Shear Thinning Phenomenon Research Articles

Effects of Transpiration and Internal Heat Generation/Absorption on the Unsteady Flow of a Maxwell Fluid at a Stretching Surface

The effect of transpiration on unsteady two-dimensional flow of an MHD non-Newtonian Maxwell fluid over a stretching surface in the presence of a heat source/sink is investigated. The upper convected Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Using a similarity transformation the governing partial differential equations of the problem are reduced to a system of ordinary differential equations (ODEs), and the ODEs are solved numerically by a shooting method. The flow features and the heat transfer characteristics are analyzed and discussed in detail for several sets of values of the governing parameters. Though the velocity of the fluid initially decreases with increasing unsteady parameter but it increases finally. Quite the opposite is true with the temperature. Furthermore, the velocity of the fluid decreases with an increasing magnetic or Maxwell parameter. But the temperature is enhanced with an increasing Maxwell parameter. It is observed that the effect of the transpiration is to decrease the fluid velocity as well as the temperature. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Unsteady flow and heat transfer in a thin film of Ostwald–de Waele liquid over a stretching surface

In this paper, the effects of viscous dissipation and the temperature-dependent thermal conductivity on an unsteady flow and heat transfer in a thin liquid film of a non-Newtonian Ostwald–de Waele fluid over a horizontal porous stretching surface is studied. Using a similarity transformation, the time-dependent boundary-layer equations are reduced to a set of non-linear ordinary differential equations. The resulting five parameter problem is solved by the Keller–Box method. The effects of the unsteady parameter on the film thickness are explored numerically for different values of the power-law index parameter and the injection parameter. Numerical results for the velocity, the temperature, the skin friction and the wall-temperature gradient are presented through graphs and tables for different values of the pertinent parameter. One of the important findings of the study is that the film thickness increases with an increase in the power-law index parameter (as well as the injection parameter). Quite the opposite is true with the unsteady parameter. Furthermore, the wall-temperature gradient decreases with an increase in the Eckert number or the variable thermal conductivity parameter. Furthermore, the surface temperature of a shear thinning fluid is larger compared to the Newtonian and shear thickening fluids. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.

Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

Abstract The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t 1 and t 2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Diffusion of a chemically reactive species of a power-law fluid past a stretching surface

A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the Keller–Box method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress.

The Effect of Sample Handling on the Rheological Measurement of Regenerated Silk Fibroin Formic Acid Solution using Parallel Plate Geometry

The effect of sample handling condition on the rheological measurement of regenerated silk fibroin formic acid solution using parallel plate geometry was investigated. In case of loading method, the loading by pouring sample solution resulted in the best reproducibility of rheological measurement. Loading with spoon showed a high variance of viscosity value at low shear rate region (<TEX>$0.01{\sim}1sec^{-1}$</TEX>) while loading with syringe exhibited a low reproducibility of viscosity at high shear region (<TEX>$1{\sim}100sec^{-1}$</TEX>) with a disappearance of shear thinning phenomenon. It was revealed that the sample loading with small extra amount lead to the most reproducible result. The sample loading with the exact amount for the measuring plate resulted in a lack of reproducibility of high shear viscosity, while the loading with large extra volume produced a limited consistency of low shear viscosity. It was turned out that 3 min. of waiting time before measurement was the optimum condition for reliable result. When the waiting time was less than 1 min., the low shear viscosity was obtained with a lack of consistency. On the other hand, the sample solution started drying when the waiting time increased up to 5 min.

The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum

The peristaltic flow of a Jeffrey fluid in a vertical porous stratum with heat transfer is studied under long wavelength and low Reynolds number assumptions. The nonlinear governing equations are solved using perturbation technique. The expressions for velocity, temperature and the pressure rise per one wave length are determined. The effects of different parameters on the velocity, the temperature and the pumping characteristics are discussed. It is observed that the effects of the Jeffrey number λ 1, the Grashof number Gr, the perturbation parameter N = EcPr, and the peristaltic wall deformation parameter ϕ are the strongest on the trapping bolus phenomenon. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear-thinning reduces the wall shear stress.

