppler anemometry are presented together with pressure-drop data for the flow through a concentric annulus (radius ratio κ = 0.506) of a Newtonian (a glycerine–water mixture) and non-Newtonian fluids—a semi-rigid shear-thinning polymer (a xanthan gum) and a polymer known to exhibit a yield stress (carbopol). A wider range of Reynolds numbers for the transitional flow regime is observed for the more shear-thinning fluids. In marked contrast to the Newtonian fluid, the higher shear stress on the inner wall compared to the outer wall does not lead to earlier transition for the non-Newtonian fluids where more turbulent activity is observed in the outer wall region. The mean axial velocity profiles show a slight shift (～5%) of the location of the maximum velocity towards the outer pipe wall within the transitional regime only for the Newtonian fluid.     

Soret and Dufour effect on double diffusion mixed convection from a vertical surface in a porous medium saturated with a non-Newtonian fluid

A non-similar boundary layer analysis is presented to study the flow, heat and mass transfer characteristics of non-Darcian mixed convection of a non-Newtonian fluid from a vertical isothermal plate embedded in a homogeneous porous medium with the effect of Soret and Dufour and in the presence of either surface injection or suction. The value of the mixed-convection parameter lies between 0 and 1. In addition, the power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastics n = 1 for Newtonian fluids and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection, from the pure forced-convection limit to the pure free-convection limit, and the whole domain of non-Newtonian fluids, from pseudoplastics to dilatant fluids. The numerical solution of the problem is derived using a Runge–Kutta integration scheme with Newton–Raphson shooting technique. Distributions for velocity, temperature and concentration, as well as for the rate of wall heat and mass transfer, have been obtained and discussed for various physical parametric values.     

New contributions on laminar flow of inelastic non-Newtonian fluid in the two-dimensional symmetric expansion: Creeping and slowly moving flow conditions

The steady flow of generalized Newtonian fluid in a two-dimensional 1:3 sudden expansion was studied numerically. Finite volume method was applied to solve the momentum equations along with the continuity equation and the Power law rheological model within the laminar flow regime for a range of Reynolds number and Power law index values. The values of generalized Reynolds number, based on physical and rheological properties, upstream channel height and bulk velocity, were varied between 0.0001 ≤ Re_gen ≤ 10, while the Power law index values mapped the 0.60 ≤ n ≤ 1.40 range, allowing for the investigation of both shear-thinning and shear-thickening effects at creeping as well as slowly moving fluid flow conditions. We report accurate results of a systematic study with a focus on most important characteristics of recirculating fluid flow in the downstream section of sudden expansion geometry. It is shown that for the creeping flow regime there exist finite sized redevelopment length, extra pressure drop (Couette correction) and recirculation zones (also called as Moffatt vortices) that are influenced by the non-Newtonian viscous behaviour.     

Laminar flow of power-law fluids past a rotating cylinder

In this work, the continuity and momentum equations have been solved numerically to investigate the flow of power-law fluids over a rotating cylinder. In particular, consideration has been given to the prediction of drag and lift coefficients as functions of the pertinent governing dimensionless parameters, namely, power-law index (1 ≥ n ≥ 0.2), dimensionless rotational velocity (0 ≤ α ≤ 6) and the Reynolds number (0.1 ≤ Re ≤ 40). Over the range of Reynolds number, the flow is known to be steady. Detailed streamline and vorticity contours adjacent to the rotating cylinder and surface pressure profiles provide further insights into the nature of flow. Finally, the paper is concluded by comparing the present numerical results with the scant experimental data on velocity profiles in the vicinity of a rotating cylinder available in the literature. The correspondence is seen to be excellent for Newtonian and inelastic fluids.     

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).     

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.      

Some exact solutions for rotating flows of a generalized Burgers’ fluid in cylindrical domains

The velocity field and the adequate shear stress corresponding to the flow of a generalized Burgers’ fluid model, between two infinite co-axial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is due to the inner cylinder that applies a time dependent torsional shear to the fluid. The solutions that have been obtained, presented in series form in terms of usual Bessel functions J₁( ? ), J₂( ? ), Y₁( ? ) and Y₂( ? ), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for Burgers’, Oldroyd-B, Maxwell, second grade, Newtonian fluids and large-time transient solutions for generalized Burgers’ fluid are also obtained as special cases of the present general solutions. The effect of various parameters on large-time and transient solutions of generalized Burgers’ fluid is also discussed. Furthermore, for small values of the material parameters, λ₂ and λ₄ or λ₁, λ₂, λ₃ and λ₄, the general solutions corresponding to generalized Burgers’ fluids are going to those for Oldroyd-B and Newtonian fluids, respectively. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.     

