
Leslie V. Woodcock- MA, PhD, DSc, FRSC, FInstP
- Professor at University of Algarve
Leslie V. Woodcock
- MA, PhD, DSc, FRSC, FInstP
- Professor at University of Algarve
Thermodynamic description of gas-liquid phase transitions
Thermodynamic explanation of global warming from 1970-2020
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180
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Introduction
We are researching the thermodynamic description of both supercritical and subcritical fluids based upon a symmetry between clusters in the gaseous state below the Boyle line and clusters in the voids in liquid state that have the exactly the same fluctuations in density, characterized by a rigidity symmetry line and percolation lines. This research will enable the development of physical-constant reduced equations of state, with zero ad hoc parameters. and hence requiring zero maintenance.
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Education
October 1967 - September 1970
Publications
Publications (180)
A two-dimensional system of 10000 hard disks with square periodic boundary conditions, at a density in the middle of the 2-phase region predicted from equation-of-state data, when subjected to a weak external uniform force, is seen to phase separate. Thermodynamic profiles of the inhomogeneous two-phase system agree with the local density approxima...
High-temperature and pressure boundaries of the liquid and gas states have not been defined thermodynamically. Standard liquid-state physics texts use either critical isotherms or isobars as ad hoc boundaries in phase diagrams. Here we report that percolation transition loci can define liquid and gas states, extending from super-critical temperatur...
Using argon as the exemplary fluid, we report a representation of equations-of-state in fluid regions bounded by percolation loci with mainly physical constants that define state bounds and characterize the fluid phase diagram. Both gas- and liquid-state pressures can be represented by 3- or 4-term virial expansions. Gaseous states require only kno...
Woodcock replies -I reported the discovery a substantial area of pressure difference (DeltaP) between the f.c.c. and h.c.p. single-occupancy-cell models, which arises from a difference in order-disorder transition pressures. The result was a free-energy difference in favour of f.c.c., corresponding to an entropy difference 0.005NkB, over the range...
We investigate a representation of thermodynamic equations-of-state for water and steam using only physical constants and zero ad hoc parameters. Following the reported phase equilibria of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions, the state functions density (p,T), and Gibbs energy G(p,T...
We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO2 , H2O and argon exhibit a symmet...
We review an editorial article in the climate journal Earth Systems Dynamics (ESD 14, 241-242, 2023): the headline title of which makes two scientifically incorrect assertions: (i) that the greenhouse-gas hypothesis, i.e., cause of global warming by ~1K in 1950-2020, is an established scientific truth, and (ii) that heat emissions from global fuel...
Background: The COVID-19 pandemic priorities have focused on prevention by detection and response. National governments' prevention response decisions are based upon detection statistics from PCR (polymerase chain reaction) tests that are used to define numbers of (i) COVID-19 infected persons, (ii) COVID-19 hospitalisations, and (iii) COVID-19 dea...
Using the Gibbs concept of state functions to define the first and second laws of thermodynamics, we analyse the effects of changes in atmospheric average temperatures and pressures arising from anthropogenic emissions of enthalpy and water, besides CO2, into the atmosphere. An application of the Hess-Gibbs 1 st law of thermodynamics (H is a state...
This letter explains why subsidised solar panel electricity is a bad deal for taxpayers and that the C-net zero policy of the IPCC (International Panel on Climate Change) that conceived it is inconsistent with the scientific facts that invalidate both the greenhouse-gas hypothesis of global warming, and the climate-change consequence hypothesis.
The greenhouse-gas hypothesis (GGH), i.e., CO2 is the cause of global warming by ~1K from ~1950-2023, is popularly believed to be established scientific truth. It is generally assumed that heat emissions from global fuel combustion are, by comparison, negligible. An application of the Hess-Gibbs 1 st law of thermodynamics, however, shows that the e...
We respond to an editorial article in the climate journal Earth Systems Dynamics (ESD 14, 241–242, 2023): the headline title of which makes two scientifically incorrect assertions: (i) that the greenhouse-gas hypothesis, i.e., cause of global warming by ~1K in 1950-2020, is an established scientific truth, and (ii) that heat emissions from global f...
HIGHLIGHTS • The Andrews 1869 'continuity of liquid and gas' hypothesis (van der Waals, Nobel lecture 1910), has never agreed with experiment: a supercritical mesophase bounded by percolation lines delineates gas and liquid states above a 1 st order transition at Tc. • Experimental heat capacities confirm the 'universality' hypothesis in Wilson's R...
