Newtonian Regime Research Articles

Establishing rheological models of lignin-based solutions via molecular parameters using machine learning

The rheological models of natural polymer-based solutions are difficult to be established because of the significant non-Newtonian behavior and highly discrete rheological data caused by different molecular parameters including the molecular weights and size of clusters. In this study, a typical natural polymer-lignin was selected and dissolved in polyethylene glycol (PEG) as the lignin-based solutions. The experimental rheological data of different PEG-lignin solutions were trained with machine learning. The rheological models were established considering the molecular parameters including the molecular weights and size of clusters. The models show a high accuracy in predicting the viscosities of different PEG-lignin solutions with the coefficient of determination over 0.9815, mean absolute error less than 0.0132, and average absolute relative deviation less than 6.95 % in both Newtonian and non-Newtonian regimes. The models and relevant methodology can provide scenarios for further application of natural polymer solutions in process industries.

Toward a covariant framework for post-Newtonian expansions for radiative sources

We consider the classic problem of a compact fluid source that behaves nonrelativistically and that radiates gravitational waves. The problem consists of determining the metric close to the source as well as far away from it. The nonrelativistic nature of the source leads to a separation of scales resulting in an overlap region where both the 1/c and (multipolar) G expansions are valid. Standard approaches to this problem (the Blanchet-Damour and the DIRE approach) use the harmonic gauge. We define a “post-Newtonian” class of gauges that admit a Newtonian regime in inertial coordinates. In this paper we set up a formalism to solve for the metric for any post-Newtonian gauge choice. Our methods are based on previous work on the covariant theory of nonrelativistic gravity (a 1/c expansion of general relativity that uses post-Newton-Cartan variables). At the order of interest in the 1/c and G expansions we split the variables into two sets: transverse and longitudinal. We show that for the transverse variables the problem can be reduced to inverting Laplacian and d’Alembertian operators on their respective domains subject to appropriate boundary conditions. The latter are regularity in the interior and asymptotic flatness with a Sommerfeld no-incoming radiation condition imposed at past null infinity. The longitudinal variables follow from the gauge choice. The full solution is then obtained by the method of matched asymptotic expansion. We show that our methods reproduce existing results in harmonic gauge to 2.5PN order. Published by the American Physical Society 2024

Testing MOND on Small Bodies in the Remote Solar System

Modified Newtonian dynamics (MOND), which postulates a breakdown of Newton's laws of gravity/dynamics below some critical acceleration threshold, can explain many otherwise puzzling observational phenomena on galactic scales. MOND competes with the hypothesis of dark matter, which successfully explains the cosmic microwave background and large-scale structure. Here we provide the first solar system test of MOND that probes the subcritical acceleration regime. Using the Bekenstein–Milgrom “aquadratic Lagrangian” (or AQUAL) formulation, we simulate the evolution of myriads of test particles (planetesimals or comets) born in the trans-Neptunian region and scattered by the giant planets over the lifetime of the Sun to heliocentric distances of 102–105 au. We include the effects of the Galactic tidal field and passing stars. While Newtonian simulations reproduce the distribution of binding energies of long-period and Oort-cloud comets detectable from Earth, MOND-based simulations do not. This conclusion is robust to plausible changes in the migration history of the planets, the migration history of the Sun, the MOND transition function, effects of the Sun's birth cluster, and the fading properties of long-period comets. For the most popular version of AQUAL, characterized by a gradual transition between the Newtonian and MOND regimes, our MOND-based simulations also fail to reproduce the orbital distribution of trans-Neptunian objects in the detached disk (perihelion q > 38 au). Our results do not rule out some MOND theories more elaborate than AQUAL, in which non-Newtonian effects are screened on small spatial scales, at small masses, or in external gravitational fields comparable in strength to the critical acceleration.

Effects of expansion-free condition on adiabatic collapse in [formula omitted] gravity

This study explores the impact of f(G,T) gravity, where G is the Gauss Bonnet invariant and T is the trace of the energy–momentum tensor, on the adiabatic anisotropic spherical gravitating source under the expansion-free condition. We coupled the relativistic matter with spherical symmetric structure by applying f(G,T)=αGn+λT Gauss–Bonnet model with a linear trace. To derive the collapse equation, we used the perturbation method on the field equations and the contracted Bianchi identities. The dynamics of instability range is depicted in Newtonian (N) and post-Newtonian (pN) regimes. Furthermore, instead of using the adiabatic index, we establish the instability range by looking at the density profile and anisotropic pressure configuration. We investigate the analytic solutions that meets the expansion-free condition. Finally, we have successfully achieved the original results obtained by Herrera et al. (2012) in General Relativity by setting α=λ=0 in proposed cosmological model.

