Shear-dependent Viscosity Research Articles

Equilibrium molecular dynamics simulation of shear viscosity of two-dimensional complex (dusty) plasmas

Shear viscosity is examined throughout the entire range of strongly coupled states of two-dimensional complex (dusty) plasma liquids (CDPLs). We have employed equilibrium molecular dynamics (EMD) simulation to compute the shear viscosity coefficients of CDPLs. In the strongly coupled liquid region, the values of valid viscosity coefficient can be estimated only in order of magnitude. The variations in the valid viscosity coefficients with screening strength (κ) and Coulomb coupling strengths (Γ) are observed. A systematic dependence of shear viscosity on κ is observed for an intermediate and higher Γ. The investigations showed that the position of the minimum viscosity coefficient shifts towards higher Γ as κ increases. The computational results for the entire range of liquid states of the strongly coupled dusty plasma obtained using the shear autocorrelation functions are in good agreement with the available simulation results and experimental data. It is shown that new simulations extended the range of plasma states (Γ, κ) used in our earlier simulation results for the existence of a finite minimum possible viscosity coefficient and it is also dependent on plasma states.

Three-dimensional stability, receptivity and sensitivity of non-Newtonian flows inside open cavities

We investigate the stability properties of flows over an open square cavity for fluids with shear-dependent viscosity. Analysis is carried out in context of the linear theory using a normal-mode decomposition. The incompressible Cauchy equations, with a Carreau viscosity model, are discretized with a finite-element method. The characteristics of direct and adjoint eigenmodes are analyzed and discussed in order to understand the receptivity features of the flow. Furthermore, we identify the regions of the flow that are more sensitive to spatially localized feedback by building a spatial map obtained from the product between the direct and adjoint eigenfunctions. Analysis shows that the first global linear instability of the steady flow is a steady or unsteady three-dimensionl bifurcation depending on the value of the power-law index n. The instability mechanism is always located inside the cavity and the linear stability results suggest a strong connection with the classical lid-driven cavity problem.

Regularity criterion for generalized Newtonian fluids in bounded domains

The regularity of a non-Newtonian flow in a domain with a boundary cannot be treated easily because of the nonlinear viscosity term and the global property of the pressure. A distance function was used in a previous study to obtain a strong solution. In the present study, using the distance function idea, we obtain Serrin-type regularity criteria for the vorticity and the velocity with regard to non-Newtonian equations with shear-dependent viscosity in a bounded domain.

Regularity Results for a Cahn-Hilliard-Navier-Stokes System with Shear Dependent Viscosity

We analyze a diffuse interface model describing the behavior of a mixture of two incompressible fluids. More precisely, we consider Navier-Stokes type equations with power-law like shear dependent viscosity. Such equations are nonlinearly coupled with a convective Cahn-Hilliard equation for the order parameter. The resulting system is endowed with no-slip and no-flux boundary conditions. We prove some regularity properties of weak solutions under rather general conditions. This is a generalization of previous results already proven for single fluids. Some consequences of such results are also addressed.

Time-Dependent and Shear-Dependent Transient Viscosity of an Alumina Suspension

The transient viscosity of a well-dispersed Alumina–polyvinyl butyral tape-casting slurry have been investigated at the shear domain of 1–8 s−1 with the help of a conventional Couette device. The slurry under these shear rates shows a combination of shear dependence and time dependence based upon the applied shear. Attempts have been made to explain the diverse rheological behavior of the slurry. Many studies involving powder loading, milling time, extended shear up ramp, extended shear down ramp, time- and shear-dependent viscosities of the supernatant, and continual shearing have been conducted to explore the probable reasons behind such diverse behavior of the slurry. The findings of these studies strongly suggest that at the shear rates, shear-induced hydrodynamic diffusion plays a major role in dictating the time-dependent viscosity profile of the suspension. Further analysis of the results points out that the observed viscosity profiles are the resultant of the two major competitive processes of shear-induced hydrodynamic disffusion and shear rejuvenation. The results obtained in the present investigation also strongly indicate that the time-dependent behavior of the suspensions under shear opens up an alternative route of characterization of well-dispersed ceramics suspensions.

Oscillatory and steady shear viscosity: The Cox–Merz rule, superposition, and application to EHL friction

The new quantitative approach to elastohydrodynamic lubrication requires a description of the steady shear dependent viscosity for calculations of film thickness and friction. This property can be obtained from measurements in pressurized thin-film Couette viscometers. However, frequency dependent viscosity can be obtained from a torsionally vibrating quartz crystal viscometer at high pressure or a relatively simple ambient pressure measurement with a shear impedance spectrometer. Here it is shown for squalane and for a cyclic hydrocarbon and for a diester that both the steady shear dependent viscosity and the frequency dependent viscosity obey time-temperature-pressure superposition with the simplest shifting rule over the range of conditions investigated. Flow curves shift along a constant steady stress path or a constant complex modulus path. The Cox–Merz rule has been confirmed only for squalane and then only near the transition. The EHL friction for squalane at low pressure may be predicted with fair accuracy from the frequency dependent viscosity measured at ambient pressure. It appears that the Cox–Merz rule only applies to low-molecular-weight liquids when the molecule is composed of a long chain.