Turbulent channel flow of dilute polymeric solutions: Drag reduction scaling and an eddy viscosity model

Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Re_τ, and Weissenberg number, We_τ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; 0 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 74) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.     

Instantaneous flow field above the free end of finite-height cylinders and prisms

The flow above the free ends of surface-mounted finite-height circular cylinders and square prisms was studied experimentally using particle image velocimetry (PIV). Cylinders and prisms with aspect ratios of AR = 9, 7, 5, and 3 were tested at a Reynolds number of Re = 4.2 × 10⁴. The bodies were mounted normal to a ground plane and were partially immersed in a turbulent zero-pressure-gradient boundary layer, where the boundary layer thickness relative to the body width was δ/D = 1.6. PIV measurements were made above the free ends of the bodies in a vertical plane aligned with the flow centreline. The present PIV results provide insight into the effects of aspect ratio and body shape on the instantaneous flow field. The recirculation zone under the separated shear layer is larger for the square prism of AR = 3 compared to the more slender prism of AR = 9. Also, for a square prism with low aspect ratio (AR = 3), the influence of the reverse flow over the free end surface becomes more significant compared to that for a higher aspect ratio (AR = 9). For the circular cylinder, a cross-stream vortex forms within the recirculation zone. As the aspect ratio of the cylinder decreases, the reattachment point of the separated flow on the free end surface moves closer to the trailing edge. For both the square prism and circular cylinder cases, the instantaneous velocity vector field and associated in-plane vorticity field revealed small-scale structures mostly generated by the separated shear layer.     

Experimental investigation on thermal properties of silver nanofluids

This paper reports on an experimental investigation of the thermal properties behavior of 0.5 wt% silver nanoparticle-based nanofluids (NF) containing oleic acid (OA) and potassium oleate surfactant (OAK⁺) with concentrations of 0.5, 1, and 1.5 wt% respectively. The experiments were conducted from 20 °C to 80 °C. It was shown that the NF with 1 wt% OAK⁺ yielded the highest thermal behavior enhancement of about 28% at 80 °C compared to deionized water. The thermal performance had higher than the base fluid/nanofluids at approximately 80%. Moreover, the NF containing OAK⁺ showed higher thermal conductivity and dynamics of specific heat capacity than deionized water in all of the experimental conditions in this study. The rheological experiment showed that viscosity of NF was significantly dependant on temperature. As shear rate increased, the shear stress of the NF increased; however, the viscosity of the nanofluids decreased first and then stabilized. It was further found that NF containing OAK⁺ at a range of operating temperatures produced Newtonian behavior.     

Smoothed particle hydrodynamics simulation of non-Newtonian moulding flow

Smoothed particle hydrodynamics (SPH) has been widely applied in simulating fluid flow because of its attractive properties, for example, it is fully Lagrangian and mesh free. However, this method usually uses the explicit method to solve the conservation equations and in this form it is only suitable to momentum dominated flows with low viscosity. In polymer processing, the fluid is non-Newtonian with high viscosity, O(10³) to O(10⁴) Pa-s say, and the pressure is high as O(10⁶) to O(10¹⁰) Pa. The algorithm of the standard SPH is infeasible in this case, because only very small time steps can be used for a stable simulation. We have developed an implicit SPH for non-Newtonian flow, which is completely matrix free, to solve the equation system iteratively and robustly. The artificial pressure is introduced between particles to stabilize the SPH system avoiding the tensile instability. The fluid is compressible under high pressure. Realistic state equations for polymers, such as the Tait and SSY [16] equations are adopted to describe the density/pressure relations. The method is finally applied to the simulation of moulding flow of a modified power law fluid with the zero shear rate viscosity of 1.22 × 10⁴ Pa-s, Reynolds number of 3 × 10^?4 to 6 × 10^?5 and the highest pressure of O(10⁸) to O(10¹⁰) Pa.     