Badania reologiczne kompozytow poliolefinowych o wysokim stopniu napelnienia z uwzglednieniem charakterystyk p-v-T

A general characteristic of fillers, the various modification possibilities and the consequences of their modification on the properties of composites prepared with their participation was initially presented. The results of rheological studies of highly-filled (48-64 wt. %) polyolefin composites, in which calcium carbonate in the form of i-PP/CaCO3 was used as filler for PE-HD, have been presented (Table 1). Common analysis instruments - rotational cone/plate rheometer, extrusion plastometer of varying piston load and a twin-barrel capillary rheometer were used for rheological measurements. The viscosity curves (off-line method) of the composites were compared to those obtained directly during extrusion (in-line) in an extrusion rheometer, equipped with an rheological head with removable nozzles (Figs. 3-9). The studies were carried out on three types of composites comprising mixtures of PE-HD with i-PP, commercial concentrates and concentrates produced under laboratory conditions, depicted as R, H and M groups, respectively. The shear thinning phenomenon which can be described as an observed decrease in the viscosity of the composites caused by an increase in the shear rate and also in the filler content. The latter was observed especially in the low shear rate region and barely noticeable under high shear rate conditions. A comparison of the viscosity curves obtained for the studied materials in the off-line and in-line methods reveals a similar dependence in both cases. This clearly emphasizes the importance of taking into consideration the changes in density as well as the slippage effect caused basically by the modifying filler (in this case stearic acid and waxes) occurring during analysis. This slippage directly influences the rheological properties of components with a high filling degree of modified calcium carbonate.

RHEOLOGICAL BEHAVIOR OF LOACH SURFACE MUCUS

The rheological behavior of loach surface mucus was investigated in this paper. The steady shear curves of loach surface mucus can be divided into three regions. The initial shear-independent value attained in the low shear horizontal region of such plots is known as the zero shear or Newtonian viscosity (η0),which is called as the first Newtonian region. Subsequent decrease in viscosity with increasing shear rate ( γ) maybe attributed to progressive breakdown of intermolecular network character,which is called as shear thinning phenomenon. With γ increasing further,viscosity of loach surface mucus becomes shear-independent again. This region is the second Newtonian region. The relationship between apparent viscosity ( ηa ) of loach surface mucus and γ can be well described by the Carreau model. The relationship between specific viscosity ( ηsp ) and concentration ( c) follows ηsp ∝ c1. 5,which is in excellent agreement with that of semidilute entangled polyelectrolyte aqueous solution without salt,suggests it is in the semidilute entangled regime. In the tested angle frequency (ω) region,the storage modulus (G′) and the loss modulus (G″) neither changes a lot with ω. G′ G″ suggests the loach surface mucus exhibits more elasticity than viscidity. There is a critical temperature,35℃ ,for loach surface mucus. Below 35℃ ,ηa of loach surface mucus changes little with temperature. Above 35℃ ,the loach surface mucus appears heat-denature and exhibits thoroughly different rheological responses.

Analytical and numerical results for the Swift–Hohenberg equation

The problem of the Swift–Hohenberg equation is considered in this paper. Using homotopy analysis method (HAM) the series solution is developed and its convergence is discussed and documented here for the first time. In particular, we focus on the roles of the eigenvalue parameter α and the length parameter l on the large time behaviour of the solution. For a given time t, we obtain analytical expressions for eigenvalue parameter α and length l which show how different values of these parameters may lead to qualitatively different large time profiles. Also, the results are presented graphically. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Unsteady boundary layers: convective heat transfer over a vertical flat plate

In this paper, we extend the results in the literature for boundary layer flow over a horizontal plate, by considering the buoyancy force term in the momentum equation. Using a similarity transformation, we transform the partial differential equations of the problem into coupled nonlinear ordinary differential equations. We first analyse several special cases dealing with the properties of the exact and approximate solutions. Then, for the general problem, we construct series solutions for arbitrary values of the physical parameters. Furthermore, we obtain numerical solutions for several sets of values of the parameters. The numerical results thus obtained are presented through graphs and tables and the effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results obtained reveal many interesting behaviours that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress. doi:10.1017/S1446181109000297

