arXiv subjects

Mario Liu

Publications and source records attributed to Mario Liu.

At least 19 recordsLinked to original sources

arXiv2024

Transient Elasticity -- A Unifying Framework for Thixotropy, Polymers, and Granular Media

Thixotropic yields stress fluids are complex materials such as paint, drilling mud, and food products like ketchup or yogurt. They behave as a solid below a certain shear stress (called yield stress), and flows as a liquid above it. The viscosity decreases over time and recovers when being at rest again. The usual picture is that a web of interacting particles exists at rest, which breaks down under stirring, shaking or shear rates, such that the system fluidizes into a viscous fluid with lumps. These decrease in size at higher rates, rendering the fluid less viscous. Back at rest, the lumps reconnect, re-establishing the web. In contrast, polymeric solutions have no yield stress, they always flow and deform elastically instead of breaking. The differences being clear-cut, these are two distinct systems, to be emulated by very different models. This paper presents an alternative picture: When fluidized, structural destruction is not complete, and sufficient connections are left intact, rendering thixotropic yield stress fluids transiently elastic, such that they behave viscous if stationary, with little evidence of recoverable elastic strain, but it is elasticity that underlines its non-Newtonian behavior, not a complex viscosity. They obey the same evolution equations as polymers, differing only in their parameters. With this idea, it turns out quite simple to account for a wide range of thixotropic effects, including some that fail to fit the viscous picture. More technically, starting from solid-dynamics and letting the elastic strain relax, interpolates between solid- and fluid-dynamics. Realizing in addition that complex systems such as structured fluids often sustain two temperatures, yields a nonlinear model called Transient Elasticity (TE). Its adequacy for polymers and granular media was shown in previous papers. Here, it is applied to thixotropic yield-stress fluids.

cond-mat.soft↗

arXiv2022

A Thermodynamic Treatment\\ of Partially Saturated Soils \\ Revealing the Structure of Effective Stress

A rigorous thermodynamic treatment of partially saturated soils is developed using a minimal number of assumptions. The derivation is carried out in a way that does not require to explicitly track the complex shapes of interfaces between the solid, fluid and gas domains. Instead, suction is the property being recovered explicitly through the minimisation of energy around an ideal `suctionless limit', while considering the different compressibilities of the three domains. In interpreting experimental data the derivation ensures the thermodynamic equilibrium between the chemical potentials of the soil and measurement cells, while carefully distinguishing intrinsic from measured pressures and suctions. A most general expression for the effective stress of partially saturated soils is then derived that is strictly linked to the soil-water retention curve (SWRC). The structure of the effective stress broadly depends on the three thermodynamic densities characterising the solid, fluid and gas domains. Special cases of SWRC are explored, which reveals conditions for which the structure of the effective stress may agree with previously proposed empirical relationships.

cond-mat.soft↗

arXiv2022

Superfluid Dynamics, Equilibrium Conditions, and Centripetal Forces

Thermodynamics of superfluids is revisited, clarifying two points. First, the density and pressure distribution for given equilibrium velocities is obtained, with the finding that counter heat currents give rise to a pressure depression and a centripetal force. Second, it is shown that the ideal two-fluid hydro\-dynamics is simply an assembly of \textit{equilibrium conditions} -- expressions of entropy being maximal.

cond-mat.stat-mech↗

arXiv2022

Temperatures in Grains and Plasma

Grains are widely assumed to be characterized by a single temperature -- derived either from the configurational entropy, or employing the kinetic theory. Yet granular media do have two temperatures, $T_g$ and $T$, pertaining to the grains and atoms. It is argued here that a two-temperature plasma yields a more useful analogy for grains than a molecular gas: (1)~Irreversible collisions also occur in plasma, to reach the equilibrium of equal temperature. (2)~The plasma energy is not linear in the two temperatures; it is quadratic in the temperature difference, minimal at equilibrium. Both points have valid analogues in grains, yielding useful insights.