On the tension between the radial acceleration relation and Solar system quadrupole in modified gravity MOND

ABSTRACT Modified Newtonian dynamics (MOND), postulating a breakdown of Newtonian mechanics at low accelerations, has considerable success at explaining galaxy kinematics. However, the quadrupole of the gravitational field of the Solar system (SS) provides a strong constraint on the way in which Newtonian gravity can be modified. In this paper, we assess the extent to which the AQUAdratic Lagrangian (AQUAL) and QUasilinear MOND (QUMOND) modified gravity formulations of MOND are capable of accounting simultaneously for the radial acceleration relation (RAR), the Cassini measurement of the SS quadrupole and the kinematics of wide binaries in the Solar neighbourhood. We achieve this by inferring the location and sharpness of the MOND transition from the Spitzer Photometry and Accurate Rotation Curves (SPARC) RAR under broad assumptions for the behaviour of the interpolating function and external field effect. We constrain the same quantities from the SS quadrupole, finding that this requires a significantly sharper transition between the deep-MOND and Newtonian regimes than is allowed by the RAR (an 8.7σ tension under fiducial model assumptions). This may be relieved somewhat by allowing additional freedom in galaxies’ mass-to-light ratios – which also improves the RAR fit – and more significantly (to 1.9σ) by removing galaxies with bulges. For the first time, we also apply to the SPARC RAR fit an AQUAL correction for flattened systems, obtaining similar results. Finally, we show that the SS quadrupole constraint implies, to high precision, no deviation from Newtonian gravity in nearby wide binaries, and speculate on possible resolutions of this tension between SS and galaxy data within the MOND paradigm.

A cosmic glitch in gravity

We investigate a model that modifies general relativity on cosmological scales, specifically by having a `glitch' in the gravitational constant between the cosmological (super-horizon) and Newtonian (sub-horizon) regimes, as motivated e.g. in the Hořava-Lifshitz proposal or in the Einstein-aether framework. This gives a single-parameter extension to the standard ΛCDM model, which is equivalent to adding a dark energy component, but where the energy density of this component can have either sign. Fitting to data from the Planck satellite, we find that negative contributions are, in fact, preferred. Additionally, we find that roughly one percent weaker superhorizon gravity can somewhat ease the Hubble and clustering tensions in a range of cosmological observations, although at the expense of spoiling fits to the baryonic acoustic oscillation scale in galaxy surveys. Therefore, the extra parametric freedom offered by our model deserves further exploration, and we discuss how future observations may elucidate this potential cosmic glitch in gravity, through a four-fold reduction in statistical uncertainties.

Order-disorder transition during shear thickening in bidisperse dense suspensions

Shear thickening of multimodal suspensions has proven difficult to understand because the rheology depends largely on the microscopic details of stress-induced frictional contacts at different particle size distributions (PSDs). Our discrete particle simulations below a critical volume fraction ϕc over a broad range of shear rates and PSDs elucidate the basic mechanism of order–disorder transition. Around the theoretical optimal PSD (relative content of small particles ζ1= 0.26), particles order into a layered structure in the Newtonian regime. At the onset of shear thickening, this layered structure transforms to a disordered one, accompanied by an abrupt viscosity jump. Minor increase in large-large particle contacts after the order–disorder transition causes apparent increase in radial force along the compressional axis. Bidisperse suspensions with less regular but stable layered structure at ζ1= 0.50 show good fluidity in the shear thickening regime. This work shows that in inertial flows where particle collisions dominate, order–disorder transition could play an essential role in shear thickening for bidisperse suspensions.

Geometric Origin of the Galaxies’ Dark Side

We show that Einstein’s conformal gravity can explain, simply, and on the geometric ground, galactic rotation curves, without the need to introduce any modification in both the gravitational as well as in the matter sector of the theory. The geometry of each galaxy is described by a metric obtained, making a singular rescaling of Schwarzschild’s spacetime. The new exact solution, asymptotically anti-de Sitter, manifests an unattainable singularity at infinity that cannot be reached in finite proper time; namely, the spacetime is geodetically complete. It deserves to be noticed that, in this paper, we have a different opinion from the usual one. Indeed, instead of making the metric singularity-free, we make it apparently but harmlessly even more singular than Schwarzschild’s. Finally, it is crucial to point out that Weyl’s conformal symmetry is spontaneously broken into the new singular vacuum rather than the asymptotically flat Schwarzschild’s one. The metric is unique according to the null energy condition, the zero acceleration for photons in the Newtonian regime, and the homogeneity of the Universe at large scales. Once the matter is conformally coupled to gravity, the orbital velocity for a probe star in the galaxy turns out to be asymptotically constant consistent with the observations and the Tully–Fisher relation. Therefore, we compare our model with a sample of 175 galaxies and show that our velocity profile very well interpolates the galactic rotation curves after a proper choice of the only free parameter in the metric. The mass-to-luminosity ratios of galaxies turn out to be close to 1, consistent with the absence of dark matter.

