Effects Of non-Newtonian Flow Research Articles

Effect of non-Newtonian flow due to thermally-dependent properties over an inclined surface in the presence of chemical reaction, Brownian motion and thermophoresis

The aim of present study is to investigate the convective heat and mass transfer in steady MHD boundary layer flow of an electrically conducting micropolar fluid over an inclined surface. Partial differential equations resulting from the mathematical modeling of the phenomenon are reduce to nonlinear ODEs, and a finite difference based scheme has been adopted to iteratively find the numerical solution by employing the successive over-relaxation (SOR) method. A self-developed computer code has been used in the MATLAB environment. Influence of chemical reaction, Brownian motion, thermophoresis, and viscous dissipation on the relevant features of the flow are discussed and analyzed through graphs and tables. Temperature dependent thermal conductivity and viscosity enhances the flow velocity. Wall suction slows down the flow in the boundary layer and brings the optimum value of the velocity very nearer to the inclined plane. The magnetic field affects the shear stress and viscous dissipation that is parallel due to suction. A decrease in the fluid temperature is noticed throughout the boundary layer for Prandtl number, Schmidt number, and suction parameter whereas an opposite trend is seen for temperature-dependent thermal conductivity, injection parameter, magnetic field, Brownian motion, and thermophoresis.

Non-Newtonian flow effects in supercooled water

The viscosity of supercooled water has been a subject of intense study, in particular with respect to its temperature dependence. Much less is known, however, about the influence of dynamical effects on the viscosity in its supercooled state. Here we address this issue for the first time, using molecular dynamics simulations to investigate the shear-rate dependence of the viscosity of supercooled water as described by the TIP4P/Ice model. We show the existence of a distinct cross-over from Newtonian to non-Newtonian behavior characterized by a power-law shear-thinning regime. The viscosity reduction is due to the decrease in the connectivity of the hydrogen-bond network. Moreover, the shear thinning intensifies as the degree of supercooling increases, whereas the cross-over flow rate is approximately inversely proportional to the Newtonian viscosity. These results stimulate further investigation into possible fundamental relations between these nonequilibrium effects and the quasi-static Newtonian viscosity behavior of supercooled water.

Effect of Non-Newtonian Flow on Polymer Flooding in Heavy Oil Reservoirs.

The flow of polymer solution and heavy oil in porous media is critical for polymer flooding in heavy oil reservoirs because it significantly determines the polymer enhanced oil recovery (EOR) and polymer flooding efficiency in heavy oil reservoirs. In this paper, physical experiments and numerical simulations were both applied to investigate the flow of partially hydrolyzed polyacrylamide (HPAM) solution and heavy oil, and their effects on polymer flooding in heavy oil reservoirs. First, physical experiments determined the rheology of the polymer solution and heavy oil and their flow in porous media. Then, a new mathematical model was proposed, and an in-house three-dimensional (3D) two-phase polymer flooding simulator was designed considering the non-Newtonian flow. The designed simulator was validated by comparing its results with those obtained from commercial software and typical polymer flooding experiments. The developed simulator was further applied to investigate the non-Newtonian flow in polymer flooding. The experimental results demonstrated that the flow behavior index of the polymer solution is 0.3655, showing a shear thinning; and heavy oil is a type of Bingham fluid that overcomes a threshold pressure gradient (TPG) to flow in porous media. Furthermore, the validation of the designed simulator was confirmed to possess high accuracy and reliability. According to its simulation results, the decreases of 1.66% and 2.49% in oil recovery are caused by the difference between 0.18 and 1 in the polymer solution flow behavior indexes of the pure polymer flooding (PPF) and typical polymer flooding (TPF), respectively. Moreover, for heavy oil, considering a TPG of 20 times greater than its original value, the oil recoveries of PPF and TPF are reduced by 0.01% and 5.77%, respectively. Furthermore, the combined effect of shear thinning and a threshold pressure gradient results in a greater decrease in oil recovery, with 1.74% and 8.35% for PPF and TPF, respectively. Thus, the non-Newtonian flow has a hugely adverse impact on the performance of polymer flooding in heavy oil reservoirs.