This article explains why the NY-Times global warming world map from 1949-2019 does not support the greenhouse gas climate-change hypothesis. The experimental data reveals hotspots that will never disperse with time. A thermodynamic analysis confirms that <3+ K> warming effects in these regions are permanent geothermal heat transfer changes to the...
Hypothetical dry adiabatic lapse rate (DALR) air expansion processes in atmosphere climate models that predict global warming cannot be the causal explanation of the experimentally observed mean lapse rate (approx.−6.5 K/km) in the troposphere. The DALR hypothesis violates the 2nd law of thermodynamics. A corollary of the heat balance revision of c...
A recent article (Casey et al. in J Failure Anal Prev 22:1252–1259, 2022) finds a thermodynamic explanation for the catastrophic effect of water as an extinguisher in aluminum-clad tower block fires (Entropy 22: 14, 2020) to be “unsubstantiated hypotheses” and “suppositions unsupported by data”. The article by Casey et al., however, is misleading b...
We review the scientific content of a recent research article* published by Casey
et al. [1]: Investigating the Effects of H2O Interaction with Rainscreen Façade ACMs During Fire Exposure | SpringerLink that purports to address the fundamental question of the Grenfell Inquiry “what caused, or did not cause, the rapid acceleration of the fire that...
A fundamental, hitherto unanswered, question in liquid-state physics is: "What is the minimum requirement of a molecular interaction Hamiltonian for the existence of a stable liquid that can coexist with its vapor phase?". It has been the subject of speculation in the thermophysical property literature since Hagen et al. (Nature 1993) reported 'no...
HIGHLIGHTS • The Andrews 1869 'continuity of liquid and gas' hypothesis (van der Waals, Nobel lecture 1910), has never agreed with experiment: a supercritical mesophase bounded by percolation lines delineates gas and liquid states above a 1 st order transition at Tc. • Experimental heat capacities confirm the 'universality' hypothesis in Wilson's R...
This article reviews the principles of thermodynamic equilibrium in climate computer models underlying the greenhouse-gas CO2 global warming hypothesis. We show that fundamental assumptions, in IPCC and NCAR type climate models, violate the 2nd law of thermodynamics in predicting the temperature gradient in the Earth's troposphere that determines c...
Science consists of testing hypothesis. However, this Scientific Method is used ever more scarcely, and is replaced by general research to help making society a better place. In the current work we analyze how the approach of a solution to the sanitary problem caused by the SARS-CoV-2 virus has been done in a non-scientific way leading to erroneous...
We explain why a very large fraction of PCR tests are registering false positive results due to lack of specifity in vivo caused by exosomes that are not present in the specifications from tests in vitro. We discuss the fallout effects caused to false positive tests, not least artificial post original pandemic peaks. For further discussion see:
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This letter analyses and explains the large difference in European countries between offical COVID-19 deaths (within 28 days of a positive PCR test) and the probability of false positives which can create false pseudo-epidemic peaks in 'cases'. The false positive fallout disaster can be blamed on the increasing reliance on subjective scientific adv...
This is a follow-up feedback response from an article submitted 1st Aug.2018: https://www.researchgate.net/publication/326782413_Thermochemistry_of_Grenfell_Tower_Fire_Disaster_Catastrophic_Effects_of_Water_as_an_%27Extinguisher%27_in_Aluminium_Conflagrations
Since the Grenfell Inquiry, London Interim Report of 30-Oct.2019, millions of Al-clad apa...
We review the experimental evidence, from both historic and modern literature of thermodynamic properties, for the non-existence of a critical-point singularity on Gibbs density surface, for the existence of a critical density hiatus line between 2-phase coexistence, for a supercritical mesophase with the colloidal characteristics of a one-componen...
We respond to recent articles (Int. J. Thermophysics 39 139 2018, ibid.40 21 2019) that seek to deny the veracity of the empirical discovery and thermodynamic description of a gas–liquid supercritical mesophase. These IJT articles are misleading because they are based upon a false premise that the mesophase is a hypothetical concept. There is no “m...