On the nonlocal Newtonian cosmology

In the absence of an exact development of the cosmological models based on the Mashhoon nonlocal gravity, the Newtonian regime clarifies some aspects of it. To improve this model more reliable, going through some semi-Post-Newtonian considerations may be useful. One important feature to consider is the formation of horizons, which can be understood as a consequence of the finite interaction velocity. This highlights the importance of extending the integration across the entire space–time, rather than solely focusing on the spatial sector. In this context, we show that the density of effective dark matter would increase, while the density of Baryonic matter decreases, during the deep matter-dominated era. This finding is in contradiction with the predictions of the standard model of cosmology and it raises concerns about the compatibility of using Tohline–Kuhn kernel and considering the nonlocal effects as an effective dark matter in ΛCDM.

Impact of Xanthan Gum on Stability and Rheological Properties of Multiple Emulsions Type Water-in-Oil-in-Water

The aim of this study was to improve the stability and rheological properties of water-in-oil-in-water (W/O/W) multiple emulsions containing 30 wt% paraffin oil, and 4 wt% polyglycerol-3-polycinoleate (PGPR) as a lipophilic surfactant. This was done by adding different concentrations of xanthan gum (GX) and the hydrophilic surfactants (Polyoxyethylene (80) sorbitan monooleate (Tween® 80), poloxamer 407(Lutrol® F127) using the emulsification in a two-steps process. The stability of the W/O/W multiple emulsions was analyzed over one-month storage period using physicochemical and rheological measurements. An excellent structure appeared with 0.175 wt% of xanthan gum in the outer aqueous phase and 1 wt% of Tween® 80. The modified Cross model was successfully applied to fit the flow curves of multiple W/O/W emulsions at different concentrations of xanthan gum. The incorporation of xanthan gum in a concentration range of 0.05-0.175 wt% induced an increase in the yield stress, in the zero-shear rate viscosity, and in the infinite shear rate viscosity of the multiple emulsions. The study also showed that adding xanthan gum in a concentration range of 0.05-0.175 wt% to W/O/W emulsions caused an increase in the viscosity of the system in the Newtonian regime and viscoelastic behavior.

STUDY OF THE VARIABILITY OF RHEOLOGICAL PROPERTIES OF WATER-BASED BIOPOLYMER DISPERSIONS IN DRILLING FLUIDS

Link for citation: Lambin A.I., Averkina E.V. Study of the variability of rheological properties of water-based biopolymer dispersions in drilling fluids. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 8, рр. 91-97. In Rus. The relevance. Water-based biopolymer drilling fluids have become quite widespread in the technology of oil and gas well construction. Much attention is paid to the methods of regulating the physical and mechanical properties of biopolymer systems. In particular, rheological properties of solutions based on xanthan gum are of great practical interest. The effectiveness of the use of polymers is determined by the amount of the main reagent and modifying additives necessary to impart the required properties to the washing liquid. Biopolymer water drilling fluids based on xanthan gum have shown their effectiveness in many regions of the Russian Federation. However, the evaluation of the effectiveness of the solutions is difficult due to the differences in the saleable products of the producing companies in solubility, swelling and composition, which affects the optimized performance of the drilling mud. The main aim: consideration of the differences in aqueous solutions of a number of samples of xanthan gum in terms of power dependence: K-coefficient of consistency and n-degree of deviation from the Newtonian flow regime of the study. Objects: rheology of aqueous solutions of several xanthan samples, both purely aqueous and based on aqueous brines of potassium chloride (KCl) and sodium (NaCl). Methods: instrumental methods for determining the parameters of drilling fluids according to SS 33213-2014; the difference in the parameters of the power rheological dependence was determined by comparing its indicators after measuring the viscosity of solutions on a viscometer with direct indications. Results. The influence of a fixed concentration of NaCl and KCl salts on the considered indicators of the power model is shown. A generalized optimization indicator is proposed for solutions obeying a power-law rheological law. The calculated dependence of the accuracy of approximation of experimental data by a power model, which showed acceptable accuracy, is presented.