Modeling Blood Flow Through Intracranial Aneurysms: A Comparison of Newtonian and Non-Newtonian Viscosity

The effect of non-Newtonian blood flow on the value of wall shear stress (WSS) of an intracranial aneurysm was investigated using computational fluid dynamics. For cerebral arteries, blood is often assumed to behave as a Newtonian fluid, though the effects of non-Newtonian flow on the prediction of areas of low WSS associated with aneurysm rupture are not clear. Geometry was based on published data and a Newtonian model validated against experimental results. Newtonian, unrestricted non-Newtonian, and viscosity-limited non-Newtonian models were compared under pulsatile conditions. Peak WSS of the Newtonian model was 28.7 Pa, and the lowest value of peak WSS for the unrestricted non-Newtonian models was 16.5 Pa. Viscosity-limited non-Newtonian models predicted flow velocity and WSS similar to those predicted by the Newtonian model in high-shear-rate regions, though maximum areas of critically low WSS were up to 42 % smaller than those predicted by the Newtonian model. In conclusion, viscosity limits are required to prevent excessive thinning of non-Newtonian models and the effects of non-Newtonian viscosity are significant for blood flow within low-shear-rate regions of an intracranial aneurysm.

Investigating the impact of non-Newtonian blood models within a heart pump.

A detailed computational fluid dynamics (CFD) study of transient, turbulent blood flow through a positive displacement left ventricular assist device is performed. Two common models for non-Newtonian blood flow are compared to the Newtonian model to investigate their impact on predicted levels of shear rate and wall shear stress. Given that both parameters are directly relevant to the evaluation of risk from thrombus and haemolysis, there is a need to assess the sensitivity to modelling non-Newtonian flow effects within a pulsatile turbulent flow, in order to identify levels of uncertainly in CFD. To capture the effects of turbulence, the elliptic blending Reynolds stress model is used in the present study, on account of superior performance of second moment closure schemes previously identified by the present authors. The CFD configuration includes two cyclically rotating valves and a moving pusher plate to periodically vary the chamber volume. An overset mesh algorithm is used for each instance of mesh motion, and a zero gap technique was employed to ensure full valve closure. The left ventricular assist device was operated at a pumping rate of 86BPM (beats per minute) and a systolic duration of 40% of the pumping cycle, in line with existing experimental data to which comparisons are made. The sensitivity of the variable viscosity models is investigated in terms of mean flow field, levels of turbulence and global shear rate, and a non-dimensional index is used to directly evaluate the impact of non-Newtonian effects. The clinical relevance of the results is reported along with a discussion of modelling uncertainties, observing that the turbulent kinetic energy is generally predicted to be higher in non-Newtonian flow than that observed in Newtonian flow. Copyright © 2016 John Wiley & Sons, Ltd.

Non-Newtonian flow effects on the coalescence and mixing of initially stationary droplets of shear-thinning fluids.

The coalescence of two initially stationary droplets of shear-thinning fluids in a gaseous environment is investigated numerically using the lattice Boltzmann method, with particular interest in non-Newtonian flow effects on the internal mixing subsequent to coalescence. Coalescence of equal-sized droplets, with one being Newtonian while the other is non-Newtonian, leads to the non-Newtonian droplet wrapping around the Newtonian one and hence minimal fine-scale mixing. For unequal-sized droplets, mixing is greatly promoted if both droplets are shear-thinning. When only one of the droplets is shear-thinning, the non-Newtonian effect from the smaller droplet is found to be significantly more effective than that from the larger droplet in facilitating internal jetlike mixing. Parametric study with the Carreau-Yasuda model indicates that the phenomena are universal to a wide range of shear-thinning fluids, given that the extent of shear thinning reaches a certain level, and the internal jet tends to be thicker and develops more rapidly with increasing extent of the shear-thinning effect.