We review the thermodynamics of combustion reactions involved in aluminum fires in the light of the spate of recent high-profile tower-block disasters, such as the Grenfell fire in London 2017, the Dubai fires between 2010 and 2016, and the fires and explosions that resulted in the 9/11 collapse of the World Trade Center twin towers in New York. Th...
Following on from two previous JETC (Joint European Thermodynamics Conference) presentations, we present a preliminary report of further advances towards the thermodynamic description of critical behavior and a supercritical gas-liquid coexistence with a supercritical fluid mesophase defined by percolation loci. The experimental data along supercri...
This comment is in response to a recent “new comment” by Umirzakov on the article “Gibbs density surface of fluid argon: revised critical parameters.” It was incorrectly asserted that van der Waals equation “proves” the existence of a scaling singularity with a divergent isochoric heat capacity (Cv). Van der Waals’ equation, however, is inconsisten...
We review the thermochemistry of combustion reactions involved in the Grenfell Tower fire that occurred during the early hours of 14thJune 2017. London Fire Brigade (LFB), having advised all the occupants to stay in their apartments, attempted to extinguish the fire with water. The Grenfell Tower 24-storey block had recently been re-clad with an in...
We review the scientific evidence, from both historic and modern laboratory measurements of thermodynamic properties, for the non-existence of a critical-point singularity on Gibbs density surface, for the existence of a critical dividing line between 2-phase coexistence, for a supercritical mesophase with the colloidal characteristics of a one-com...
Review to be extended and resubmitted as a Journal of Physical Chemistry Letter
As experimental measurements of thermodynamic properties have improved in accuracy, to five or six figures, over the decades, cubic equations that are widely used for modern thermodynamic fluid property data banks require ever-increasing numbers of terms with more fitted parameters. Functional forms with continuity for Gibbs density surface ρ(p,T)...
This comment is in response to a comment by Sengers and Anisimov on the article “Gibbs density surface of fluid argon” that contradicts prevailing theory. It has not “been established experimentally that the thermodynamic properties of fluids satisfy scaling laws with universal critical exponents asymptotically close to a single critical point of t...
Percolation transitions define gas- and liquid-state limits of existence. For simple model fluids percolation phenomena vary fundamentally with dimensionality (d). In 3d the accessible volume (VA) and excluded volume (VE = V-VA) percolation transitions occur at different densities, whereas in 2d they coincide. The region of overlap for 3d fluids ca...
Percolation transition define gas and liquid state boundaries. Computer experiments on a simple penetrable cohesive sphere model reaffirm the conclusions from many previous computer experiments and the experimental literature on real atomic and molecular fluids, that there is no van der Waals critical point singularity on Gibbs density surface, and...
High-temperature and pressure boundaries of the liquid and gaseous states have not been defined thermodynamically. Standard liquid-state physics texts use either critical isotherms or isobars as ad hoc boundaries in phase diagrams. Here we report that percolation transition loci can define liquid and gas states, extending from super-critical temper...
The thermodynamic state function rigidity, defined simply as (Formula Presented.), where p is the pressure, ρ is the density and T is the temperature, is the work required to reversibly increase the density of a fluid. Along any isotherm, rigidity (ω) decreases with density for a gas phase and increases with density for a liquid. Thermodynamics, th...
submitted to JCP 19-07-2015 shows that both liquid-liquid criticality and liquid gas criticality does not conform with contemporary ideas; there is no "critical point" on Gibbs composition surface, or on Gibbs density surface for gas-liquid transcription of W-R model.
We review the scientific history of random close packing (RCP) of equal spheres, advocated by J D Bernal as a more plausible alternative to the non-ideal gas or imperfect crystal as a structural model of simple liquids. After decades of neglect, computer experiments are revealing a central role for RCP in the theory of liquids. These demonstrate th...
It has been reported that at temperatures above the critical there is no “continuity of liquid and gas”, as originally hypothesized by van der Waals [1]. Rather, both gas and liquid phases, with characteristic properties as such, extend to supercritical temperatures [2]-[4]. Each phase is bounded by the locus of a percolation transition, i.e. a hig...
A revised phase diagram for water shows three distinct fluid phases. There is no continuity of liq-uid and gas, and no "critical point" on Gibbs' density surface as hypothesized by van der Waals. A supercritical colloidal mesophase bounded by percolation transition loci separates supercritical liquid water and gas-phase steam. The water phase is bo...