Flow of a quasi-Newtonian fluid through a planar contraction

Flows through abrupt contractions are dominated by the rapid extension experienced in passing through the contraction. Thus, it is useful to employ a fluid model which considers the extensional viscosity explicitly in its constitutive equation. In this paper, the quasi-Newtonian fluid model, which admits shear thinning and extension thickening of the viscosity depending on the local type of flow as proposed by Schunk and Scriven [P. Schunk, L. Scriven, J, Rheol 34 (1990) 1085], is applied to the numerical simulation of the flow of a dilute polyacrylamide solution through a planar 4 : 1 contraction. In this theory the extra stress tensor does not only depend on the rate of strain tensor but also on the relative rate of rotation of the fluid. The material function – the viscosity function – is allowed to depend on the invariants of these two kinematic tensors yielding a local distinction between extensional, shear or rotation dominated flow. The governing equations are discretized using a finite volume method. Different model parameters are varied and the simulation results are compared with the generalized Newtonian fluid and experimental data.     

Flow of dilute to semi-dilute polystyrene solutions through a benchmark 8:1 planar abrupt micro-contraction

We have studied the flow of thermodynamically ideal solutions of a high molecular weight (M_w = 6.9 MDa) atactic polystyrene in the θ solvent dioctyl phthalate (aPS in DOP) through a micro-fabricated 8:1 planar abrupt contraction geometry. The channel is much deeper than most micro-scale geometries, providing an aspect ratio of 16:1 and a good approximation to 2D flow in the narrow channel. The solutions span a range of concentration 0.03 wt.% < c < 0.6 wt.%, encompassing the dilute to semi-dilute regimes and providing a range of fluid viscosities and relaxation times such that we achieve a range of Weissenberg numbers (8.7 < Wi < 1562) and Reynolds numbers (0.07 < Re < 11.2), giving elasticity numbers between 31 < El < 295. We study the flow using a combination of micro-particle image velocimetry (μ-PIV) to characterize the flow field, pressure measurements to evaluate the non-Newtonian viscosity, and birefringence measurements to assess macromolecular strain. Flow field observations reveal three broad flow regimes characterized by Newtonian-like flow, unstable flow and vortex growth in the upstream salient corners. Transitions between the flow regimes scale with Wi, independent of El, indicating the dominance of elastic over inertial effects in all the fluids. Transitions in the flow field are also reflected by transitions in the relative viscosity (determined from the pressure drop) and the macromolecular strain (determined from birefringence measurements). The strain through the 8:1 contraction saturates at a value of ～4–5 at high Wi. The results of these experiments broaden the limited set of literature on flow through micro-fluidic planar contractions and should be of significant value for optimizing lab-on-a-chip design and for comparison with modeling studies with elasticity dominated fluids.     

Criteria for the appearance of recirculating and non-stationary regimes behind a cylinder in a viscoplastic fluid

The appearance of a recirculation zone and the formation of non-stationary vortices behind a cylinder in the unconfined flow of a Herschel–Bulkley fluid have been studied by numerical simulation. The Herschel–Bulkley constitutive equation was regularised by using the Papanastasiou model. Special attention was paid to determining the numerical parameters and comparing them to existing results. The influence of the Oldroyd number and power-law index on flow morphology and, in particular, on the unyielded zones was studied over a wide spectrum (0 ≤ Od ≤ 10) and (0.3 ≤ n ≤ 1.8). It was seen that the greater the Oldroyd number, the greater the critical Reynolds numbers and Strouhal number for the two flow regimes. The influence of the power-law index is more complex.     

Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids

Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-layer flows that are linearly stable for Re = ∞. The basic methodology consists of two steps. First we eliminate interfacial instabilities by using a yield stress fluid in one fluid layer and ensuring that for the base flow configurations studied we maintain an unyielded plug region at the interface. Secondly we eliminate linear shear instabilities by ensuring a strong enough Couette component in the second fluid layer, imposed via the moving interface. We show that this technique can be applied to both shear-thinning and visco-elastic fluids.     

