On the Stagnation Point Flow of a Special Class of Non-Newtonian Fluids

Abstract

The two-dimensional boundary layer equations for a class of non-Newtonian fluids, for which the apparent viscosity can be expressed as a polynomial in the second scalar invariant of the rate of strain tensor, have been derived. These equations have been employed to analyse the flow near a stagnation point over a stationary impermeable wall. The non-Newtonian effects on the boundary layer velocity profile and the wall skin friction have been studied, and compared with the corresponding Newtonian fluid. The fluid velocity in the boundary layer has been shown to be retarded by the non-Newtonian effect while the skin friction increases proportionate to it.     

Bifurcational analysis of the isotropic-nematic phase transition of rigid rod polymers subjected to biaxial stretching flow

A bifurcational analysis is performed on Doi's equation of nematodynamics that describes the non-equlibrium isotropic-nematic phase transition of rigid rod polymers in the presence of steady biaxial stretching flow. The symmetry of the flow and of the governing order parameter equations are shown to be the source of a rich bifurcation, symmetry breaking, and multistability behavior involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. According to the relative intensity of the nematic ordering field and stretching rate, the uniaxial isotropic-biaxial nematic transition may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non-equilibrium phase transition point. The solutions to the Doi equations of nematodynamics are found to be consistent with those of Khokhlov and Semenov [Macromolecules 15 , 1272 (1982)], which are based on a version of the Onsager theory of isotropic-nematic phase transitions. The present simulations provide a useful guide for orientation control in biaxial stretching flows.     

Comparative PIV and LDA studies of Newtonian and non-Newtonian flows in an agitated tank

The paper presents results of an experimental study of the fluid velocity field in a stirred tank equipped with a Prochem Maxflo T (PMT) type impeller which was rotating at a constant frequency of N = 4.1 or 8.2 s^?1 inducing transitional (Re = 499 or 1307) or turbulent (Re = 2.43 × 10⁴) flow of the fluid. The experiments were performed for a Newtonian fluid (water) and a non-Newtonian fluid (0.2 wt% aqueous solution of carboxymethyl cellulose, CMC) exhibiting mild viscoelastic properties. Measurements were carried out using laser light scattering on tracer particles which follow the flow (2-D PIV). For both the water and the CMC solution one primary and two secondary circulation loops were observed within the fluid volume; however, the secondary loops were characterized by much lower intensity. The applied PMT-type impeller produced in the Newtonian fluid an axial primary flow, whilst in the non-Newtonian fluid the flow was more radial. The results obtained in the form of the local mean velocity components were in satisfactory agreement with the literature data from LDA. Distribution of the shear rate in the studied system was also analyzed. For the non-Newtonian fluid an area was computed where the elastic force dominates over the viscous one. The area was nearly matching the region occupied by the primary circulation loop.     

Effect of pressure on the flow behavior of polybutene

The rheology of submicron thick polymer melt is examined under high normal pressure conditions by a recently developed photobleached‐fluorescence imaging velocimetry technique. In particular, the validity and limitation of Reynold equation solution, which suggests a linear through‐thickness velocity profile, is investigated. Polybutene (PB) is sheared between two surfaces in a point contact. The results presented in this work suggest the existence of a critical pressure below which the through‐thickness velocity profile is close to linear. At higher pressures however, the profile assumes a sigmoidal shape resembling partial plug flow. The departure of the sigmoidal profile from the linear profile increases with pressure, which is indicative of a second‐order phase/glass transition. The nature of the transition is confirmed independently by examining the pressure‐dependent dynamics of PB squeeze films. The critical pressure for flow profile transition varies with molecular weight, which is consistent with the pressure‐induced glass transition of polymer melt. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 708–715     

Critical molecular weight for onset of non-newtonian flow and upper newtonian viscosity of polydimethylsiloxane

The flow curves of fractionated polydimethylsiloxanes of different molecular weights were obtained over a wide range of shear rates, from 3 × 10^?1 to 4.3 × 10⁶ sec^?1, by use of a gas-driven capillary viscometer designed to decrease the experimental error in high shear rate region. Non-Newtonian flow can occur at molecular weights below the critical molecular weight M_c for the entanglement of polymer chain. The critical molecular weight M′_c for the onset of the non-Newtonian flow is identical with that of the segment of viscous flow. For the polymer of molecular weights from M′_c to M_c, the upper Newtonian viscosity increases with an increase in molecular weight. Above M_c, the upper Newtonian viscosity is almost independent of the molecular weight.     

