Imperial College London

Dr Raphael (Rafi) Blumenfeld

Faculty of EngineeringDepartment of Earth Science & Engineering

Research Fellow
 
 
 
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Contact

 

r.blumenfeld Website

 
 
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Location

 

Royal School of MinesSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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127 results found

He J, Blumenfeld R, Zhu H, 2021, Mechanical Behaviors of Sandy Sediments Bearing Pore-Filling Methane Hydrate under Different Intermediate Principal Stress, INTERNATIONAL JOURNAL OF GEOMECHANICS, Vol: 21, ISSN: 1532-3641

Journal article

Liu P, Ran X, Cheng Q, Tang W, Zhou J, Blumenfeld Ret al., 2021, Locomotion of Self-Excited Vibrating and Rotating Objects in Granular Environments, APPLIED SCIENCES-BASEL, Vol: 11

Journal article

Sun X, Kob W, Blumenfeld R, Tong H, Wang Y, Zhang Jet al., 2020, Friction-Controlled Entropy-Stability Competition in Granular Systems, PHYSICAL REVIEW LETTERS, Vol: 125, ISSN: 0031-9007

Journal article

Wanjura C, Gago P, Matsushima T, Blumenfeld Ret al., 2020, Structural evolution of granular systems: theory, Granular Matter, Vol: 22, ISSN: 1434-5021

A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very dense systems; and the general approach to steady state. We find that all the steady states are stable and that they satisfy a detailed balance-like condition when the CO≤6. Illustrative numerical solutions of the evolution are shown. Our theoretical results are validated against an extensive simulation of a sheared system. The formalism can be readily extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems.

Journal article

Ouyang H, Xiao Y, Hu S, Tang X, Lei G, Blumenfeld Ret al., 2020, Establishment and application of comprehensive evaluation method for automobile technical performance, Zhongnan Daxue Xuebao (Ziran Kexue Ban)/Journal of Central South University (Science and Technology), Vol: 51, Pages: 650-660, ISSN: 1672-7207

A multidimensional evaluation scheme was constructed consisting of a technical performance indicator H, a mass-weighted measure of the effect of the technical parameters W and a measure of the price efficiency N.These indexes were functions of primary performance indicators,which included constant speed fuel consumption,braking distance in the maximum speed 0-100 km/h, engine volume, mass and price.Vehicle indetified method was proposed taking W as the most useful indicator for comparing different vehicles and models. The correlations between the technical performance, price and sales of several major car models in Chinese market were studied.The results show that different car models have significantly different performance indices with joint-venture generally outperforming domestic ones on technical performance, but underperforming on price. There are distinct differences in consumers' selection criteria for cars, SUVs and MPVs. Consumers care more about the technical performance and brand of products for cars,while they care more about the comprehensive ability for SUVs, practicality and cost-effectiveness for MPVs. Breakthrough in high performance and small engines, high capacity battery and motor system, light weight and intelligent vehicles and driving technology (oil-electric vehicles, extended-range vehicles, especially all-wheel drive and integration of driving and braking system) can boost the Chinese vehicle industry development.

Journal article

Blumenfeld R, 2020, The unusual problem of upscaling isostaticity theory for granular matter, GRANULAR MATTER, Vol: 22, ISSN: 1434-5021

Journal article

Feng Y, Blumenfeld R, Liu C, 2019, Support of modified Archimedes' law theory in granular media, SOFT MATTER, Vol: 15, Pages: 3008-3017, ISSN: 1744-683X

Journal article

Revell C, Blumenfeld R, Chalut KJ, 2019, Force-based three-dimensional model predicts mechanical drivers of cell sorting, Proceedings of the Royal Society B: Biological Sciences, Vol: 286, ISSN: 0962-8452

© 2019 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Many biological processes, including tissue morphogenesis, are driven by cell sorting. However, the primary mechanical drivers of sorting in multicellular aggregates (MCAs) remain controversial, in part because there is no appropriate computational model to probe mechanical interactions between cells. To address this important issue, we developed a three-dimensional, local force-based simulation based on the subcellular element method. In our method, cells are modelled as collections of locally interacting force-bearing elements. We use the method to investigate the effects of tension and cell - cell adhesion on MCA sorting. We predict a minimum level of adhesion to produce inside-out sorting of two cell types, which is in excellent agreement with observations in several developmental systems. We also predict the level of tension asymmetry needed for robust sorting. The generality and flexibility of the method make it applicable to tissue self-organization in a myriad of other biological processes, such as tumorigenesis and embryogenesis.