Hydromagnetic flow and heat transfer of a non-Newtonian power law fluid over a vertical stretching sheet

We consider the steady state, viscous, incompressible two-dimensional magneto hydrodynamic flow of an electrically conducting power law fluid over a vertical stretching sheet. The stretching of the surface velocity and the prescribed surface temperature are assumed to vary linearly with the distance from the slit. The coupled partial differential equations governing the flow and heat transfer are transformed into non-linear coupled ordinary differential equations by a similarity transformation. The transformed boundary layer equations are solved numerically by Keller-Box method for several sets of values of the parameters governing the flow and heat transfer. The flow and heat transfer characteristics are analysed and discussed for different values of the parameters. We observe that the local skin friction coefficient and the local Nusselt number decrease as the magnetic parameter Mn increase for fixed value of the buoyancy parameter λ. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Rheology of decamethylceclopentasiloxane (cyclomethicone) W/O emulsion system

A highly dispersed W/O emulsion of silicone oil (cyclomethicone)/water system was prepared with a nonionic surfactant. The surface and interfacial tension between the oil and water were characterized in terms of the droplet size distribution and viscosity change of the emulsion. When the dispersed phase concentration was relatively high, the viscosity of the emulsion was rapidly increased and the droplet size of the emulsion was decreased. The rheological behavior of the emulsion system showed non-Newtonian and shear thinning phenomena depending upon the content of the dispersed phase. The droplet size of the emulsion was decreased with increasing surfactant content and water concentration. The relative viscosity of the emulsion was better predicted with the Choi-Schowalter model than with the Taylor model. The value of the complex modulus increased with increasing surfactant concentration. The linear viscoelastic region was expanded with a dispersed phase concentration. According to the change in the viscosity, the behavior was classified into three distinct regions: [I] linear viscoelastic, [II] partially viscoelastic, and [III] viscous. The creep/recovery behaviors in each region were characterized.

Rheological Properties of Aircraft Grease Containing Nano-Additives

The apparent viscosity of aircraft grease with different nano-particles content, temperature and shear rates were studied using a rotational viscometer. The rheological properties of two types of aircraft grease, the basic grease and the one with nano-particles additives, were investigated using a rheometer. The results indicated that the apparent viscosity increases with the increase of nanoparticle concentration with the given ratio of nano-particles added. It was also found that the grease with and without the nano-particles both have yield stresses and clear shear-thinning properties. The shear-thinning phenomenon of the grease containing nano-particles is more evident than that of the basic grease. The experimental results also reveal that the rheological characteristics of both types of grease fall in Herschel-Bulkley class, and the nano-particles have a significant influence on the rheological parameters. At the end, the rheology mechanism was discussed based on the entanglement and orientation theories.

Numerical solution of peristaltic transport of an Oldroyd 8-constant fluid in a circular cylindrical tube

The present paper is concerned with the peristaltic flow of a non-Newtonian fluid in circular cylindrical tube. Long wavelength and low Reynolds number approximations are adopted in the problem definition. The non-Newtonian behaviour of the fluid is characterized by the constitutive equation of an Oldroyd 8-constant fluid. The governing nonlinear equation and boundary conditions are solved numerically by a suitable finite-difference method with an iterative scheme. It is seen that shear-thinning and shear-thickening phenomena can be explained through the chosen fluid model. The interaction of shear-thinning and shear-thickening effects with peristaltic motion is studied in detail with particular focus on the basic features of peristalsis such as flow characteristics, pumping characteristics, and trapping. It is found that pressure rise per wavelength against which peristalsis has to work as a positive displacement pump decreases in going from shear-thickening to shear-thinning fluids. Moreover, for strong shear-thinning fluids trapping does not appear. However, a trapped bolus occurs for a weak shear-thinning fluid and its size increases as the fluid is changing from shear thinning towards weak shear thickening. For strong shear-thickening fluids such increase in the size and circulation of bolus stops.

