Newtonian Regime Research Articles

Athermal analogue of sheared dense Brownian suspensions

The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low-shear-rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time scale, both related to the normal confining pressure. This pressure-controlled approach, originally developed for granular flows, reveals a striking physical analogy between the colloidal glass transition and granular jamming.

Shear-free condition and dynamical instability in f(R, T) gravity

The implications of the shear-free condition on the instability range of an anisotropic fluid in f(R, T) are studied in this manuscript. A viable f(R, T) model is chosen to arrive at stability criterion, where R is Ricci scalar and T is the trace of energy-momentum tensor. The evolution of a spherical star is explored by employing a perturbation scheme on the modified field equations and contracted Bianchi identities in f(R, T). The effect of the imposed shear-free condition on the collapse equation and adiabatic index $$\Gamma $$ is studied in the Newtonian and post-Newtonian regimes.

F(R) gravity on non-linear scales: the post-Friedmann expansion and the vector potential

Many modified gravity theories are under consideration in cosmology as the source of the accelerated expansion of the universe and linear perturbation theory, valid on the largest scales, has been examined in many of these models. However, smaller non-linear scales offer a richer phenomenology with which to constrain modified gravity theories. Here, we consider the Hu-Sawicki form of f(R) gravity and apply the post-Friedmann approach to derive the leading order equations for non-linear scales, i.e. the equations valid in the Newtonian-like regime. We reproduce the standard equations for the scalar field, gravitational slip and the modified Poisson equation in a coherent framework. In addition, we derive the equation for the leading order correction to the Newtonian regime, the vector potential. We measure this vector potential from f(R) N-body simulations at redshift zero and one, for two values of the fR0 parameter. We find that the vector potential at redshift zero in f(R) gravity can be close to 50% larger than in GR on small scales for |fR0|=1.289 × 10−5, although this is less for larger scales, earlier times and smaller values of the fR0 parameter. Similarly to in GR, the small amplitude of this vector potential suggests that the Newtonian approximation is highly accurate for f(R) gravity, and also that the non-linear cosmological behaviour of f(R) gravity can be completely described by just the scalar potentials and the f(R) field.

Wall slip of polydisperse linear polymers using double reptation

The slip behavior of several high-density polyethylenes (HDPEs) is studied as a function of molecular weight (MW) and its distribution for a broad range of MW distributions. The slip velocity increases with decrease of MW, which is the case for several other linear polymers including monodisperse polybutadienes (PBDs), polystyrenes (PSs), and polylactides reported in the literature. For such polymers, the slip velocity, Vs, scales with weight or number average MW (due to monodispersity) as VS∝Mwβ, where β is about −2 for PBDs and −3.2 for PSs. For polydisperse HDPEs concepts from double reptation theory is used to develop an expression to relate slip velocity with MW and its distribution. Moreover, the slip velocity of linear polymers scales nonlinearly with the wall shear stress, namely, VS∝σWm. Using de Gennes' theory for slip, the values of m reported in the literature are explained on a theoretical basis and they are found to be equal to 1/n, where n is the local slope of the flow curve of the corresponding polymer, n≡ log(σw)/ log(γ̇w), which changes from 1 (Newtonian flow regime) to a constant value in the power-law flow regime.

Stress and strain amplification in a dilute suspension of spherical particles based on a Bird–Carreau model

A numerical study of a dilute suspension based on a non-Newtonian matrix fluid and rigid spherical particles was performed. In particular, an elongational flow of a Bird–Carreau fluid around a sphere was simulated and numerical homogenization has been used to obtain the effective viscosity of the dilute suspension ηhom for different applied rates of deformation and different thinning exponents. In the Newtonian regime the well-known Einstein result for the viscosity of dilute suspension is obtained: ηhom=(1+[η]φ)η with the intrinsic viscosity [η]=2.5. Here φ is the volume fraction of particles and η is the viscosity of the matrix fluid. However in the transition region from Newtonian to non-Newtonian behavior lower values of the intrinsic viscosity [η] are obtained, which depend on both the applied rate of deformation and the thinning exponent. In the power-law regime of the Bird–Carreau model, i.e. at high deformation rates, it is found that the intrinsic viscosity [η] depends only on the thinning exponent. Utilizing the simulation results a modification of the Bird–Carreau model for dilute suspensions with a non-Newtonian matrix fluid is proposed.