The transverse curvature effects of non-Newtonian flow past a slender parabolic body of revolution

The Levy Lee transformations are modified with the aim of transforming nonlinear partial differential equations of boundary value type governing the steady two dimensional incompressible boundary layer flows of non-Newtonian power-law fluids past a slender parabolic body of revolution into nonlinear ordinary differential equation with appropriate boundary conditions. The transverse curvature effect of the present flow situation is studied theoretically using group-theoretic initial value technique. It is concluded that the slope of the velocity profile is greatly influenced by transverse curvature and suction or blowing parameters.

Computational study of pulsatile blood flow in prototype vessel geometries of coronary segments

The spatial and temporal distributions of wall shear stress (WSS) in prototype vessel geometries of coronary segments are investigated via numerical simulation, and the potential association with vascular disease and specifically atherosclerosis and plaque rupture is discussed. In particular, simulation results of WSS spatio-temporal distributions are presented for pulsatile, non-Newtonian blood flow conditions for: (a) curved pipes with different curvatures, and (b) bifurcating pipes with different branching angles and flow division. The effects of non-Newtonian flow on WSS (compared to Newtonian flow) are found to be small at Reynolds numbers representative of blood flow in coronary arteries. Specific preferential sites of average low WSS (and likely atherogenesis) were found at the outer regions of the bifurcating branches just after the bifurcation, and at the outer-entry and inner-exit flow regions of the curved vessel segment. The drop in WSS was more dramatic at the bifurcating vessel sites (less than 5% of the pre-bifurcation value). These sites were also near rapid gradients of WSS changes in space and time – a fact that increases the risk of rupture of plaque likely to develop at these sites. The time variation of the WSS spatial distributions was very rapid around the start and end of the systolic phase of the cardiac cycle, when strong fluctuations of intravascular pressure were also observed. These rapid and strong changes of WSS and pressure coincide temporally with the greatest flexion and mechanical stresses induced in the vessel wall by myocardial motion (ventricular contraction). The combination of these factors may increase the risk of plaque rupture and thrombus formation at these sites.

Non-Newtonian flow effects during spin coating large-area optical coatings with colloidal suspensions

Multilayer sol-gel optical high reflectors with greater than 99% reflection have been prepared on substrates up to 20 cm in diameter by spin coating silica/alumina colloidal suspensions. These coatings are radially nonuniform, owing to the extensive shear-thinning rheology of the high-index alumina suspension. To a large degree the film thickness nonuniformity can be compensated for by the reflection bandwidth. The rheological properties of the alumina suspension under steady shear have been measured. The low-shear reduced viscosity and the shear-thinning time constant are shown to vary exponentially with φ2, where φ is the solids volume fraction. At φ=0.1 the sol has effectively gelled. A model for spincoating with a non-Newtonian fluid has been developed that uses the Carreau rheology model to fit the measured viscometric data. Modeling and experimental results show that as long as these non-Newtonian effects are sufficiently large (as in this case) the radial film uniformity is determined only by these parameters and cannot be significantly influenced by spin rate, initial solids fraction, or any other parameters under the control of the operator. However, most of the film thickness variation occurs in the first 1–2 cm from the substrate center, leaving the remainder almost uniform. Therefore the degree of nonuniformity does not appreciably increase with increasing substrate size.

The influence of couple stresses on the flow of fluid through a channel with injection

A theoretical study of non-newtonian flow effects is carried out for the flow of a couple stress fluid between two parallel horizontal stationary plates due to fluid injection through the lower porous plate. The governing equations are solved to determine the velocity field and pressure. It is found that the presence of couple stresses in the fluid will enhance the load-bearing capacity of the fluid to a great extent which in turn helps to determine the couple stress parameter of the fluid experimentally.