On the solvability of models for two-phase flows of viscous incompressible fluid with shear-dependent viscosity

In this paper we consider a model describing the motion of a mixture of two incompressible and (partially) immiscible fluids in d-dimension (d≤4) space domain whose viscosities have a p-structure depending on the shear rate (or called with shear-dependent viscosity). The existence of weak solutions is established for the exponent p≥p1≐d+3d2+4dd+2 under the no-slip boundary condition to velocity and non-flux boundary condition to relative density. This improves the known results proved for p≥3d+2d+2 in Kim et al. (2006).

Shear dependent viscosity of poly(ethylene oxide) in two protic ionic liquids

Steady shear viscosity measurements have been performed on 100kDa poly(ethylene oxide) (PEO) dissolved in the protic ionic liquids ethylammonium nitrate (EAN) and propylammonium nitrate (PAN) and in water. The zero shear viscosity in all three solvents increases with polymer concentration, falling into three concentration regimes corresponding to dilute, semi-dilute and network solutions. Huggins plots reveal three distinct solvent conditions: good (water), good-theta (EAN) and theta (PAN). However, differences in the transition concentrations, power law behaviour of the viscosities, and relaxation times arising from shear thinning in the two ILs can be directly related to the effects of solvent nanostructure.

Flow and mixing analysis of non-Newtonian fluids in straight and serpentine microchannels

Numerical simulations were carried out to investigate the flow dynamics and mixing behavior in T-shaped and serpentine microchannels with non-Newtonian working fluids using shear-dependent viscosity models. As an illustrative case study, the microfluidic transport of blood was considered. The Carreau–Yasuda and Casson non-Newtonian blood viscosity models were used to capture the non-Newtonian characteristics. Steady Navier–Stokes equations with a diffusion-convection model for species concentration were solved in flow and mixing analyses. Under similar operating conditions, flow dynamics and mixing were compared between the working fluids: water (a Newtonian fluid), and blood using the Carreau–Yasuda non-Newtonian model. For a mass flow rate of ṁ<10−2kg/h, the mixing performances of both the fluids were found to be nearly equivalent, and decreased with flow rate. With increased flow rate, the mixing with water was significantly improved. However, a negligible change in mixing performance was observed using the Carreau–Yasuda model for blood. Also, the pumping power needed was considerably higher for the blood sample (~1bar) than for water (~0.40bar) at the same flow rate. The mixing behavior with the Carreau–Yasuda blood model was compared for T-shaped and serpentine channels over a fixed mixing length. The serpentine channel showed better mixing performance over the flow rate range considered.

The elliptic flow and the shear viscosity of the QGP within a kinetic approach

We use a relativistic transport approach to study the role of a temperature dependent shear viscosity to entropy density ratio, η/s(T), on the build-up of the elliptic flow, v2. The recent results from = 62.4GeV at RHIC up to 2.76 TeV at LHC have shown an intriguing property of the v2(pT), which appears to be nearly invariant with energy. We show that in our transport approach this surprising behavior can be described by a particular temperature dependence of η/s(T), typical of matter that undergoes a phase transition or a cross-over, with a rise and fall and the minimum close to critical temperature Tc.

Shear thinning behavior of linear polymer melts under shear flow via nonequilibrium molecular dynamics.

The properties of both untangled and entangled linear polymer melts under shear flow are studied by nonequilibrium molecular dynamics simulations. The results reveal that the dependence of shear viscosity η on shear rate γ, expressed by n ~ γ(-n), exhibits three distinct regimes. The first is the well-known Newtonian regime, namely, η independent of shear rate at small shear rates γ < τ0(-1) (where τ0 is the longest polymer relaxation time at equilibrium). In the non-Newtonian regime (γ > τ0(-1)) the shear dependence of viscosity exhibits a crossover at a critical shear rate γc dividing this regime into two different regimes, shear thinning regime I (ST-I) and II (ST-II), respectively. In the ST-I regime (τ0(-1) < γ < γc), the exponent n increases with increasing chain length N, while in the ST-II regime (γ > γc) a universal power law n ~ γ(-0.37) is found for considered chain lengths. Furthermore, the longer the polymer chain is, the smaller the shear viscosity for a given shear rate in the ST-II regime. The simulation also shows that a characteristic chain length, below which γc will be equal to τ0(-1), lies in the interval 30 < N < 50. For all considered chain lengths in the ST-II regime, we also find that the first and second normal stress differences N1 and N2 follow power laws of N1 ~ γ(2/3) and N2 ~ γ(0.82), respectively; the orientation resistance parameter mG follows the relation mG ~ γ(0.75) and the tumbling frequency ftb follows ftb ~ γ(0.75). These results imply that the effects of entanglement on the shear dependences of these properties may be negligible in the ST-II regime. These findings may shed some light on the nature of shear thinning in flexible linear polymer melts.