The universe dominated by the extended Chaplygin gas

In this paper, we consider a universe dominated by the extended Chaplygin gas which was recently proposed as the last version of Chaplygin gas models. Here, we only consider the second-order term which recovers quadratic barotropic fluid equation of state. The density perturbations are analyzed in both relativistic and Newtonian regimes and show that the model is stable without any phase transition and critical point. We confirmed stability of the model using thermodynamics point of view.

Cosmological variation of the MOND constant: Secular effects on galactic systems

The proximity of the MOND acceleration constant with cosmological accelerations -- for example, a0 cH0/2pi -- points to its possibly decreasing with cosmic time. I begin to consider the secular changes induced in galactic systems by such presumed variations, assumed adiabatic. It is important to understand these effects, in isolation from other evolutionary influences, in order to identify or constrain a0 variations by detection of induced effects, or lack thereof. I find that as long as the system is fully in the deep-MOND regime -- as applies to many galactic systems -- the adiabatic response of the system obeys simple scaling laws. For example, in a system that would be stationary for fixed a0, the system expands homologously as a0^{-1/4}, while internal velocities decrease uniformly as a0^{1/4}. If a0 is proportional to cH at all relevant times, this change amounts to a factor of ~ 2.5 since redshift 10. For a system stationary in a rotating frame, the angular frequency decreases as a0^{1/2}. The accelerations increase relative to a0 as a0^{-1/4}, pushing the system towards the Newtonian regime. All this follows from the appearance of a0 in MOND and the scale invariance of the deep-MOND limit -- two basic tenets of MOND. More complicated evolution ensues when parts of the system become Newtonian, or are so from inception. For example, these parts may become unstable, not being protected by MOND's stabilizing effects. The existence of such regions also modifies the MONDian regime, since they affect the potential everywhere, and since constituents might migrate between the Newtonian and MONDian regimes. Studying these last effects would require detailed numerical calculations.

CFD simulation for secondary breakup of coal–water slurry drops using OpenFOAM

The main objective of this study is to gain insight into dynamic behavior of coal–water slurry (CWS) drops during secondary breakup. In the case of Bingham liquids (CWS) considered here, this endeavor requires a thorough understanding of the influence of the shear-thinning and viscoplastic fluid rheology on the flow inside the deforming drops. In numerical analysis, a coupled technique including Large Eddy Simulation (LES) and smoothed volume of fluid (VOF) was used with a dynamic adaptive mesh. The effects of variations in secondary breakup and viscoplastic liquid rheological parameters on Sauter mean diameter (SMD), droplet aspect ratio, and dynamic average viscosity were studied in detail. The results show good predictions for the breakup regimes. Moreover, an effective constant viscosity leading to a similar Newtonian breakup regime was detected in all cases. According to the analogy between secondary and primary breakups, the results can be used to better understand the CWS jet breakup.

Dynamical Instability of Expansion-Free Collapse in f(T) Gravity

In this paper, we analyze the dynamical instability of a spherically symmetric collapsing star in the context of f(T) gravity. For this purpose, we assume power-law f(T) model with non-dissipative anisotropic fluid distribution under expansion-free condition. The perturbation scheme is applied to all matter, metric and f(T) functions. We formulate dynamical equations using contracted Bianchi identities to investigate dynamical instability ranges in Newtonian and post-Newtonian regimes. It is found that the instability ranges of expansion-free fluid are independent of adiabatic index but depend on radial density profile, anisotropic pressure and torsion terms.

Nonlocal General Relativity

A brief account of the present status of the recent nonlocal generalization of Einstein’s theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenböck’s torsion and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline–Kuhn approach to modified gravity. To account for the observational data regarding dark matter, nonlocality is associated with a characteristic length scale of order 1 kpc. The confrontation of nonlocal gravity with observation is briefly discussed.

