Newtonian Counterparts Research Articles

Measurements of the Low-acceleration Gravitational Anomaly from the Normalized Velocity Profile of Gaia Wide Binary Stars and Statistical Testing of Newtonian and Milgromian Theories

Low-acceleration gravitational anomaly is investigated with a new method of exploiting the normalized velocity profile v˜≡vp/vc of wide binary stars as a function of the normalized sky-projected radius s/r M, where v p is the sky-projected relative velocity between the pair, v c is the Newtonian circular velocity at the sky-projected separation s, and r M is the MOND radius. With a Monte Carlo method, Gaia observed binaries and their virtual Newtonian counterparts are probabilistically distributed on the s/r M versus v˜ plane, and a logarithmic velocity ratio parameter Γ is measured in the bins of s/r M. With three samples of binaries covering a broad range in size, data quality, and implied fraction of hierarchical systems including a new sample of 6389 binaries selected with accurate distances and radial velocities, I find a unanimous systematic variation from the Newtonian flat line. With Γ = 0 at s/r M ≲ 0.15 or s ≲ 1 kau, I get Γ = 0.068 ± 0.015 (stat) −0.015+0.024 (syst) for s/r M ≳ 0.7 or s ≳ 5 kau. The gravitational anomaly (i.e., acceleration boost) factor given by γ g = 102Γ is measured to be γg=1.37−0.09+0.10 (stat) −0.09+0.16 (syst). With a reduced χ 2 test of Newtonian and Milgromian nonrelativistic theories, I find that Newtonian gravity is ruled out at 5.8σ ( χν2=9.4 ) by the new sample (and 9.2σ by the largest sample used). The Milgromian AQUAL theory is acceptable with 0.7≲χν2≲3.1 . These results agree well with earlier results with the “acceleration-plane analysis” for a variety of samples and the “stacked velocity profile analysis” for a pure binary sample.

A comprehensive model for viscoplastic flows in channels with a patterned wall: longitudinal, transverse and oblique flows

We develop a comprehensive model for the creeping Poiseuille Bingham flow in channels equipped with a patterned wall, i.e. decorated with grooves or stripes that may represent a superhydrophobic (SH) or a chemically patterned (CP) surface, respectively, with longitudinal, transverse and oblique groove (stripe) orientations with respect to the applied pressure gradient. We rely on the Navier slip law to model the boundary condition on the slippery grooves. We develop semi-analytical, explicit-form and complementary computational fluid dynamics models, with solutions that have reasonable agreement. In contrast to its Newtonian analogue, a distinct solution for the oblique configuration, with an a priori unknown transform matrix, must be developed due to the viscoplastic nonlinear rheology. Our focus is to systematically analyse the effects of the Bingham number ( $B$ ), slip number ( $b$ ), groove periodicity length ( $\ell$ ), slip area fraction ( $\varphi$ ) and groove orientation angle ( $\theta$ ), on the slip velocities, effective slip length ( $\chi$ ), slip angle difference ( $\theta -s$ ), mixing index ( $I_M$ ), flow anisotropy and flow regimes. In particular, we demonstrate that, as $B$ increases, the maximum values of the shear component of $\chi$ , $\theta -s$ and $I_M$ occur progressively at smaller values of $\theta$ , compared with their Newtonian counterparts.

Wall-modeled large-eddy simulation of turbulent non-Newtonian power-law fluid flows

For high-fidelity predictions of turbulent flows in complex practical engineering problems, the Wall-Modeled (WM) Large-Eddy Simulation (LES) has aroused great interest. In the present study, we prove that the conventional Wall-Stress Models (WSMs) developed for WMLES of Newtonian fluids fail to predict the shear-thinning-induced drag reduction in power-law fluids. Therefore, we propose novel algebraic, integrated, and Ordinary-Differential-Equation (ODE) WSMs, for the first time, for WMLES of power-law Non-Newtonian (NN) fluids and assess their performance against reference Wall-Resolved (WR) LES solutions. In addition, the effects of the key model parameters, including the WSM type, sampling height, sampling cell, and axial grid resolution are explored, and it is revealed that turbulent NN flow predictions have a much higher sensitivity to the choice of WSM, compared to their Newtonian counterparts. It is manifested that, in contrast to WRLES, accurate modeling of the mean apparent and subgrid-scale NN viscosities in the Non-Newtonian ODE (NNODE) model can improve the predictions considerably. Therefore, closures with lower uncertainties on coarse WMLES grids are sought for these terms. Finally, the best performance for the present test cases is obtained via the integrated NN WSM, sampling at the lower edge of the log layer within the third off-the-wall grid cell. Nevertheless, the new NNODE WSM can have an advantage in the presence of non-equilibrium effects in more complex problems.