Journal article

Schwartz M, Blumenfeld R, 2018, Stress-strain rate relation in plug-free flow of dense granular fluids: A first-principles derivation, PHYSICAL REVIEW E, Vol: 98, ISSN: 2470-0045

Journal article

Verstreken CM, Chalut KJ, Blumenfeld R, 2018, Equally probable positive and negative Poisson's ratios in disordered planar systems, SOFT MATTER, Vol: 14, Pages: 6554-6560, ISSN: 1744-683X

Journal article

Kang W, Feng Y, Liu C, Blumenfeld Ret al., 2018, Archimedes' law explains penetration of solids into granular media, NATURE COMMUNICATIONS, Vol: 9, ISSN: 2041-1723

Journal article

Cheng Q, Ran X-W, Liu P, Tang W-H, Blumenfeld Ret al., 2018, Numerical simulation of a spinning sphere moving in granular matter, ACTA PHYSICA SINICA, Vol: 67, ISSN: 1000-3290

Journal article

Amitai S, Bertei A, Blumenfeld R, 2017, Theory-based design of sintered granular composites triples three-phase boundary in fuel cells, PHYSICAL REVIEW E, Vol: 96, ISSN: 2470-0045

Journal article

Blumenfeld R, Amitai S, Jordan JF, Hihinashvili Ret al., 2017, Comment on "Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation" Reply, PHYSICAL REVIEW LETTERS, Vol: 119, ISSN: 0031-9007

Journal article

Amitai S, Blumenfeld R, 2017, Affine and topogical structural entropies in granular statistical mechanics: Explicit calculations and equation of state, Physical Review E, Vol: 95, ISSN: 1539-3755

We identify two orthogonal sources of structural entropy in rattler-free granular systems: affine, involving structural changes that only deform the contact network, and topological, corresponding to different topologies of the contact network. We show that a recently developed connectivity-based granular statistical mechanics separates the two naturally by identifying the structural degrees of freedom with spanning trees on the graph of the contact network. We extend the connectivity-based formalism to include constraints on, and correlations between, degrees of freedom as interactions between branches of the spanning tree. We then use the statistical mechanics formalism to calculate the partition function generally and the different entropies in the high-angoricity limit. We also calculate the degeneracy of the affine entropy and a number of expectation values. From the latter, we derive an equipartition principle and an equation of state relating the macroscopic volume and boundary stress to the analog of the temperature, the contactivity.

Journal article

Blumenfeld R, Ma J, 2017, Bending back stress chains and unique behaviour of granular matter in cylindrical geometries, GRANULAR MATTER, Vol: 19, ISSN: 1434-5021

We analyse the general solutions for the stress field in planar annuli of isostatic media, a model often used for marginally rigid granular materials in Couette cells. We demonstrate that these solutions are much richer than in rectangular symmetries. Even for uniform media, stress chains are found to curve, broaden away from the stress source, attenuate and leak stress into a cone of influence. Most spectacularly, stress chains may bend back and transmit forces oppositely to the original direction. None of these phenomena arises in solutions for uniform media in Cartesian coordinates. We further analyse non-uniform media, which exhibit chain branching and stress leakage from the chains. These results are directly relevant to the many experiments on granular materials, carried out in Couette cells. They also shed light on, and are supported by, hitherto unexplained experimental observations of curved and back-bending chains, which we point out. In particular, we use our results to provide a new interpretation for the pattern of slip lines observed experimentally.