A Generalized Double Chaplygin Model for Anisotropic Matter: The Newtonian Case

In this work, we investigate astrophysical systems in a Newtonian regime using anisotropic matter. For this purpose, we considered that both radial and tangential pressures satisfy a generalized Chaplygin-type equation of state. Using this model, we found the Lane–Emden equation for this system and solved it numerically for several sets of parameters. Finally, we explored the mass supported by this physical system and compared it with the Chandrasekhar mass.

Analytical Solutions of the Riccati Differential Equation: Particle Deposition in a Viscous Stagnant Fluid

In this communication, the solution of the differential Riccati equation is shown to provide a closed analytical expression for the transient settling velocity of arbitrary non-spherical particles in a still, unbounded viscous fluid. Such a solution is verified against the numerical results of the integrated differential equation, establishing its accuracy, and validated against previous experimental, theoretical and numerical studies, illustrating the effect of particle sphericity. The developed closed analytical formulae are simple and applicable to general initial velocity conditions in the Stokes, transitional and Newtonian regimes, extending the range of application of former published analytical approximate solutions on this subject.

Investigation of blood flow characteristics saturated by graphene/CuO hybrid nanoparticles under quadratic radiation using VIM: study for expanding/contracting channel

The importance of heat transfer in nanoliquids cannot avoided because it playing crucial role in the applied research fields. The potential area of applications included but restricted to applied thermal, biomedical, mechanical and chemical engineering. Therefore, it is the need of time to introduce new efficient way to enhance the heat transport rate in common fluids. The major aim of this research is to develop a new heat transport BHNF (Biohybrid Nanofluid Model) model in a channel having expanding/contracting walls up to Newtonian regimes of blood. The two sort of nanomaterials (Graphene + CuO) along with blood as base solvent are taken for the formation of working fluid. After that, the model analyzed via VIM (Variational Iteration Method) to examine the influence of involved physical parameters on the behavior of bionanofluids. The model results revealed that the bionanofluids velocity rises towards the lower and upper channel end when the expanding/contracting of the walls in the range of 0.1–1.6 (expanding case) and - , 0.1 to 1.6 (contraction case). The working fluid attained high velocity in the neighboring of center portion of the channel. By increasing the walls permeability ({A}_{1}=text{0.1,0.2,0.3,0.4}), the fluid movement can be reduced and optimum decrement observed about eta =0.0. Further, inclusion of thermal radiation (Rd) and temperature coefficient ({theta }_{r}) observed good to enhance thermal mechanism in both hybrid and simple bionanofluids. The present ranges of Rd and {theta }_{r} considered from 0.1 to 0.9 and 0.1 to 1.4, respectively. Thermal boundary layer reduced in the case of simple bionanoliquid keeping {P}_{r}=21.0.

ECG QT interval estimation with a transfer deep learning model

An experimental study of flows of the green non-motile Chlorella micro-alga in a plane micro-channel is presented. Depending on the value of the cell volume fraction, three distinct flow regimes are observed. For low values of the cell volume fraction a Newtonian flow regime characterised by a Poiseuille like flow field, absence of wall slip and hydrodynamic reversibility of the flow states is observed. For intermediate values of the cell volume fraction, the flow profiles are consistent with a Poiseuille flow of a shear thinning fluid in the presence of slip at the channel’s wall. For even larger cell volume fractions, a yield stress like behaviour manifested through the presence of a central solid plug is observed. Except for the Newtonian flow regime, a strong hydrodynamic irreversibility of the flow and wall slip are found. The calculation of the wall shear rate and wall stress based on the measured flow fields allows one to identify the mechanisms of wall slip observed in the shear thinning and yield stress regimes.

The effect of heat treatment of starch on its crystal structure and dynamic viscosity of starch pastes

Analysis of literature data shows the uncertainty of a number of issues of the starch dextrinization process, namely the patterns of the change in the crystal structure of starch during heat treatment and the dependence of the viscosity of starch pastes of dextrins on the conditions of starch heat treatment. These questions were chosen as the topic of this study. A decrease in the average size of starch particles by 2.7 m and an increase in the intensity of reflexes of diffractograms in the range of 2=10–200 after its heat treatment at 1350C (the temperature at which the dextrinization process starts) are well explained by dehydration and a change in the degree of crystallization of biopolymer macromolecules due to their thermal transformations. The dependence of the dynamic viscosity of hot pastes on their shear rate was studied. The steady shear flow curves showed the presence of dilatant areas as a transition from the Newtonian flow regime to the pseudoplastic flow of starch pastes. It was found that the viscosities of heat-treated starch pastes depend on the processing conditions; the viscosities increase in the following order: starch heat-treated in the presence of an acid catalyst; native starch; starch heat-treated without a catalyst for 5 hours; and starch heat-treated without a catalyst for 2.5 hours. It was proposed to divide dextrins into two separate groups: with an increased and with a reduced degree of amylose polymerization.