Convection in a variable-viscosity fluid: Newtonian versus power-law rheology

A number of finite-element calculations of convection in a variable-viscosity fluid have been carried out to investigate the effects of non-Newtonian flow when rheology is also subject to a strong temperature and pressure influence. A variety of cases has been studied in the range of effective Rayleigh numbers between 10 4 and 10 6, including different modes of heating and a range of values for activation energy and activation volume. Power-law creep with a stress exponent of 3 turns out to lead to considerably different flow pattern and heat transfer properties than Newtonian rheology. In general, the effect is to reduce viscosity contrasts imposed by p,T dependence, which can lead in some circumstances to the mobilisation of otherwise stagnant regions within the cell. The properties of non-Newtonian flow can be closely imitated by a Newtonian fluid with a reduced value of the activation enthalpy bH * with b≅0.3–0.5. It appears possible that non-Newtonian rheology plays a key role in determining the convective style in a planetary mantle.

On the compensation of geoid anomalies due to subducting slabs

Candidate models of the forces that oppose the sinking of slabs are all constrained to produce results consistent with the following observation: relative geoid highs, which one assumes are due to slabs, characteristically occur over subduction zones. However, certain models of subduction‐induced flow, such as one based on a Newtonian half‐space mantle, yield surface depressions and concomitant geoid lows that more than fully compensate the geoid highs due to the slab alone. This study has extended a published model of viscous corner flow in subduction zones in order to demonstrate that it can—in certain cases—produce the requisite net geoid highs. Specifically, the relative geoid highs are produced if mantle flow is distinctly non‐Newtonian (stress exponent n > 2). Results in the form of geoid slope or horizontal gravity disturbance profiles are computed for typical values of the slab parameters; they are compared with a representative profile of geoid slopes derived from SEASAT altimeter data in order to show qualitative similarities. It is concluded that the effect of non‐Newtonian flow as opposed to Newtonian is to spread out the induced surface deformation, thereby stretching out the regional compensation to wavelengths (transverse to the trench) of many thousand kilometers.

The influence of couple stresses in squeeze films

A theoretical study of non-Newtonian flow effects in a squeeze film configuration is carried out with special reference to synovial joints. The material model taken is that of the Stokes' couple stress fluid. It is found that the bearings with couple stresss fluid as lubricant provide significant load supporting capacities which result in longer bearing life. The squeeze film time is found to be considerably longer for couple stress fluid than in the case of Newtonian fluid of the same viscosity. These are the most desirable advantages which render the model close to the natural characteristics of synovial joints.

Normal stress effects in viscoelastic fluid lubrication

Non-Newtonian flow effects are evaluated in a slider-bearing configuration. The material model taken is that of the Coleman—Noll second-order fluid. An explicit result is given for the portion of the bearing load supported by the non-Newtonian normal stresses as well as that portion resulting from the usual lubrication theory (Newtonian effect). Particular attention is given to the non-Newtonian effect of a high-polymer additive applied to a Newtonian base stock. The non-Newtonian effect has a particular dependence on the bearing geometry as well as a dependence on the relaxation time of the addtive and the amount by which the additive increases the viscosity. The strength of the non-Newtonian effect is assessed in realistic conditions of bearing operation. We find that under certain conditions the non-Newtonian effect could provide a significant load-supporting capability. However, with slight changes in the conditions of the bearing operation, the non-Newtonian load support is negligible. These results are interpreted and qualified with respect to the limitations of the second-order theory, which does not include shear thinning effects.

Concentration effect in gel permeation chromatography : II. Viscocity phenomena n the interstitial volume

The effect of the viscosity of the injected polymer solution in gel permeation chromatography was investigated using samples of polystyrene standards with molecular weights above the exclusion limit of the column packing used. It was confirmed that a relationship existed between the specific viscosity of the injected polymer solution and the elution volume in the range of the flow-rates in which there was no essential effect of non-Newtonian flow. At higher flow-rates of the solvent, non-Newtonian behaviour of the polymer solution in the chromatographic column was observed.