A revised phase diagram for water shows three distinct fluid phases. There is no continuity of liquid and gas and no critical point on Gibbs density surface. A liquid state, water, spans all temperatures. A thermodynamic rigidity function, which distinguishes gas and 'liquid, shows a remarkable symmetry between complimentary corresponding states of...
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / f l u i d a b s t r a c t Critical properties for Lennard–Jones fluids are seen to be consistent with an alternative description of liquid–gas criticality to the van der Waals hypothesis. At the critical temperature (T c) there is a critical divid...
In the late eighteenth and early nineteenth centuries, communities of Dissenters and Evangelical Anglicans played a key role in setting the political agenda, transforming literary taste, and founding cultural institutions such as academies and libraries. They included some of the most important intellectuals of the period. This conference will inve...
An amorphous ground state reminiscent of random close packing (RCP) of spheres terminates a liquid phase that spans all temperatures. On the Gibbs density surface, the liquid phase has bounded by a supercritical percolation line, two-phase liquid–gas coexistence line, and below the triple point, the metastable liquid branch terminating at T = 0 K w...
A phase diagram of argon based upon percola-tion transition loci determined from literature experimental p-V isotherms, and simulation val-ues using a Lennard-Jones model shows three fluid phases. The liquid phase spans all temper-atures, from a metastable amorphous ground state at 0K, to ultra-high T. There is a supercriti-cal mesophase bounded by...
Thermodynamics of the coexisting states of gas and liquid ststes of Lennard-Jones fluid in the vicinity of the critical temperature; there is a line of critical states but no singularity critical point as generally believed.
Review of Book by Norman and Elaine Beale
We extend previous investigations into the thermodynamics of liquid state boundaries by focusing on the origins of liquid–gas criticality. The singular point hypothesis of van der Waals is re-examined in the light of recent knowledge of the hard-sphere percolation transitions and further analysis of simulation results for the supercritical properti...
A phase diagram of simple fluids, based upon percolation transition loci determined from literature experimental density-pressure isotherms of argon, shows three fluid phases. The liquid phase spans all temperatures from a metastable amorphous ground state to supercritical temperatures. There is a supercritical mesophase of a colloidal nature betwe...
A phase diagram of argon based upon percolation transition loci determined from literature experimental density-pressure isotherms, and simulation values using a Lennard-Jones model shows three fluid phases. The liquid phase spans all temperatures, from a metastable amorphous ground state at 0K, to ultra-high T. There is a supercritical mesophase b...
We find a thermodynamic description of gas-liquid criticality that is
different from van der Waals and mean-field theories. At the critical
temperature there is no critical point; a liquid phase coexists with a vapor phase with densities determined by an intersection of 2nd-order percolation transition loci. There is a line of critical states of co...
A state of random close packing (RCP) of spheres is found to have a thermodynamic status and a fundamental role in the description of liquid-state equilibria. The RCP limiting amorphous ground state, with reproducible density and well-characterized structure, is obtained by well-defined irreversible and reversible processes. The limiting packing fr...
A correlation between maxima in virial coefficients (B n), and "kissing" numbers for hard hy-per-spheres up to dimension D = 5, indicates a virial equation and close-packing relationship. Known virial coefficients up to B 7 , both for hard parallel cubes and squares, indicate that the limiting differences B n-B (n-1) behave similar to spheres and d...
A correlation between maxima in virial coefficients (Bn), and "kissing"
numbers for hard hyper-spheres up to dimension D=5, indicates a virial equation and close-packing relationship. Known virial coefficients up to B7, both for hard parallel cubes and squares, indicate that the limiting differences Bn-B(n-1) behave similar to spheres and disks, in...
The number densities (ν/V) above or below which “pockets” of additional-sphere excluded volume (ρpe) and available volume (ρpa) begin to percolate the whole volume of the system, sometimes referred to as percolation thresholds, have been determined for the equilibrium hard-sphere fluid of diameter σ using a Monte Carlo (MC) approach. Values obtaine...
Corresponding states analyses for understanding the freezing temperatures of existing ionic liquids, and predicting freezing properties of ionic liquids yet to be discovered are described. “Room temperature” ionic liquids exist as such because they broadly obey a scaling relationship that describes all 1:1 electrolytes, including the alkali halides...