Dynamic crushing performance of bio-inspired sandwich structures with beetle forewing cores

A novel design of Sandwich Structure inspired by Beetle Forewing (SSBF) is proposed in this study by mimicking the internal structure of beetle forewing. The viscoelastic material and the arch shape of hollow cavity structures found inside the forewing structure of the beetle are imitated by utilising the shear thickening fluid (STF) and semi-arch cores, respectively. The coupling interaction between fluid and structural components is analysed using a fluid-structure interaction (FSI) technique in LS-DYNA. It is found that the proposed SSBF by partially filling the core with STF generates a higher mean crushing force and stabilises the crushing force-displacement profile without a noticeably high initial peak crushing force as compared with the empty, polyurethane (PU) foam-filled, or Newtonian viscous fluid-filled counterparts. Furthermore, this stable crushing force of SSBF enhances with the increase of crushing speed, showing ideal behaviour for energy absorption and crushing resistance for the adaptation to the design of structures to resist impact loads.

Hydrodynamics of electro-capillarity propelled non-Newtonian droplets through micro-confinements.

In this article, we theoretically explore the dynamics of droplet motion and its evolution during electro-capillarity propelled actuation within microfluidic systems. The study covers a wide gamut of fluids, wherein we investigate the dynamics of both pseudoplastic and dilatant fluid droplets. It is observed that change in the fluid rheology of the non-Newtonian fluids leads to significant morphing of the droplet dynamics during the actuation and propulsion event when compared to the Newtonian counterparts. We validate the theory using experimental reports on similar systems employing Newtonian droplets. The influence of governing parameters such as the actuation voltage and its transients, dielectric layer thickness on the electrodes and electrode spacing is probed. We also explore the influence of the interfacial properties of the system, such as channel wall friction, droplet wettability, and capillary friction, and establish that the fluid rheology, in conjunction with the interfacial features regulate the electro-actuation and propulsion of the droplets. We further provide theoretical estimates on the optimal design of the electro-actuation system in terms of a proposed electro-interfacial tension parameter. The findings may hold significance towards design and development of microfluidics with electro-actuation systems.Graphical Supplementary InformationThe online version contains supplementary material available at 10.1140/epje/s10189-022-00196-0.

Direct numerical simulation of inertio-elastic turbulent Taylor–Couette flow

The flow physics of inertio-elastic turbulent Taylor–Couette flow for a radius ratio of $0.5$ in the Reynolds number ( $Re$ ) range of $500$ to $8000$ is investigated via direct numerical simulation. It is shown that as $Re$ is increased the turbulence dynamics can be subdivided into two distinct regimes: (i) a low $Re \leqslant 1000$ regime where the flow physics is essentially dominated by nonlinear elastic forces and the main contribution to transport and mixing of momentum, stress and energy comes from large-scale flow structures in the bulk region and (ii) a high $Re \geqslant 5000$ regime where inertial forces govern the flow physics and the flow dynamics is mainly governed by small-scale flow structures in the near-wall region. Flow–microstructure coupling analysis reveals that the elastic Görtler instability in the near-wall region is triggered via significant polymer extension and commensurately high hoop stresses. This instability gives rise to small-scale elastic vortical structures identified as elastic Görtler vortices which are present at all $Re$ considered. In fact, these vortices develop herringbone streaks near the inner wall that have a longer average life span than their Newtonian counterparts due to their elastic origin. Examination of the budgets of mean streamwise enstrophy, mean kinetic energy, turbulent kinetic energy and Reynolds shear stress demonstrates that increasing fluid inertia hinders the generation of elastic stresses, leading to a monotonic reduction of the elastic-related effects on the flow physics.

Modelling vertical concentration distributions of solids suspended in turbulent visco-plastic fluid

Abstract Vertical concentration distributions of solids conveyed in Newtonian fluids can be modelled using Rouse-Schmidt type distributions. Observations of solids conveyed in turbulent low Reynolds number visco-plastic carriers, suggest that solids are more readily suspended than their Newtonian counterparts, producing higher concentrations in the centre of the pipe. A Newtonian concentration profile model was adapted to include typical turbulent viscosity distributions within the pipe and particle motion calculated using non-Newtonian sheared settling. Predictions from this and the unmodified model, using the same wall viscosity, are compared with the chord averaged profile extracted from tomographic data obtained using a 50 mm horizontal pipe.