A Novel Approach for Modeling the Non-Newtonian Behavior of Simple Liquids: Application to Liquid Water Viscosity from Low to High Shear Rates

The aim of this paper is to present a model for the rheological behavior of simple liquids as a function of the amplitude of the imposed shear stress or strain. The elastic mode theory is first generalized to take into account the fact that, during a flow experiment, mechanical energy is injected in a system initially at thermodynamic equilibrium. This generalized theory can be seen as a particular aspect of the general problem of perturbation by the measurement, associated with that of the coupling between fluctuation and dissipation. This generalization leads to a “finitary” character of the model. It is then combined with the inertial mode theory. The formalism thus obtained allows us to model the rheological behavior of liquids over a wide range of velocity gradients, including the intermediate narrow range corresponding to the Newtonian regime. As experimental tests, viscosity measurements with two kinds of moving rotor rheometers were performed. Only data obtained with liquid water at room temperature are presented and quantitatively analyzed here. It is also shown that liquid n-octane exhibits the same qualitative behaviors as those of liquid water. In the appendices, connection of this theory with quantum mechanics and turbulence phenomena are discussed, and the notion of viscous mass is introduced.

Surface Density of Disk Galaxies in MOND

In this paper, we extend a paper by Milgrom (2009, MNRAS 398, 1023) dealing with the existence of a quasi-universal surface density for object of all mass and structure, if they are in the Newtonian regime, i.e., that their mean acceleration is larger than MOND typical acceleration a0. This result is in agreement with Donato et al. (2009)’s results, claiming the existence of a quasi-universal surface density in all masses in galaxies. The Milgrom paper also predicts that objects with mean inner acceleration smaller than the values discussed do not show the quasi-universal behavior of the surface density discussed. In the present paper, we extend the result of Milgrom’s paper, based on a point mass model, considering spiral galaxies, modelled with a double exponential disk. Similar to Milgrom’s results, we find the existence of a universal surface density for galaxies with large surface density, and a different behavior for galaxies having small surface density.

Newtonian approximation in (1 + 1) dimensions

We study the possible existence of a Newtonian regime of gravity in 1 + 1 dimensions, considering metrics in both the Kerr-Schild and conformal forms In the former case, the metric gives the exact solution of the Poisson equation in flat space, but the weak-field limit of the solutions and the non-relativistic regime of geodesic motion are not trivial. We show that using harmonic coordinates, the metric is conformally flat and a weak-field expansion is straightforward. An analysis of the non-relativistic regime of geodesic motion remains non-trivial and the weak-field potential only satisfies the flat space Poisson equation approximately.

Spatiotemporal linear stability of viscoelastic Saffman–Taylor flows

The temporal and spatiotemporal linear stability analyses of a displaced Oldroyd-B fluid with the mean flow in a horizontally aligned, square, Hele–Shaw cell are reported to identify the regions of topological transition of the advancing interface. The viscosity of the displacing fluid is negligible in comparison to the displaced fluid. While all the inertial terms in the model are retained, the interface is assumed to evolve on a slow timescale compared with the timescale of the perturbation (or the so-called “quasi-stationary” approximation). The parameters governing stability are the Reynolds number Re=b2ρU012η2L, the elasticity number E=12λ(1−ν)η2ρb2, and the ratio of the solvent to the polymer solution viscosity ν=ηsη2, where b,L,U0,ρ,λ are the cell gap, the cell length (or width), the mean flow velocity, the density of the driven fluid, and the polymer relaxation time, respectively. Reasonably good agreement on the relative finger width data computed with our model and the experimental data in the Stokes and the inertial Newtonian regime is found. In the asymptotic limit E(1−ν)≪1, the critical Reynolds number, Rec, diverges as Rec∼[E(1−ν)]−5/3 and the critical wavenumber, αc, increases as αc∼[E(1−ν)]−2/3. In a confined domain, the temporal stability analysis indicates (a) the destabilizing influence of the inertial terms, (b) the destabilizing impact of the finite boundaries near the wall, and (c) the stabilizing impact of elasticity until a critical Reynolds number. The Briggs idea of analytic continuation is deployed to classify regions of absolute and convective instabilities as well as the evanescent modes. The phase diagram reveals the presence of an absolutely unstable region at high values of Reynolds and elasticity number, confirming the role of fluid inertia in triggering a pinch-off.