A nonadditive hard-sphere (NAHS) reference model for ionic liquids with truncated ion−ion pair interaction potentials represented by collision diameters defined as is investigated. In a reference 1:1 ionic salt (e.g., AB = NaCl), the nonadditivity parameter (ε) is positive; hence, like ions interact with a larger diameter than unlike ions; that is,...
A closed virial equation-of-state for the low density fluid phase of hard disks is obtained from the known virial coefficients. The equation exhibits 6-figure accuracy for the thermodynamic (MD) pressure up to the reduced number density ~ 0.4 Interpolation of the discrepancy at higher densities indicates a higher-order thermodynamic phase transitio...
Most textbooks quote four anonymous laws of thermodynamics (zeroth, first, second, and third), but it seems that every author has their own idiosyncratic statements. Why are there so many versions? Why are the laws of thermodynamics not credited with names of their discoverers? We revisit the history of the laws of thermodynamics and consider wheth...
Hard-sphere molecular dynamics (MD) simulation results, with six-figure accuracy in the thermodynamic equilibrium pressure, are reported and used to test a closed-virial equation-of-state. This latest equation, with no adjustable parameters except known virial coefficients, is comparable in accuracy both to Padé approximants, and to numerical param...
Rheology and Mythology: 25 years of Computer Simulation 2009 marks the 25 th anniversary of the appearance of the first mesoscopic simulations in the field of " computational rheology ". Professor Les Woodcock of Manchester University, author of one of those early papers in 1984, offers a personal reflection, and asks " why have the computational s...
This is the published version of Guest Lecture presented to History of Anaesthesia Meeting in June 2008 and is published in the proceedings.
The Reference is:
Woodcock, L. V. , Discovering Priestley's Discoveries: Historical Legacy of Dephlogisticated Air, Proceedings of the History of Anaesthesia Society, Volume 39, pages 97-108 (2008)
The lectur...
Virial coefficients for the two-dimensional hard-disk fluid, when expressed in powers of density relative to maximum close packing, lead to an accurate closed equation-of-state for the equilibrium fluid, analogous to that recently found for hard spheres. The 2D series also converges for all densities up to a negative pole at close packing density....
Recent values for virial coefficients up to B12, when expressed in powers of density relative to maximum close packing,lead to a closed equation-of-state for the equilibrium fluid. The series obtained converges for all densities;it becomes negative and diverges to a negative pole at maximum packing. MD data for 64000 spheres in the metastable regio...
A reproducible RCP state is obtained by a well-defined rate process, which is first-order in free volume, starting from an equilibrium thermodynamic state of the hard-sphere fluid. The RCP state is also reproduced by a thermodynamic pathway that inhibits the frequent production of small crystal nucleites which can lead to heterogeneities at close p...
We investigate the effect of isochoric cooling of the Lennard–Jones liquid at the triple point i.e. ρ⁎=1.20 r0, T⁎=0.70 into the negative pressure region of crystal+vapor phase with temperatures varying from T⁎=1.00 to 0.0001. Along this line, initially, the liquid remains stable with respect to its crystallization, and is metastable with respect t...
A one-parameter model constitutive transport equation for the viscosity of the Lennard-Jones (L-J) fluid that is accurate for all equilibrium states of liquid and gas is proposed:
The form of this equation is based upon the soft-sphere scaling laws for the residual density-dependent viscosity discovered originally by Ashurst and Hoover and uses th...
State-of-the-art molecular and atomic simulation technology for modelling fluids and materials has remained static for 50 years; being restricted to pair-wise additive site-site Hamiltonians. A wide range of commercial programs are presently available that deliver "animation", but are of limited value as a predictive research tool. If n-body potent...
To mark the bicentennial of the extraordinary life of achievements the Priestley Society of Birstal and Heckmondwike in Yorkshire commissioned a local artist (Stephen Barlow) to paint historical pictures that depict Yorkshire's heritage of Joseph Priestley, past and present. The preface text and commentary is written by Priestley Society Chairman (...
A local density functional approximation for predicting the surface crystallization of a thermodynamically small system under gravity is described and tested. Using the model of the classical soft-sphere fluid, the state parameters for such systems are identified. A generalized phase diagram based upon the scaling variables is obtained; systems wit...
The Henderson and Chan (HC) formulae for the contact values of the radial distribution functions (RDFs) of a highly asymmetric hard sphere mixture are reconsidered in light of a recent formula of Roth, Evans and Dietrich for the RDF of a pair of exceedingly large spheres at zero concentration in a solvent of small hard spheres. Two modifications of...