High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation

Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of exponential gradients in polymeric stress fields, which can lead to catastrophic instabilities if not carefully handled. A key development to overcome this issue is the log-conformation formulation, which has been applied to a range of numerical methods, but not previously applied to Smoothed Particle Hydrodynamics (SPH). Here we present a 2D incompressible SPH algorithm for viscoelastic flows which, for the first time, incorporates a log-conformation formulation with an elasto-viscous stress splitting (EVSS) technique. The resulting scheme enables simulations of flows at high Weissenberg numbers (accurate up to Wi=85 for Poiseuille flow). The method is robust, and able to handle both internal and free-surface flows, and a range of linear and non-linear constitutive models. Several test cases are considerd included flow past a periodic array of cylinders and jet buckling. This presents a significant step change in capabilties compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.

Heating of liquid foods in cans: Effects of can geometry, orientation, and food rheology

AbstractIn this work, the effect of geometry and orientation of food cans on the heating characteristics of processed liquid foods and the resulting lethality target values as a function of the processing times have been investigated. For this purpose, the governing differential equations have been solved numerically for elliptical and cylindrical cans of varying aspect ratios in different orientations in order to delineate their effect on the heating rate (especially of the slowest heating zone [SHZ]) and lethality values over wide ranges of rheological features including shear thinning (n < 1), Newtonian (n = 1), and shear thickening (n > 1) behaviors. The flow and heat transfer characteristics were analyzed with the help of velocity vectors, isotherm contours, average Nusselt number, SHZ temperature and heat penetration parameters, and lethality target values. Also, comparisons were made in terms of the sterilization time and heat penetration parameters to identify the preferable geometries and orientations of food cans for effective heating of non‐Newtonian foodstuffs. Finally, favorable conditions in terms of the shape and orientation of the can and the rheological properties have been delineated which lead to superior heating characteristics.Practical ApplicationsProcessed foodstuffs are produced in various forms ranging from that in solid, liquid, or as heterogeneous mixtures. Often such liquid and heterogeneous suspensions products are viscous non‐Newtonian in character and their thermal processing (including pasteurization, sterilization, etc.) tends to be much more challenging than that of their Newtonian counterparts like air and water. This work explores heating of non‐Newtonian liquid foodstuffs in cans of various shapes, geometries and in different orientations in the free convection regime. The results show that depending upon the rheological properties of the products, some orientations and/or geometries offer potential advantages in terms of shorter processing times and lethality values. This information can be of great potential in customizing the design of containers for different food products as well as of different rheological properties.

Controllable droplet generation at a microfluidic T-junction using AC electric field

We investigated the influence of an alternate current (AC) electric field on droplet generation in a T-junction device. We used sodium chloride solution with various conductivities to adjust the response time of the fluidic system. At constant flow rates of both continuous and dispersed phases, the critical parameters for the droplet formation process are the magnitude, the frequency of the applied voltage and the conductivity of the dispersed phase. The response of the droplet formation process to AC excitation is characterised by the relative area of the formed droplet. The relative response time of the fluidic system to the applied AC voltage is characterised by the relative response time that is proportional to the ratio of the AC frequency to the conductivity of the dispersed phase. An accurate prediction of the breakdown voltage for the walls also proved robustness of our model. Furthermore, experiments were repeated with 0.5 g/L and 1 g/L xanthan gum solutions as non-Newtonian fluids. The results reveal the negligible influence of viscoelasticity on the droplet formation process. On-demand size controllable generation of non-Newtonian droplets is subsequently demonstrated following the same trend of the Newtonian counterparts.