Investigation of the Wall Slip Effect in Highly Concentrated Disperse Systems by Means of Non-Invasive UVP-PD Method in the Pressure Driven Shear Flow1

A novel in-line UVP-PD non-invasive rheological measuring technique was introduced for rheological analysis of highly concentrated disperse systems. The method is based on a combination of the Ultrasonic Pulsed Echo Doppler technique (UVP, Ultrasound Velocity Profiler) and the pressure difference (PD) method. The rheological properties were derived from simultaneous recording and on-line analysis of the velocity and related radial shear stress profiles across a circular channel. Wall slip velocity was extrapolated from the on-line fit and monitored on-line simultaneously with the flow index. Two effects were found and preliminarily analyzed. The first effect refers to a transition from strongly non-Newtonian to Newtonian flow velocity profile while increasing in the absolute flow velocity. The second flow effect refers to an abrupt reduction of the wall slip velocity while increasing the absolute flow velocity. Considerable discrepancy was found between the results of the in-line UVP-PD measurement in pressure driven shear flow and the results of the conventional rheometry.     

Electrokinetic diffusioosmotic flow of Ostwald-de Waele fluids near a charged flat plate in the thin double layer limit

Electrokinetic diffusioosmotic flow of Ostwald-de Waele, or power-law, fluids near a large charged flat plate is theoretically investigated for very thin double layers. Solutions to the flow velocity both up-close and far from the flat plate as well as the effective viscosity are presented for general values of the flow behavior index. Results show that given a wall zeta potential, ζ, diffusivity difference parameter, β, and constant imposed solute concentration gradient, both the near and far field diffusioosmotic flow velocities obtained for the respective dilatant and pseudoplastic liquids considerably deviate from those obtained for Newtonian liquids as found in previous literature. This likely suggests that the electrokinetic diffusioosmosis and its complementary effect of diffusiophoresis depend sensitively not only on the ζ-β parametric pair, but also on the possible non-Newtonian characteristics of the electrolytic liquid phase of the system. The theory presented herein can also be readily modified to model or describe electrodiffusioosmosis in power-law fluids, which is likely found in flow situations where the fluid non-Newtonian response, imposed solute concentration gradient, and an additional externally applied electric current density (or electric field) are of equal importance.     

A Jeffrey-fluid model of blood flow in tubes with stenosis

In this paper, we discuss the two-layered Jeffrey-fluid model with mild stenosis in narrow tubes. The blood flow in narrow arteries is treated as a two-fluid model with the suspension of erythrocytes, leukocytes, etc., as a Jeffrey fluid, which is a non-Newtonian fluid, in the core region and plasma, a Newtonian fluid, in the peripheral region. An analytical solution has been obtained for the velocity in the core and peripheral region, volume flow rate, resistance to flow, and wall-shear stress. The effect of Jeffrey-fluid parameters, like the height of stenosis, viscosity, etc., on volume flow rate, resistance to flow (impedance), and wall-shear stress has been discussed graphically. Through the present study, it is found that the wall-shear stress and resistance to flow increases with the increase in height of stenosis and decreases with the increase in the ratio of relaxation time. It is also found that the velocity decreases with an increase in stenosis height in both the core and the peripheral region. A previous result has been also verified.     

Steady-shear viscosity of polydimethylsiloxanes over the range from the lower to the upper Newtonian region

The mechanism of non-Newtonian behavior for flow from the lower to the upper Newtonian region is explained by a modification of Graessley's theory. In the theory proposed here, a viscosity η_fric, which is based on friction between polymer segments and is almost shear-independent, is introduced in addition to Graessley's entanglement viscosity η_ent, which decreases with increasing shear rate. The theory is applied to previously obtained data on steady flow of polydimethylsiloxanes of different molecular weights. The agreement between calculated and experimental results is good. In polymers with the molecular weight above the critical molecular weight for entanglement M_c, the major contribution to viscosity near zero shear rate is η_ent. As the shear rate increases, the flow curve has an inflection where η_fric cannot be disregarded in comparison with η_ent. In the upper Newtonian region, η_fric has more influence on the viscosity than η_ent. The theory can also explain the experimental results on flow of polymers with molecular weight below M_c, which were shown to be slightly non-Newtonian in the previous paper.     

Estimation of Particle Capture Zone Characteristics in Magnetic Filtration Processes

The real properties of the geometry of the capture region of the particles in the pores of the magnetic filters which are formed by magnetized ferromagnetic microparticles are investigated. The flow velocity profile of the liquid in this region is determined and the effect of the velocity profile to keep the particles in the pores is examined. The magnetic and the hydrodynamic powers have been expressed explicitly by considering, the pore geometry, magnetized property and the flow velocity. Obtained expression was explained on the V _m /V _f ratio, which is named as magnetic and flow velocities rate in filtering and separation processes. According to this expression, the volume and surface ratios of the particles which are accumulated in the particles capture region are taken into account. From theory and practice point of view, the derived expressions and results are put into a form to make easy to use for design, control and optimization of the filters.     