Laminar and steady free convection in power-law fluids from a heated spheroidal particle: A numerical study

In this work, the effects of aspect ratio and shear-dependent viscosity on the laminar free convection heat transfer from a heated spheroid immersed in unbounded quiescent power-law fluids have been investigated. In particular, the coupled momentum and energy equations have been solved numerically over the following ranges of the pertinent governing parameters: Grashof number, 10⩽Gr⩽105; Prandtl number, 0.72⩽Pr⩽100; power-law index, 0.3⩽n⩽1.5 and aspect ratio, 0.2⩽e⩽5. Detailed structures of the flow and temperature fields in the vicinity of the spheroid are visualized in terms of the streamline and isotherm patterns, whereas the gross flow and heat transfer phenomena are resolved in terms of the local Nusselt number and its surface averaged value and drag coefficient (CD). Broadly speaking, shear-thinning fluid behaviour (n<1) facilitates heat transfer whereas shear-thickening (n>1) impedes it in comparison to that seen in Newtonian fluids (n=1) under otherwise identical conditions. At fixed values of the Grashof number (Gr), Prandtl number (Pr) and power-law index (n), the value of Nusselt number gradually increases as the spheroid shape progressively passes from the oblate (e>1) to the prolate (e<1) configurations via the spherical shape (e=1). The reverse trend occurs, however, for the drag coefficient (CD). Finally, the present values of the average Nusselt number and drag coefficient are correlated using a simple analytical form based on a general composite parameter proposed for power-law fluids. The paper is concluded by presenting some comparisons with the limited previous analytical and experimental results available in the literature which are limited to Newtonian fluids.

Compact bubble clusters in Newtonian and non-Newtonian liquids

We studied the terminal velocity of a packed array of bubbles, a bubble cluster, rising in different fluids: a Newtonian fluid, an elastic fluid with nearly constant viscosity (Boger fluid), and a viscoelastic fluid with a shear dependent viscosity, for small but finite Reynolds numbers (1 × 10−4 &amp;lt; Re &amp;lt; 4). In all three cases, the cluster velocity increased with the total volume, following the same trend as single bubbles. For the case of clusters in elastic fluids, interestingly, the so-called velocity discontinuity was not observed, unlike the single bubble case. In addition to the absence of jump velocity, the clusters did not show the typical teardrop shape of large bubbles in viscoelastic fluids and the strength of the negative wake is much weaker than the one observed behind single bubbles. Dimensional analysis of the volume-velocity plots allowed us to show that, while the equivalent diameter (obtained from the total cluster volume) is the appropriate length to determine buoyancy forces and characteristic shear rates, the individual bubble size is the appropriate scale to account for surface forces.

Annular Frictional Pressure Losses During Drilling—Predicting the Effect of Drillstring Rotation

Controlling the annular frictional pressure losses is important in order to drill safely with overpressure without fracturing the formation. To predict these pressure losses, however, is not straightforward. First of all, the pressure losses depend on the annulus eccentricity. Moving the drillstring to the wall generates a wider flow channel in part of the annulus which reduces the frictional pressure losses significantly. The drillstring motion itself also affects the pressure loss significantly. The drillstring rotation, even for fairly small rotation rates, creates unstable flow and sometimes turbulence in the annulus even without axial flow. Transversal motion of the drillstring creates vortices that destabilize the flow. Consequently, the annular frictional pressure loss is increased even though the drilling fluid becomes thinner because of added shear rate. Naturally, the rheological properties of the drilling fluid play an important role. These rheological properties include more properties than the viscosity as measured by API procedures. It is impossible to use the same frictional pressure loss model for water based and oil based drilling fluids even if their viscosity profile is equal because of the different ways these fluids build viscosity. Water based drilling fluids are normally constructed as a polymer solution while the oil based are combinations of emulsions and dispersions. Furthermore, within both water based and oil based drilling fluids there are functional differences. These differences may be sufficiently large to require different models for two water based drilling fluids built with different types of polymers. In addition to these phenomena washouts and tool joints will create localised pressure losses. These localised pressure losses will again be coupled with the rheological properties of the drilling fluids. In this paper, all the above mentioned phenomena and their consequences for annular pressure losses will be discussed in detail. North Sea field data is used as an example. It is not straightforward to build general annular pressure loss models. This argument is based on flow stability analysis and the consequences of using drilling fluids with different rheological properties. These different rheological properties include shear dependent viscosity, elongational viscosity and other viscoelastic properties.