New insights of foam flow dynamics in a high-complexity 2D micromodel

In this work, we present direct observation of foam flow through a 2D porous microfluidic device. Through a specially designed image processing workflow, we perform individual bubble tracking and establish flow dynamics within the micromodel structure. In addition to our experimental data, we provide 2D and 3D numerical Newtonian flow simulations on equivalent digitized versions of the model, carried out using Lattice Boltzmann simulation codes for comparison. The results show that foam flow in our experimental conditions, low gas fraction and high injection velocity, demonstrate a high degree of similarity to the flow of a Newtonian fluid in both 2D and 3D simulations, in aspects of large-scale flow distribution homogeneity and specific flow passage activation. However, the foam data shows a larger spread of pore-scale flow velocities, spanning from blocked off areas of quasi-zero flow, to zones of high velocity, with velocities well above the Newtonian counterparts. For our model depth and characteristics, the 2D simulation demonstrates slightly more flow heterogeneity and is closer to the foam case. Detailed bubble tracking gives access to other characteristics of the foam flow inside the medium such as the dichotomy between the flow patterns of the smallest bubbles, typically dispersing and accessing most regions available, and the largest bubbles, which travel in long straight preferential paths exclusively. We show that intrinsically tied to these different flow patterns is the relationship between bubble velocity and bubble size, as we demonstrate distinct populations of trapped and flowing bubbles with distinct sizes. Finally, we explore the relationships between microstructural parameters and flow intensity and note a weak correlation to local structural parameters. Our study, which combines high spatial and time resolution, small network dimensions, high network complexity and efficient bubble tracking, therefore sheds new light on the study of foam flow in porous media.

Temporal analysis of breakup for a power law liquid jet in a swirling gas

The breakup mechanism and instability of a power law liquid jet are investigated in this study. The power law model is used to account for the non-Newtonian behavior of the liquid fluid. A new theoretical model is established to explain the breakup of a power law liquid jet with axisymmetric and asymmetric disturbances, which moves in a swirling gas. The corresponding dispersion relation is derived by a linear approximation, and it is applicable for both shear-thinning and shear-thickening liquid jets. Analysis results are calculated based on the temporal mode. The analysis includes the effects of the generalized Reynolds number, the Weber number, the power law exponent, and the air swirl strength on the breakup of the jet. Results show that the shear-thickening liquid jet is more unstable than its Newtonian and shear-thinning counterparts when the effect of the air swirl is taken into account. The axisymmetric mode can be the dominant mode on the power law jet breakup when the air swirl strength is strong enough, while the non-axisymmetric mode is the domination on the instability of the power liquid jet with a high We and a low Re n . It is also found that the air swirl is a stabilizing factor on the breakup of the power law liquid jet. Furthermore, the instability characteristics are different for different power law exponents. The amplitude of the power law liquid jet surface on the temporal mode is also discussed under different air swirl strengths.

Center of mass and spin for isolated sources of gravitational radiation

We define the center of mass and spin of an isolated system in general relativity. The resulting relationships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their Newtonian counterparts, though only variables at the null boundary of an asymptotically flat spacetime are used for their definition. We also derive equations of motion linking their time evolution to the emitted gravitational radiation. The results are then compared to other approaches. In particular, one obtains unexpected similarities as well as some differences with results obtained in the post-Newtonian literature. These equations of motion should be useful when describing the radiation emitted by compact sources, such as coalescing binaries capable of producing gravitational kicks, supernovas, or scattering of compact objects.

Effectively universal behavior of rotating neutron stars in general relativity makes them even simpler than their Newtonian counterparts.

Recently, it was shown that slowly rotating neutron stars exhibit an interesting correlation between their moment of inertia I, their quadrupole moment Q, and their tidal deformation Love number λ (the I-Love-Q relations), independently of the equation of state of the compact object. In the present Letter a similar, more general, universality is shown to hold true for all rotating neutron stars within general relativity; the first four multipole moments of the neutron star are related in a way independent of the nuclear matter equation of state we assume. By exploiting this relation, we can describe quite accurately the geometry around a neutron star with fewer parameters, even if we don't know precisely the equation of state. Furthermore, this universal behavior displayed by neutron stars could promote them to a more promising class of candidates (next to black holes) for testing theories of gravity.

The Poisson equation at second order in relativistic cosmology

We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field.

Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by direct numerical simulations

Direct numerical simulations (DNS) were performed for the forced homogeneous isotropic turbulence (FHIT) with/without polymer additives in order to elaborate the characteristics of the turbulent energy cascading influenced by drag-reducing effects. The finite elastic non-linear extensibility-Peterlin model (FENE-P) was used as the conformation tensor equation for the viscoelastic polymer solution. Detailed analyses of DNS data were carried out in this paper for the turbulence scaling law and the topological dynamics of FHIT as well as the important turbulent parameters, including turbulent kinetic energy spectra, enstrophy and strain, velocity structure function, small-scale intermittency, etc. A natural and straightforward definition for the drag reduction rate was also proposed for the drag-reducing FHIT based on the decrease degree of the turbulent kinetic energy. It was found that the turbulent energy cascading in the FHIT was greatly modified by the drag-reducing polymer additives. The enstrophy and the strain fields in the FHIT of the polymer solution were remarkably weakened as compared with their Newtonian counterparts. The small-scale vortices and the small-scale intermittency were all inhibited by the viscoelastic effects in the FHIT of the polymer solution. However, the scaling law in a fashion of extended self-similarity for the FHIT of the polymer solution, within the presently simulated range of Weissenberg numbers, had no distinct differences compared with that of the Newtonian fluid case.