Viscoelasticity of vibrated granular suspensions

We propose, in this paper, a model for predicting the rheological response of both vibrated and sheared 3D granular suspensions in stationary and nonstationary conditions. The major assumption of this model is the inherent bimodal behavior of chain forces in granular packings. The model is set up from a kinetic equation describing the dynamic exchange between a population of strongly correlated caged particles and a population of slightly correlated free particles. To compare the predictions of the model to experimental results, the kinetic equation is transformed into a differential constitutive equation, relating stress to strain, by including the effect of the interstitial fluid on the suspension. With only four adjustable parameters intrinsic to the system (i.e., independent of the type of rheological test used), the model is in very close agreement with experiments. Despite the fact that our approach remains at a mean-field level, it is able to predict and describe several rheological behaviors, in stationary, nonstationary conditions, linear and nonlinear regimes, including Newtonian and frictional Coulombian regimes, as well as elastic Hookean and viscoelastic Maxwellian behaviors. It then appears that this two-state approach allows capturing both the viscoelastic behavior of dry granular materials and granular suspensions. Vibrated dense suspensions and granular media are thus unified under a common framework.

Relativistic MOND from modified energetics

We begin to investigate the question of what modifications in energy-momentum tensor can yield correct MOND regime. As a starting study, we refrain from insisting on an action principle and focus exclusively on the equations of motion. The present work, despite the absence of an explicit action functional, can be regarded to extend Milgrom's modified inertia approach to relativistic domain. Our results show that a proper MOND limit arises if energy-momentum tensor is modified to involve determinant of the metric tensor in reference to the flat metric, where the latter is dynamically generated as in gravitational Higgs mechanism. This modified energy-momentum tensor is conserved in both Newtonian and MONDian regimes.

Scaffold Structures by Telechelic Rodlike Polymers: Nonequilibrium Structural and Rheological Properties under Shear Flow

The nonequilibrium structural and rheological properties of suspension of rodlike polymers with attractive ends are investigated by mesoscale hydrodynamic simulations. The hybrid simulation approach combines the multiparticle collision dynamics method for the fluid with molecular dynamics simulations for the polymers. In equilibrium, the rodlike polymers self-organize into scaffold-like network structures above a critical density and attraction strength. Shear flow induces significant structural changes. We identify three major regimes. At low Weissenberg numbers, the scaffold structure is compactified accompanied by a phase separation into a fluid domain and a dense scaffold-like structure. The shear viscosity shows a Newtonian plateau, which is determined by the fluid layer. At intermediated shear rates, shear bands appear with bundles of polymers. Again, we observe a nearly Newtonian viscosity regime governed by the fluid bands. At high shear rates, any structure is dissolved and a paranematic phase appears, with rods well aligned with the flow, and shear thinning appears.

Stability of spherical star in Brans–Dicke gravity

This paper explores dynamical instability of a spherically symmetric anisotropic collapsing model in the context of Brans–Dicke gravity. For this purpose, we develop two dynamical equations using contracted Bianchi identities and apply perturbation approach to Brans–Dicke as well as dynamical equations to obtain collapse equation. We use equation of state involving adiabatic index (Γ) along with collapse equation to study the instability ranges in both Newtonian and post-Newtonian regimes that depend on the structural variables of collapsing star. Finally, we construct some constraints on the positivity of physical variables and conclude that 0 1 leads to instability only for one special case.

Galaxy clusters in presence of dark energy: a kinetic approach

Context. The external regions of galaxy clusters may be under strong influence of the dark energy, discovered by observations of the SN Ia at redshift z < 1. Aims. The presence of the dark energy in the gravitational equilibrium equation, with the Einstein $\Lambda$ term, contrasts the gravity, making the equilibrium configuration more extended in radius. Methods. In this paper we derive and solve the kinetic equation for an equilibrium configuration in presence of the dark energy, by considering the Newtonian regime, being the observed velocities of the galaxies inside a cluster largely smaller than the light velocity. Results. The presence of the dark energy in the gravitational equilibrium equation leads to wide regions in the $W_0-\rho_{\Lambda}$ diagram where the equilibrium solutions are not permitted, due to the prevalence of the effects of the dark energy on the gravity.