Viscosity of alumina nanoparticles dispersed in car engine coolant

The present paper, describes our experimental results on the viscosity of the nanofluid prepared by dispersing alumina nanoparticles (<50 nm) in commercial car coolant. The nanofluid prepared with calculated amount of oleic acid (surfactant) was tested to be stable for more than 80 days. The viscosity of the nanofluids is measured both as a function of alumina volume fraction and temperature between 10 and 50 °C. While the pure base fluid display Newtonian behavior over the measured temperature, it transforms to a non-Newtonian fluid with addition of a small amount of alumina nanoparticles. Our results show that viscosity of the nanofluid increases with increasing nanoparticle concentration and decreases with increase in temperature. Most of the frequently used classical models severely under predict the measured viscosity. Volume fraction dependence of the nanofluid viscosity, however, is predicted fairly well on the basis of a recently reported theoretical model for nanofluids that takes into account the effect of Brownian motion of nanoparticles in the nanofluid. The temperature dependence of the viscosity of engine coolant based alumina nanofluids obeys the empirical correlation of the type: log (μ_nf) = A exp(BT), proposed earlier by Namburu et al.     

Comparison of a quasi-Newtonian fluid with a viscoelastic fluid in planar contraction flow

The flow of a 5.0 wt.% solution of polyisobutylene in tetradecane through a planar 4 : 1 contraction exhibiting a shear thinning viscosity is simulated using the flow-type sensitive quasi-Newtonian fluid model. The shear viscosity is fitted by the Giesekus model, which, with the chosen parameters, leads to an extension thickening elongational viscosity. The stress and velocity fields of the numerical simulations are compared with the experimental results of Quinzani et al. [J. Non-Newtonian Fluid Mech. 52 (1994) 1–36] and the numerical results of the viscoelastic simulation using the Giesekus model of Azaiez et al. [J. Non-Newtonian Fluid Mech. 62 (1996) 253–277]. It can be shown that the quasi-Newtonian fluid qualitatively predicts the essential features of the flow in the vicinity of the contraction.     

Electroviscous effects in steady fully developed flow of a power-law liquid through a cylindrical microchannel

Electroviscous effects in steady, fully developed, pressure-driven flow of power-law liquids through a uniform cylindrical microchannel have been investigated numerically by solving the Poisson–Boltzmann and the momentum equations using a finite difference method. The pipe wall is considered to have uniform surface charge density and the liquid is assumed to be a symmetric 1:1 electrolyte solution. Electroviscous resistance reduces the velocity adjacent to the wall, relative to the velocity on the axis. The effect is shown to be greater when the liquid is shear-thinning, and less when it is shear-thickening, than it is for Newtonian flow. For overlapping electrical double layers and elevated surface charge density, the electroviscous reduction in the near-wall velocity can form an almost stationary (zero shear) layer there when the liquid is shear-thinning. In that case, the liquid behaves approximately as if it is flowing through a channel of reduced diameter. The induced axial electrical field shows only a weak dependence on the power-law index with the dependence being greatest for shear-thinning liquids. This field exhibits a local maximum as surface charge density increases from zero, even though the corresponding electrokinetic resistance increases monotonically. The magnitude of the electroviscous effect on the apparent viscosity, as measured by the ratio of the apparent and physical consistency indices, decreases monotonically as the power-law index increases. Thus, overall, the electroviscous effect is stronger in shear-thinning, and weaker in shear-thickening liquids, than it is when the liquid is Newtonian.     

The dynamics of a simple model for a thixotropic yield stress fluid

We study the dynamics of a model for thixotropic yield stress fluids which was recently proposed in [1]. This is based on the partially extended convected model (PEC), modified to allow for a non-zero shear stress limit for large shear rates (PECR), and combined with a Newtonian solvent to enable yielding to homogeneous shear flow (PECR-N) under a prescribed shear stress. We define ? to be the ratio of retardation time to relaxation time and focus on the limit ? → 0. Multiple time scales arise and the solutions are investigated with perturbation methods, in conjunction with direct computation of the full set of equations. Both PEC-N and PECR-N capture the experimentally observed phenomenon that the value of yield stress depends on the observation time. For the PECR-N model, we find transient solutions that are not expected from prior work on the PEC-N model, such as blow-up in finite time on the slow manifold, and yielded time-periodic flow.