Interfacial instabilities affect microfluidic extraction of small molecules from non-Newtonian fluids

As part of a project to develop an integrated microfluidic biosensor for the detection of small molecules in saliva, practical issues of extraction of analytes from non-Newtonian samples using an H-filter were explored. The H-filter can be used to rapidly and efficiently extract small molecules from a complex sample into a simpler buffer. The location of the interface between the sample and buffer streams is a critical parameter in the function of the H-filter, so fluorescence microscopy was employed to monitor the interface position; this revealed apparently anomalous fluorophore diffusion from the samples into the buffer solutions. Using confocal microscopy to understand the three-dimensional distribution of the fluorophore, it was found that the interface between the non-Newtonian sample and Newtonian buffer was both curved and unstable. The core of the non-Newtonian sample extended into the Newtonian buffer and its position was unstable, producing a fluorescence intensity profile that gave rise to the apparently anomalously fast fluorophore transport. These instabilities resulted from the pairing of rheologically dissimilar fluid streams and were flowrate dependent. We conclude that use of non-Newtonian fluids, such as saliva, in the H-filter necessitates pretreatment to reduce viscoelasticity. The interfacial variation in position, stability and shape caused by the non-Newtonian samples has substantial implications for the use of biological samples for quantitative analysis and analyte extraction in concurrent flow extraction devices.     

Mathematical modeling and simulation of peristaltic activity in Ree-Eyring fluid flow through non-uniform complaint channel: Different varying conditions

The current study incorporates variable viscosity and thermal conductivity on modeling Ree-Eyring fluid flow inside a peristaltic non-uniform complaint channel. The small Reynolds number and long-wavelength approximations are employed for resolve the governing nonlinear differential equations. Temperature expression is obtained with the help of series solution method. The graphs are drawn on relevant parameters to investigate its effect on velocity, temperature, concentration, and streamlines through MATLAB 2020b. The results confer more velocity in the Newtonian fluid in comparison with non-Newtonian fluid. Also, the model discloses that the size of the bolus can be varied by varying the viscosity parameter. This result helps in understanding the thrombus formation in blood vessels.     

Analysis of the shape of dendrimers under shear

Nonequilibrium molecular-dynamics simulations are used to investigate the molecular shape of dendrimers and linear polymers in a melt and under shear. Molecules are modeled at the coarse-grained level using a finitely extensible nonlinear elastic bead-spring model. The shape of dendrimers and linear polymers at equilibrium and undergoing planar Couette flow is analyzed quantitatively and it is related to the shear viscosity. The shape of dendrimers responds differently to the influence of shear compared with linear polymers of equivalent molecular mass. However, in both cases the transition from Newtonian to non-Newtonian viscosity behavior corresponds to significant changes in molecular symmetry. This suggests that a shape analysis could be used to estimate the onset of shear thinning in polymers.     

Magnetic field effects on natural convection flow of a non-Newtonian fluid in an L-shaped enclosure

The effect of magnetic field on natural convection heat transfer in an L-shaped enclosure filled with a non-Newtonian fluid is investigated numerically. The governing equations are solved by finite-volume method using the SIMPLE algorithm. The power-law rheological model is used to characterize the non-Newtonian fluid behavior. It is revealed that heat transfer rate decreases for shear-thinning fluids (of power-law index, n?<?1) and increases for shear-thickening fluids (n?>?1) in comparison with the Newtonian ones. Thermal behavior of shear-thinning and shear-thickening fluids is similar to that of Newtonian fluids for the angle of enclosure α?<?60° and α?>?60°, respectively.     

Non-Newtonian flow curves including lower and upper Newtonian regions for dilute and moderately concentrated polystyrene solutions

The non-Newtonian viscosity in steady flow was measured for solutions of polystyrene (M?_w/M?_n = 1.1) in diethyl phthalate at 30.0°C. In the moderately concentrated solutions, from 6.03 × 10^?2 to 5.62 × 10^?1g/cm³, the viscosity data modified by frictional parameters fit the Graessley theoretical curve for a narrow distribution polymer. The dilute solutions, from 3.26 × 10^?3 to 1.57 × 10^?2 g/cm³, were nonentangled systems whose non-Newtonian properties could be explained by the excluded volume effect as proposed by Fixman. On the basis of the non-Newtonian data, it was concluded that the solution of 3.30 × 10^?2 g/cm³ was a lower critical entanglement concentration, which was distinguished from the usual higher critical concentration for entanglement. This lower critical concentration was also found in the concentration dependence of the activation energy of flow and the absorbance at 310 nm.     