cond-mat.soft↗

arXiv2017

Similarities between GSH, Hypoplasticity and KCR

Accounting for elasto-plastic motion in granular media, hypoplasticity is a state-of-the-art constitutive model derived from data accumulated over many decades. In contrast, GSH, a hydrodynamic theory, is derived from general principles of physics, with comparatively few inputs from experiments, yet sporting an applicability ranging from static stress distribution via elasto-plastic motion to fast dense flow, including non-uniform ones such as a shear band. Comparing both theories, we find great similarities for uniform, slow, elasto-plastic motion. We also find that proportional paths and the Goldscheider rule used to construct barodesy, another, more recent constitutive model, are natural results of GSH's equations. This is useful as it gives these constitutive relations a solid foundation in physics, and in reverse, GSH a robust connection to reality. The same symbiotic relation exists between GSH and KCR, or Kamrin's non-local constitutive relation, a model that was successfully employed to account for a wide shear band in split bottom cells.

cond-mat.soft↗

arXiv2016

Why Granular Media Are Thermal, and Quite Normal, After All

Two approaches exist to account for granular dynamics: The athermal one takes grains as elementary, the thermal one considers the total entropy that includes microscopic degrees of freedom such as phonons and electrons. Discrete element method (DEM), granular kinetic theory and athermal statistical mechanics (ASM) belong to the first, granular solid hydrodynamics (GSH) to the second one. A discussion of the conceptual differences between both is given here, leading, among others, to the following insights: (1) While DEM and granular kinetic theory are well justified to take grains as athermal, any entropic consideration is far less likely to succeed. (2) In addition to modeling grains as a gas of dissipative, rigid mass points, it is very helpful take grains as a thermal solid that has been sliced and diced. (3) General principles that appear invalid in granular media are repaired and restored once the true entropy is included. These abnormalities [such as invalidity of the fluctuation-dissipation theorem, granular temperatures failing to equilibrate, and grains at rest unable to explore the phase space] are consequences of the athermal approximation, not properties of granular media.

cond-mat.soft↗

arXiv2014

Why Granular Media Are, After All, Thermal

Granular media are considered "athermal", because the grains are too large to display Brownian type thermal fluctuations. Yet being macroscopic, every grain undergoes thermal expansion, possesses a temperature that may be measured with a thermometer, and consists of many, many internal degrees of freedom that in their sum do affect granular dynamics. Therefore, including them in a comprehensive approach to account for granular behavior entails crucial advantages. The pros and cons of thermal versus athermal descriptions are considered.

cond-mat.soft↗

arXiv2014

Granular Solid Hydrodynamics (GSH): a broad-ranged macroscopic theory of granular media

A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. Derived employing the hydrodynamic approach, GSH is such a theory, though as yet a qualitative one. The behavior being accounted for includes static stress distribution, elastic wave, elasto-plastic motion, the critical state and rapid dense flow. The equations and application to a few typical experiments are presented here.

cond-mat.soft↗

arXiv2014

Applying GSH to a Wide Range of Experiments in Granular Media

Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, the range of which is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: (i)~static stress distribution, clogging; (ii)~elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; (iii)~rapid dense flow: the $\mu$-rheology, Bagnold scaling and the stress minimum; (iv)~elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: shear jamming, creep flow, visco-elastic behavior and nonlocal fluidization. With all these phenomena ordered, related, explained and accounted for, though frequently qualitatively, we believe that GSH may be taken as a unifying framework, providing the appropriate macroscopic vocabulary and mindset that help one coming to terms with the breadth of granular physics.

cond-mat.soft↗

arXiv2012

Proportional Paths, Barodesy, and Granular Solid Hydrodynamics

Propotional paths as summed up by the Goldscheider Rule (GR) -- stating that given a constant strain rate, the evolution of the stress maintains the ratios of its components -- is a characteristics of elasto-plastic motion in granular media. Barodesy, a constitutive relation proposed recently by Kolymbas, is a model that, with GR as input, successfully accounts for data from soil mechanical experiments. Granular solid hydrodynamics (GSH), a theory derived from general principles of physics and two assumptions about the basic behavior of granular media, is constructed to qualitatively account for a wide range of observation -- from elastic waves over elasto-plastic motion to rapid dense flow. In this paper, showing the close resemblance of results from Barodesy and GSH, we further validate GSH and provide an understanding for GR.