Experimental Analysis and Performance Evaluation of Magnetorheological Damper under High Impact Load

Its primary purpose of this study is to provide a comprehensive investigation on its dynamic performance of MR damper under high impact load. A test had been firstly done in order to identify its high shear viscosity of MR fluid. Then, its thermal performance of MR damper under high impact load is analyzed in order to aid its structure design of MR damper intended for weapon recoil mechanisms applications and improve its performance of elimination of heat. Further, Experimental analysis and performance evaluation of MR damper under impact load have been done by numerical simulation and hardware-in-the-loop simulation, including its acceleration response and pressure response of back cavity under different flow coefficient and the same inputting current, and its acceleration response and pressure response of back cavity under the same flow coefficient and different inputting current. Based on these simulation results, the shear-thinning phenomena and its dynamic response under saturated input current are analyzed and some useful conclusions are made. Finally, experimental results indicated that the developed MR damper under high impact load can achieve a good controllability for recoil applications.

UNSTEADY BOUNDARY LAYERS: CONVECTIVE HEAT TRANSFER OVER A VERTICAL FLAT PLATE

AbstractIn this paper, we extend the results in the literature for boundary layer flow over a horizontal plate, by considering the buoyancy force term in the momentum equation. Using a similarity transformation, we transform the partial differential equations of the problem into coupled nonlinear ordinary differential equations. We first analyse several special cases dealing with the properties of the exact and approximate solutions. Then, for the general problem, we construct series solutions for arbitrary values of the physical parameters. Furthermore, we obtain numerical solutions for several sets of values of the parameters. The numerical results thus obtained are presented through graphs and tables and the effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results obtained reveal many interesting behaviours that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Implicit differential equation arising in the steady flow of a Sisko fluid

Consideration is given to the thin film flow of a Sisko fluid on a moving belt. Using the implicit function theorem, an existence result for the solution of the resulting non-linear differential equation is established. Also, the homotopy analysis method is used to obtain approximate analytical solution of the problem for non-integer values of the power index. The numerical results thus obtained are presented graphically and the salient features of the solution are discussed for various values of the power index parameter. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear-thinning reduces the wall shear stress.

MHD flow past a stretching permeable sheet

An exact solution is obtained for a boundary layer flow of an electrically conducting fluid past a quadratically stretching, and linearly permeable sheet. Effects of magnetic, suction/injection, linear/nonlinear stretching parameters on the stream function and the skin friction are shown graphically and are discussed. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Anomalous diffusion, structural relaxation and shear thinning in glassy hard spherefluids

The stochastic nonlinear Langevin equation theory of the single-particle dynamics ofglassy hard sphere fluids and suspensions has been applied to address severalissues raised by recent experimental and simulation studies. The theoreticallypredicted degree of non-Fickian behaviour at intermediate times, and the slowstructural relaxation component of the small wavevector incoherent dynamic structurefactor, are compared quantitatively with recent measurements and reveal goodagreement. A roughly power law growth, with a common exponent, of the classic andalternative non-Gaussian parameter amplitudes with mean alpha relaxation timeis predicted, and qualitative similarities with a multi-point susceptibility thatquantifies dynamic heterogeneity effects are noted. The nonlinear rheology version ofthe theory has been quantitatively applied to explain recent measurements ofshear-induced acceleration of the single-particle relaxation time on the local cage scale.The resulting no adjustable parameter calculations are in remarkable agreementwith the experimental observations for the absolute magnitude, volume fractiondependence and fractional power law scaling aspects of the shear thinning phenomenon.

Magnetohydrodynamic flow of a viscoelastic fluid

The non-linear differential equation for the magnetohydrodynamic Poiseuille flow of Phan-Thein–Tanner (PTT) conducting fluid is derived. Using the homotopy analysis method (HAM), the series solution is developed and its convergence is discussed. Also, the results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.