Rheology of powders and nanopowders through the use of a Couette four-bladed vane rheometer: flowability, cohesion energy, agglomerates and dustiness

A new four-bladed vane powder rheometer is proposed to study powder and nanopowder rheology at low and high shear rates. As shear rates increase, the powder flow will evolve from a Newtonian regime (low shear rates) to a Coulombic regime (moderate shear rates) and then to a kinetic regime (high shear rates) at which the powder may become self-fluidized because of intense particles collisions. Viscosity measurements of noncohesive glass beads at low shear rates (Newtonian and Coulombic regimes) do not strongly depend upon the particle size and can reach values much larger than commonly used viscosities in some CFDs models. Since, in the kinetic regime, the shear stress is a strong function of the particle size, agglomerate particle size of cohesive powders can be directly inferred from rheograms. Cohesive carbon black and silica nanopowders have been tested and compared to noncohesive glass beads microparticles, chosen as reference. For noncohesive glass bead micropowders, the “agglomerate” diameter average values found from rheological measurements are of the same order of magnitude as the primary diameters of the powder. This indicates that the kinetic theory of granular flows describes well these high shear rate regimes and that such theory can be used to estimate agglomerate diameters. It is also found that estimated agglomerate sizes of nanometric cohesive materials can reach sizes of hundred micrometers depending upon their cohesion strength. Such agglomerate size measurements have been corroborated with those made by microscopy.

Stability of a class of non-static axial self-gravitating systems in f(R) gravity

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider $f(R)=R+{\epsilon}R^2$ model and assume hydrostatic equilibrium of the axial self-gravitating system at large past time. Considering perturbation from hydrostatic phase, we develop dynamical as well as collapse equations and explore dynamical instabilities at Newtonian and post-Newtonian regimes. It is concluded with the help of stiffness parameter, $\Gamma_1$, that radial profile of physical parameters like pressure anisotropy, energy density and higher curvature terms of the $f(R)$ model affect the instability ranges.

Rheology near jamming: The influence of lubrication forces

We study, by computer simulations, the roles of different dissipation forces in the rheological properties of highly dense particle-laden flows. In particular, we are interested in the close-packing limit (jamming) and the question of whether "universal" observables can be identified that do not depend on the details of the dissipation model. To this end, we define a simplified lubrication force and systematically vary the range h(c) of this interaction. For fixed h(c) a crossover is seen from a Newtonian flow regime at small strain rates to inertia-dominated flow at larger strain rates. The same crossover is observed as a function of the lubrication range h(c). At the same time, but only at high densities close to jamming, single-particle velocities as well as local density distributions are unaffected by changes in the lubrication range--they are candidates for universal behavior. At densities away from jamming, this invariance is lost: short-range lubrication forces lead to pronounced particle clustering, while longer-ranged lubrication does not. These findings highlight the importance of "geometric" packing constraints for particle motion--independent of the specific dissipation model. With the free volume vanishing at random close packing, particle motion is more and more constrained by the ever smaller amount of free space. On the other hand, macroscopic rheological observables as well as higher-order correlation functions retain the variability of the underlying dissipation model.

Observational tests of nonlocal gravity: Galaxy rotation curves and clusters of galaxies

A classical nonlocal generalization of Einstein's theory of gravitation has recently been developed via the introduction of a scalar causal "constitutive" kernel that must ultimately be determined from observational data. It turns out that the nonlocal aspect of gravity in this theory can simulate dark matter; indeed, in the Newtonian regime of nonlocal gravity, we recover the phenomenological Tohline-Kuhn approach to modified gravity. A simple generalization of the Kuhn kernel in the context of nonlocal general relativity leads to a two-parameter modified Newtonian force law that involves an additional repulsive Yukawa-type interaction. We determine the parameters of our nonlocal kernel by comparing the predictions of the theory with observational data regarding the rotation curves of spiral galaxies. The best-fitting stellar mass-to-light ratio turns out to be in agreement with astrophysical models; moreover, our results are consistent with the Tully-Fisher relation for spiral galaxies. Light deflection in nonlocal gravity is consistent with general relativity at Solar System scales, while beyond galactic scales an enhanced deflection angle is predicted that is compatible with lensing by the effective "dark matter". Furthermore, we extend our results to the internal dynamics of rich clusters of galaxies and show that the dynamical mass of the cluster obtained from nonlocal gravity is consistent with the measured baryonic mass.

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.