cond-mat.soft↗

arXiv2012

Granular Solid Hydrodynamics (GSH): from Quasi-Static Motion to Rapid Dense Flow

{\sc gsh} is a continuum mechanical theory constructed to qualitatively account for a broad range of granular phenomena. To probe and demonstrate its width, simple solutions of {\sc gsh} are related to granular phenomena and constitutive models, including (i) for vanishing shear rates: static stress distribution and propagation of elastic waves; (ii) at slow rates: critical state, shear band, the models of hypoplasticity and barodesy; (iii) at higher rates: the MIDI-model, rapid dense flow in the Bagnold regime. A unified, densely correlated understanding of granular physics emerges as a result of these phenomena ordered and explained employing a single framework.

cond-mat.soft↗

arXiv2012

Granular Gas: Vibrating Walls, Two-Peak Distribution and Hydrodynamics

Vibrating walls, used to maintain the temperature in a granular gas, modify the system strongly. Most conspicuously, the usual one-peak velocity distribution splits into two, asymmetrically positioned. A surgical repair of the usual hydrodynamic description is presented that provides an account for, and an understanding of, the situation.

cond-mat.soft↗

arXiv2012

The Physics of Granular Mechanics

The {\em hydrodynamic} approach to a continuum mechanical description of granular behavior is reviewed and elucidated. By considering energy and momentum conservation simultaneously, the general formalism of {\em hydrodynamics} provides a systematic method to {derive} the structure of constitutive relations, including all gradient terms needed for nonuniform systems. An important input to arrive at different relations (say, for Newtonian fluid, solid and granular medium) is the energy, especially the number and types of its variables. Starting from a careful examination of the physics underlying granular behavior, we identify the independent variables and suggest a simple and qualitatively appropriate expression for the granular energy. The resultant hydrodynamic theory, especially the constitutive relation, is presented and given preliminary validation.

cond-mat.soft↗

arXiv2012

An Expression for the Granular Elastic Energy

Granular Solid Hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to deform the grains. The original expression, though useful and simple, has some draw-backs. Therefore, a slightly more complicated expression is proposed here that eliminates three of them: (1) The maximal angle at which an inclined layer of grains remains stable is increased from $26^\circ$ to the more realistic value of $30^\circ$. (2)Depending on direction and polarization, transverse elastic waves are known to propagate at slightly different velocities. The old expression neglects these differences, the new one successfully reproduces them. (3) Most importantly, the old expression contains only the Drucker-Prager yield surface. The new one contains in addition those named after Coulomb, Lade-Duncan and Matsuoka-Nakai -- realizing each, and interpolating between them, by shifting a single scalar parameter.

cond-mat.soft↗

arXiv2010

Compaction in Granular Solid Hydrodynamics

Compaction is considered and embedded into broader granular behavior. Reversible compaction is related to the pressure exerted by agitated grains, a quantity relevant to dense flow. Irreversible compaction is derived from the loss of elastic deformation, the physics behind elasto-plastic flows.

cond-mat.soft↗

arXiv2010

The Critical State and the Steady-State solution in Granular Solid Hydrodynamics

The approach to the critical state -- the transition from partially elastic to perfectly plastic behavior -- is considered the most characteristic of granular phenomena in soil mechanics. By identifying the critical state as the steady-state solution of the elastic strain, and presenting the main results as transparent, analytic expressions, the physics of this important phenomenon is clarified.

physics.geo-ph↗

arXiv2010

Granular Solid Hydrodynamics: Dense Flow, Fluidization and Jamming

Granular solid hydrodynamics, constructed to describe quasi-elastic and plastic motion of granular solid, is shown also capable of accounting for the rheology of granular dense flow. This makes it a unified, though still qualitative, hydrodynamic description, enabling one to tackle fluidization and jamming, the hysteretic transition between elasto-plastic motion and uniform dense flow.

cond-mat.soft↗

arXiv2010

The propagation of Elastic Waves in Granular Solid Hydrodynamics

The anisotropic, stress-dependent velocity of elastic waves in glass beads -- as observed by Y. Khidas and X. Jia, see [Phys. Rev. E, 81:021303, Feb. 2010] -- is shown to be well accounted for by ``granular solid hydrodynamics,'' a broad-range macroscopic theory of granular behavior. As the theory makes no reference to fabric anisotropy, the influence of which on sound is in doubt.

physics.geo-ph↗