Journal article

Amitai S, Blumenfeld R, 2017, Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media, Granular Matter, Vol: 19, ISSN: 1434-5021

The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, PlPl , and waiting-time, PtPt , distributions of the random walk in the medium and it then generates presumably equivalent walks in free space, which are much faster. Here we test the usefulness of CTRW to modelling diffusion of finite-size particles in porous medium generated by loose granular packs. This is done by first simulating the diffusion process in a model porous medium of mean coordination number, which corresponds to marginal rigidity (the loosest possible structure), computing the resulting distributions PlPl and PtPt as functions of the particle size, and then using these as input for a free space CTRW. The CTRW walks are then compared to the ones simulated in the actual media. In particular, we study the normal-to-anomalous transition of the diffusion as a function of increasing particle size. We find that, given the same PlPl and PtPt for the simulation and the CTRW, the latter predicts incorrectly the size at which the transition occurs. We show that the discrepancy is related to the dependence of the effective connectivity of the porous media on the diffusing particle size, which is not captured simply by these distributions. We propose a correcting modification to the CTRW model—adding anisotropy—and show that it yields good agreement with the simulated diffusion process. We also present a method to obtain PlPl and PtPt directly from the porous sample, without having to simulate an actual diffusion process. This extends the use of CTRW, with all its advantages, to modelling diffusion processes of finite-size particles in such confined geometries.

Journal article

Blumenfeld R, Edwards SF, Walley SM, 2017, Physics of granular systems, The Oxford Handbook of Soft Condensed Matter, Pages: 167-232, ISBN: 9780199667925

This article discusses the fundamental physics of granular systems. It begins with an overview of the science of granular matter, followed by a description of the ‘micro’-structure on the granular level. It then considers stress transmission in mechanically equilibrated granular assemblies, focusing on conditions for marginal rigidity, isostaticity theory, and limitations of linear stress theories. It also examines the use of statistical mechanics to analyse and classify granular materials, taking into account the micro-canonical volume ensemble, structural degrees of freedom, the canonical volume ensemble and the quasi-particles of the volume ensemble, the stress ensemble, and the relationship between the volume and stress ensembles. The article concludes with an assessment of recent advances in the ongoing attempt to construct a statistical mechanical theory of granular systems.

Book chapter

Huang L, Ran X, Blumenfeld R, 2016, Vertical dynamics of a horizontally oscillating active object in a two-dimensional granular medium., Physical Review E, Vol: 94, ISSN: 1539-3755

We use a discrete-element method simulation and analytical considerations to study the dynamics of a self-energized object, modeled as a disk, oscillating horizontally within a two-dimensional bed of denser and smaller particles. We find that, for given material parameters, the immersed object (IO) may rise, sink, or not change depth, depending on the oscillation amplitude and frequency, as well as on the initial depth. With time, the IO settles at a specific depth that depends on the oscillation parameters. We construct a phase diagram of this behavior in the oscillation frequency and velocity amplitude variable space. We explain the observed rich behavior by two competing effects: climbing on particles, which fill voids opening under the disk, and sinking due to bed fluidization. We present a cavity model that allows us to derive analytically general results, which agree very well with the observations and explain quantitatively the phase diagram. Our specific analytical results are the following. (i) Derivation of a critical frequency, f_{c}, above which the IO cannot float up against gravity. We show that this frequency depends only on the gravitational acceleration and the IO size. (ii) Derivation of a minimal amplitude, A_{min}, below which the IO cannot rise even if the frequency is below f_{c}. We show that this amplitude also depends only on the gravitational acceleration and the IO size. (iii) Derivation of a critical value, g_{c}, of the IO's acceleration amplitude, below which the IO cannot sink. We show that the value of g_{c} depends on the characteristics of both the IO and the granular bed, as well as on the initial IO's depth.

Journal article

Blumenfeld R, Amitai S, Jordan JF, Hihinashvili Ret al., 2016, Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation, Physical Review Letters, Vol: 116, ISSN: 0031-9007

We first show that the currently accepted statistical mechanics for granular matter is flawed. The reason is that it is based on the volume function, which depends only on a minute fraction of all the structural degrees of freedom and is unaffected by most of the configurational microstates. Consequently, the commonly used partition function underestimates the entropy severely. We then propose a new formulation, replacing the volume function with a connectivity function that depends on all the structural degrees of freedom and accounts correctly for the entire entropy. We discuss the advantages of the new formalism and derive explicit results for two- and three-dimensional systems. We test the formalism by calculating the entropy of an experimental two-dimensional system, as a function of system size, and showing that it is an extensive variable.