Time-Temperature-Pressure Superposition in Polymer Thickened Liquid Lubricants

Shear-dependent viscosities have been measured over a range of temperature and pressure for seven engine oils blended to have kinematic viscosity of 14 mm2/s at 100 °C with two base oils and four viscosity modifiers. Elevated pressure measurements were performed with a pressurized thin-film Couette viscometer and ambient pressure measurements were done with a PCS USV viscometer. These measurements were fitted to a generalized Newtonian model with the effective shear modulus specified by an empirical power-law shifting rule. The use of PAO-40 as a thickener delayed the shear-thinning to very high stress as compared with the polymers. The rate sensitivity of the oils thickened with nondispersant polymers was similar. Like the Tannas TBS viscometer, the PCS Instruments USV viscometer provides shear-dependent viscosity measurements, which can be essential for the most accurate time-temperature-pressure shifting. Viscosities measured at high viscous power in the ambient pressure viscometer, however, tend to be influenced by thermal softening and at high stress by shear cavitation.

The effect of a variable plastic viscosity on the restart problem of pipelines filled with gelled waxy crude oils

The effect of a variable plastic viscosity is numerically investigated on the success of the restart operation for a pipeline filled with fully-gelled waxy crude oil. To investigate the separate effects of structure- and shear-dependent viscosity, waxy crude oil is assumed to obey the Houska rheological model. In order to precisely capture the shape and position of the yielding surface, a variational approach is used to formulate the restart problem for this particular fluid model. The numerical results show that a variable plastic viscosity has a significant effect on the restart operation. For certain set of parameters the restart operation is shown to fail if the plastic viscosity is constant but is successful if the plastic viscosity is (moderately) structure-dependent. However, the time needed by the liquefied gel to discharge from the pipe outlet section is increased if the plastic viscosity is structure-dependent. Surprisingly, the shear-thinning behavior of waxy crude oil is predicted to lower the (steady) flow rate even when the restart is successful.

On the optimal control of a class of non-Newtonian fluids

We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of viscosity functions including shear-thinning and shear-thickening behavior. We prove an existence result for such class of optimal control problems.

Axial drive to nonlinear flow between rotating cylinders

Stability of pseudoplastic rotational flow between cylinders in presence of an independent axial component is investigated. The fluid is assumed to follow the Carreau model and mixed boundary conditions are imposed. The conservation of mass and momentum equations give rise to a four-dimensional low-order dynamical system, including additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. In absence of the axial flow, as the pseudoplasticity effects increases, the purely-azimuthal base flow loses its stability to the vortex structure at a lower critical Taylor number. Emergence of the vortices corresponds to the onset of a supercritical bifurcation also present in the flow of a linear fluid. However, unlike the Newtonian case, pseudoplastic Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow induced by a pressure gradient appears to further advance each critical point on the bifurcation diagram. In continuation, complete flow field together with viscosity maps is analyzed for different flow scenarios. Through evaluation of the Lyapunov exponent, flow stability and temporal behavior of the system for cases with and without axial flow are brought to attention.

Regularity of Non-Newtonian Fluids

In this paper, we consider a non-Newtonian fluids with shear dependent viscosity in a bounded domain \({\Omega \subset \mathbb{R}^n, n = 2, 3}\) . For the power-law model with the viscosity as in (1.4), we show the global in time existence of a weak solution for \({q \geq \frac{11}{5}}\) when n = 3 (see Theorem 1.1), and the local in time existence of a weak solution for \({2 > q > \frac{3n}{n+2}}\) , when n = 2,3 (see Theorem 1.2).

Temperature evolution of the shear viscosity in a unitary Fermi gas

We present an ab initio determination of the shear viscosity for the unitary Fermi gas based on finite temperature quantum Monte Carlo (QMC) calculations and the Kubo linear-response formalism. The results are confronted with the bound for the shear viscosity originating from hydrodynamic fluctuations. Assuming smoothness of the frequency dependent shear viscosity $\ensuremath{\eta}(\ensuremath{\omega})$, we show that the bound is violated in the low temperature regime and the violation occurs simultaneously with the onset of the Cooper pairing in the system. In order to preserve the hydrodynamic bound in QMC $\ensuremath{\eta}(\ensuremath{\omega})$ has to possess a sharp structure located in the vicinity of zero frequency which is not resolved by an analytic continuation procedure.