A reassessment of the wall effect of non-newtonian flow of polymer solutions

An apparatus for checking slip interpretation of flow anomalies in the laminar capillary flow of macromolecular solutions is described. It consists of a two-dimensional flow channel, having a uniform width of 1.5 inch and an alternative, convergent taper that is adjustable. Dilute aqueous solutions of the polymers Carbopol, Natrosol, and Polyox are recirculated in steady laminar flow from a large reservoir. Velocities, pressures, and wall shear stresses are measured. Local velocities are obtained by the local injection of conductive tracer fluid, whose passage is sensed by sets of electrodes stationed along the flow. Wall shear stresses are measured on a small, freely displaceable, traction surface flush with the channel wall. The tests cover concentrations of Carbopol of 0.1% to 0.4%, Natrosol of 0.5% to 1%, and Polyox of 0.5% to 1%. Approximate viscosities range from about 10 to 1000 cP. Wall shear rates up to 1000 s−1 are attained.

Stress Relaxation Following Non-Newtonian Flow

It is assumed that the substances described in the present paper have elements of viscoelastic mechanism which are non-linear at large stresses, but become linear at small stresses in behaviors of flow and internal deformation. In this case the generalized Maxwell formula (1) may be reduced to Eq. (2) at the terminal region of stress relaxation following non-Newtonian flow.dσ(t)/dt=σmj=1dσj(t)/dt=σmj=1{-σj(t)/τj} (1)dσ(t)*/dt=σmj=1dσj(t)*/dt=σmj=1{-σj(t)*/τj°} (2)The asterisk in the equation refers to small stresses. τj°is the relaxation time of the jth mechanism in its ordinary sense at small stresses. By integrating Eq. (2), σ(t)*=σmj=1σj(0)*e-t/τj° (3)where σj(0)*, as an integration constant, is the extrapolated value of the stress to t=0, under which the viscoelastic mechanisms obey Newtonian and Hookean laws. Dividing Eq. (3) by γ:σ(t)*/γ=σmj=1ηj(0)*e-t/τj° (4)where ηj(0)*=σj(0)*/γ. On the analogy of the linear viscoelastic theory ηj(0)* seems to be equal to ηj°=τj°Gj°which may prevail in the viscoelastic behaviors under small stresses. If t>>τm°(the slowest relaxation time), Eq. (4) will become:σ(t)*/γ=ηm(0)*e-t/τm° (5)where the mechanisms of smaller relaxation time than τm°are neglected. According to the theory presented here, the relaxation curves plotted by log{σ(t)/γ}vs. t must become a single straight line at the final process of relaxations, independent of γ values under the steady flow.However, the experimental curves for the materials investigated here become almost straight lines in parallel after the initial rapid relaxations. This phenomenon may be interpreted by the following formula.ηm(0)*≡τm°Gm(0)*≠τm°Gm°≡ηm° (6)Therefore, the effects of non-Newtonian flow seem to have influence on the whole processes of the relaxation and to be characterized as follows; the maximum relaxation time is not altered, but the distribution function Gm°is depressed with increase of the shearing rate under the flow. These phenomena must be derived from the shear break-down of secondary structures under the shear, where the secondary structures seem to contribute mainly to the slowest relaxation mechanism. The evidence of structural break-down of the samples under the flow is certified by the method of Jobling et al..By comparison of dependencies of ηm(0)* and ηa on γ, the following relations are expected:limγ→0ηm(0)*=ηm°≅η=limγ→0ηa (7)log ηa vs. logγ and log ηm(0)* vs. logγ curves at various concentrations seems to be subject to reduction to the master curve, respectively, by the identically reduced variables for both cases.τm°increases exponentially with concentration in Na-PAA solutions.

The Graetz-Nusselt problem for a power-law non-newtonian fluid

The authors show how the Graetz-Nusselt problem in heat transfer theory may be extended to non-Newtonian flow. A simple rheological model, “the power law,” is used to obtain a partial differential equation for the temperature profiles, to which a semi-analytical solution may be found. The temperature profiles are then used to calculate average outlet temperatures, as well as Nusselt numbers for several degrees of non-Newtonian behaviour. Tables are given for estimating the effect of non-Newtonian flow on the heating and cooling of fluids in tubes.