Journal article

Blumenfeld R, Edwards SF, 2014, Granular statistical mechanics - a personal perspective, EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, Vol: 223, Pages: 2189-2204, ISSN: 1951-6355

Journal article

Matsushima T, Blumenfeld R, 2014, Universal Structural Characteristics of Planar Granular Packs, PHYSICAL REVIEW LETTERS, Vol: 112, ISSN: 0031-9007

Journal article

Matsushima T, Blumenfeld R, 2013, Microstructural characteristics of planar granular solids, POWDERS AND GRAINS 2013, Vol: 1542, Pages: 325-328, ISSN: 0094-243X

Journal article

Blumenfeld R, Jordan JF, Edwards SF, 2013, Granular Statistical Mechanics: Volume-Stress Phase Space, Equipartition and Equations of State, 7th International Conference on Micromechanics of Granular Media (Powders and Grains), Publisher: AMER INST PHYSICS, Pages: 1186-1189, ISSN: 0094-243X

Conference paper

Blumenfeld R, Jordan JF, Edwards SF, 2012, Interdependence of the Volume and Stress Ensembles and Equipartition in Statistical Mechanics of Granular Systems, PHYSICAL REVIEW LETTERS, Vol: 109, ISSN: 0031-9007

Journal article

Blumenfeld R, Edwards SF, 2012, Theory of Strains in Auxetic Materials, JOURNAL OF SUPERCONDUCTIVITY AND NOVEL MAGNETISM, Vol: 25, Pages: 565-571, ISSN: 1557-1939

Journal article

Hihinashvili R, Blumenfeld R, 2012, Statistical-mechanical characteristics of dense planar granular systems, Granular Matter

We demonstrate the use of a structural and statistical characterisation method on two types of planar disc packs. One is a very dense pack of mean coordination number 5.20 and the other of mean coordination number 4.0. Except for constraining the mean coordination number in the latter one, the different pack types were constructed by the same deposition process and had the same disc size distribution, for a fair statistical comparison. We show that the two types converge to limit statistics and that these limit statistics are different. We analyse the limit statistics and compare between both types of packs, demonstrating that the differences are directly related to the difference in the mean coordination numbers. We then find quantitatively the difference between the (inverse) compactivities of the two pack types: 1/X_{5.2}−1/X_{4}=1.5\pm 0.05 . This explicit result supports strongly the validity of Edwards approach and underpins it as a useful tool to characterise granular systems quantitatively. In particular, it also paves the way to quantify the elusive compactivity.

Journal article

Hihinashvili R, Blumenfeld R, 2011, Structural Characterization of Porous and Granular Materials, 16th European Symposium on Improved Oil Recovery 2011

The morphological details of permeable porous materials impact significantly their macro-scale properties and in particular transport properties (e.g. permeability). A programme to derive macroscopic behaviour and responses from pore-scale information is a holy grail in the field. We report here progress on, and tests of, a recently proposed such a programme.The main steps of the programme are as follows. The solid phase of a porous material is first skeletonised into a framework of nodes and edges. Then the local structure is quantified by means of structure tensors, which describe the shape of novel volume elements called quadrons. Next, the local tensor description is used in an entropy-based statistical formalism to compute macroscopic structural characteristics as expectation values over a certain partition function. From the structural characteristics, physical properties can be evaluated. The 'thickened' structure is taken account of with an additional partition function, giving more accurate evaluation of structural and physical properties.Here we present tests for the initial stages of the programme. The tests are carried out on numerically generated two-dimensional granular aggregates. Specifically, we describe results on the statistics of the quadrons and the structural tensors.

Conference paper

Schwartz M, Blumenfeld R, 2011, Plug flow formation and growth in da Vinci Fluids, Granular Matter, Vol: 13, Pages: 241-245

A model is discussed for flow of dense granular matter — a da Vinci fluid. The local properties of the fluid are generically different from ordinary fluids in that energy is dissipated by solid friction. We discuss the equation of flow of such a fluid and show that it gives rise to formation and growth of plug regions — a phenomenon observed fre- quently in flow of granular matter. Simple explicit examples are presented to illustrate the evolution of plug flow regions.

Journal article

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