Rheology of liquid crystalline phases of alkyloxybenzylidene toluidines

A unique viscometer of the CS rheometer viscometer class designed at the Kazan State University of Technology is used to measure viscosities of two p-n-alkyloxybenzylidene-p-toluidines in the entire temperature range of the liquid crystalline state and transition into an isotropic liquid. The measured shear stresses and flow rates are used to calculate shear rates and plot flow and viscosity curves. The liquid crystalline phase and isotropic liquid are demonstrated to possess Newtonian viscosity, whose viscous flow activation parameters are calculated in the temperature range under study. The results are discussed from the standpoint of intermolecular interactions and structural details of the liquid crystalline phase.     

Hydrodynamic Characterization of a Column-type Prototype Bioreactor

Agro-food industrial processes produce a large amount of residues, most of which are organic. One of the possible solutions for the treatment of these residues is anaerobic digestion in bioreactors. A novel 18-L bioreactor for treating waste water was designed based on pneumatic agitation and semispherical baffles. Flow patterns were visualized using the particle tracer technique. Circulation times were measured with the particle tracer and the thermal technique, while mixing times were measured using the thermal technique. Newtonian fluid and two non-Newtonian fluids were used to simulate the operational conditions. The results showed that the change from Newtonian to non-Newtonian properties reduces mixed zones and increases circulation and mixing times. Circulation time was similar when evaluated with the thermal and the tracer particle methods. It was possible to predict dimensionless mixing time (θ _m) using an equivalent Froude number (Fr _eq).     

Does macroscopic flow geometry influence wetting dynamic?

The macroscopic flow geometry has long been assumed to have little impact on dynamic wetting behavior of liquids on solid surfaces. This study experimentally studied both spontaneous spreading and forced wetting of several kinds of Newtonian and non-Newtonian fluids to study the effect of the macroscopic flow geometry on dynamic wetting. The relationship between the dynamic contact angle, θ(D), and the velocity of the moving contact line, U, indicates that the macroscopic flow geometry does not influence the advancing dynamic wetting behavior of Newtonian fluids, but does influence the advancing dynamic wetting behavior of non-Newtonian fluids, which had not been discovered before.     

Anisotropic and enhanced self-diffusion of a macromolecular chain under simple shear flow as revealed by Monte Carlo simulation on lattices

Two-dimensional simple shear flow of a self-avoiding macromolecular chain is simulated by a lattice Monte Carlo (MC) method with a pseudo-potential describing the flow field. The simulated velocity profile satisfies the requirements of simple shear flow unless the shear rate is unreasonably high. Some diffusion problems for a free-draining bead-spring chain with excluded volume interaction are then investigated at low and relatively high shear rates. Three diffusion coefficients are defined and examined in this paper: the conventional self-diffusivity in zero field, D_self, the apparent self-diffusivity in flow field, D_app, and the flow diffusivity in simulation, D_flow reflecting actually the transport coefficient. It is found that these three diffusivities for a flexible chain are different from each other. What is more important is that self-diffusion exhibits a high anisotropy in the flow field. The apparent self-diffusion along the flow direction is enhanced to a large extent. It is increased monotonically with the increase of shear time or shear strain, whereas the chain configuration can achieve a stationary anisotropic distribution following an interesting overshoot of the coil shape and size. Besides a single self-avoiding chain, an isolated Brownian bead and a group of self-avoiding beads with a quasi-Gaussian spatial distribution are also simulated. According to the comparison, the effects of the connectivity of the chain on the diffusion behavior are revealed. Some scaling relations of D_app versus t are consistent with the theoretical analyses in the pertinent literature.     

The elasticity of nematic networks

Nematic rubbers are composed of crosslinked polymer chains with stiff rods either incorporated into their backbones or pendant as side chains. When nematic effects axe strong, such rubbers exhibit discontinuous stress-strain relationships and spontaneous shape changes. We model such a rubber using Gaussian elasticity theory, including the nematic interaction via a mean field. Results are presented for the cases of uniaxial extension and compression. Under uniaxial extension the rubber can undergo a first order phase transition to a uniaxial nematic phase. Under uniaxial compression first or second order transitions are possible to genuinely biaxial nematic states with biaxial strains. When nematic effects are very small (i.e. T >> T_c where T_c is the nematic-isotropic phase transition temperature of the rubber) we postulate that the model is a good approximation to a conventional, non-nematic elastomer, and fit our model to data from an isoprene rubber.