Dispensing of rheologically complex fluids: The map of misery

AbstractRheological effects may complicate the dispensing of complex fluids, when compared to their Newtonian counterparts. In this work, fluids with tailored rheological properties have been studied using high‐speed video‐microscopy. The level of viscosity, the degree of shear thinning, and the elasticity have been varied independently. At low‐flow rates, droplets are formed that pinch off. The drop volumes, breakup mechanisms, and times have been identified. At higher‐flow rates, a continuous jet is observed, with the transition depending on the rheology of the dispensed fluid. The relevant nondimensional groups are the Ohnesorge, Deborah, and elasto‐capillary number, for when viscosity, inertia, or elastic forces dominate flow. In each of these cases, the transition between dripping and jetting dispensing occurs, controlled by a critical Weber, capillary, and Weissenberg number, respectively. This set of six nondimensional groups can be used to construct an operating space and map out areas of potential problems. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3242–3255, 2012

A weakly compressible flow model for the restart of thixotropic drilling fluids

This study presents a mathematical model to simulate the start-up flow of drilling fluids in drill pipes. The compressible transient flow approach is based on one-dimensional mass and momentum conservation equations, an equation of state and a thixotropic fluid model. In contrast with prior studies that view gel breaking as a visco-plastic phenomenon, thixotropy is approached as an elasto-visco-plastic problem. Such thixotropy model is fit to rheometer data with reasonable agreement. The start-up flow is then simulated, and the results are compared to Newtonian, Bingham and visco-plastic fluid flow models. It can be anticipated that the pressure overshoots observed in start-up flows depend not only on the thixotropy properties of the fluid but also on the flow compressibility and Reynolds number. In addition, the main differences between the visco-plastic and elasto-visco-plastic thixotropy approaches take place at low shear rates; the higher the shear rates, the more similar are the results. Finally, as expected, the pressure overshoots of the thixotropic fluids are not always larger than those of the Bingham and Newtonian counterparts.

Weakly nonlinear viscoplastic convection

The development of thermal convection is studied for a viscoplastic fluid. If the viscosity is finite at zero shear rate, the critical Rayleigh number for linear instability takes the value given by a Newtonian fluid with that viscosity. The subsequent weakly nonlinear behaviour depends on the degree of shear thinning: with moderate shear thinning, convective overturning for a given temperature difference is amplified relative to the Newtonian case. If the reduction in viscosity is sufficiently sharp the transition becomes subcritical (the relevant situation for many regularized constitutive laws). For an infinite viscosity at zero shear rate, or a yield-stress, the critical Rayleigh number for linear instability is infinite. Nonlinear convective overturning, however, is still possible; we trace out how the finite-amplitude solution branches develop from their Newtonian counterparts as the yield stress is increased from zero for the Bingham fluid. Laboratory experiments with a layer of Carbopol fluid heated from below confirm that yield strength inhibits convection but a sufficiently strong perturbation can initiate overturning.

Revisiting plane Couette–Poiseuille flows of a piezo-viscous fluid

We re-examine fully developed isothermal unidirectional plane Couette–Poiseuille flows of an incompressible fluid whose viscosity depends linearly on the pressure as previously considered in [J. Hron, J. Málek, K.R. Rajagopal, Simple flows of fluids with pressure-dependent viscosities, Proc. R. Soc. Lond. A 457 (2001) 1603–1622]. We show that the conclusion made there that, in contrast to Newtonian and power-law fluids, piezo-viscous fluids allow multiple solutions is not justified, and that the inflection velocity profiles reported in [J. Hron, J. Málek, K.R. Rajagopal, Simple flows of fluids with pressure-dependent viscosities, Proc. R. Soc. Lond. A 457 (2001) 1603–1622] cannot exist. Subsequently, we undertake a systematic parametric study of these flows and identify three distinct families of solutions which can exist in the considered geometry. One of these families has no similar counterpart for fluids with pressure-independent viscosity. We also show that the critical wall speed exists beyond which Poiseuille-type flows are impossible regardless of the magnitude of the applied pressure gradient. For smaller wall speeds channel choking occurs for Poiseuille-type flows at large pressure gradients. These features distinguish drastically piezo-viscous fluids from their Newtonian and power-law counterparts.