The identification of Priestley's phlogiston with Gibbs' chemical potential for the last chemical revolution
Granular dynamics simulations of inelastic spheres thermalised by mechanical vibrations are reported. The objective is to determine the conditions whereby inelastic spheres in a gravitational force field can behave quasi-thermodynamically. Granular temperatures and granular pressures are defined by analogy with molecular thermodynamics. Quasi-therm...
This report results from a contract tasking Scientific Simulation Services as follows: The contractor will conduct a comprehensive review of the studies of thermodynamics of small systems, including under non-negligible gravity, and its application to processing. The contractor will develop a computer program that starts with input of the material'...
In order to be able to simulate complex systems of non-pairwise additive interactions, a new computational approach, nth nearest neighbour network (n-NNN), has been proposed. In this new method, the continuous force acting on the central atom from its neighbours is a discretized multidimensional function based on the positions of the neighbours and...
In order to be able to simulate complex systems of non-pairwise additive interactions, a new computational approach, n-th Nearest Neighbor Network (n-NNN) method, has been developed. In this new method, the force acting on the central particle due to its neighbors is discretized based on the positions of the neighbors and memorized so that it can b...
The effect of depletion forces induced by the presence of much smaller B spheres (diameter ratio 10/1) in dense hard A spheres has been investigated. Simulations for systems of 104 spheres with mole fraction of larger spheres x
A
= 0.05 and with total sphere volume fraction from 0.35 to 0.655 have been carried out. The depletion force steeply incr...
Simplified computer models are used to gain insight into more complex real systems. In a reversion of this protocol, a colloidal suspension of submicron spherical particles, approximately hard and uniform, was recently crystallized in space and analyzed for crystal type. The objective was to establish how, and to what structure, hard spheres crysta...
We illustrate how emerging methods in artificial intelligence (AI) may be useful in materials science. Historically, these methods were developed in the area of materials process control and, more recently, in the nascent field of materials discovery. However, machine intelligence is of much broader import and our primary objective here is to illus...
Acoustic vibrations generated by a loud-speaker system have been applied to fluidise binary mixtures of ballotini powders with dissimilar sizes. New phase coexistence effects have been observed akin to solution and de-mixing behaviour in binary liquid mixtures. It is postulated that the size-segregated phase above a mixed phase, which occurs when a...
We give analytic expressions showing that size segregation of mixed size particles of same density results in larger particles moving in direction opposite to a gravitational field for a uniform shear.The predominant underlying effect is dilatancy. Corresponding steady-state scaling shows that the larger particlesexhibit higher dilatancy under stea...
A study of the binary hard-sphere fluid with size ratio sigma(B)/sigma(A) = 0.1 is reported. Molecular dynamics and Monte Carlo simulations have been carried out over the mole fraction (x(A)) range 0.002-0.1 and over the high density range where several recent authors have predicted a thermodynamic demixing transition on the basis of integral equat...
General discussion on paper presented at Faraday Discussion on Solid state Chemistry on applications of computer simulation methods to computation of Gibbs energy differences between alternative crystal structures of hard-sphere models.
A single-occupancy cell (SO-cell) method has been applied to calculate the free energies of different crystal structures of hard spheres via molecular dynamics (MD). The objectives are (i) to examine the nature of the phase transition in the SO-cell model, (ii) to determine the thermodynamic stability of the bcc crystal phase relative to the fcc an...
We present first-principles calculations using large-scale computer simulations, and a theoretical analysis of the rheology and microstructure of a particulate model undergoing the process of uniaxial compaction. Such a fundamental process underlies many areas of science and engineering, covering many length scales. If the particles are of the scal...
The equipartition of energy principle is tested for a simple model systemof granu;ar medis
a comprising inelastic spheres being shaken under gravity in a steady-state in a vibrating box with no roof.The result eads to a granular pressure profile from zero at the top to sample weight at the bottom and a uniform granular temperature resulting invaria...
As an alternative to gas fluidization, accoustic vibrations have been explored as a means to fluidise binary powder mixtures with different size ratios and colors. A striking phase separation is found above a mixed solution at higher pressure below, reminiscent of partially miscible liquid mixtures in thermodynamic equilibrium.