On the structure and volume growth of submanifolds in Riemannian manifolds

The aim of this note is two-fold. First, we investigate the relations between the volume growth of a submanifold and its second fundamental form. In the second part, we discuss the relations between the index of some Schrödinger operators and the structure of a submanifold, and prove some one-end theorems.     

SiOx encapsulated FeSi2–Si eutectic nanoparticles as durable anode of lithium-ion batteries

Low-cost and high-efficiency production of silicon-based material is the key to improve the energy density of lithium-ion batteries. Herein, we propose a novel structure of FeSi₂–Si eutectic nanoparticles protected by the SiO_x shell. FeSi₂, as a buffer phase can improve the electrochemical stability of the electrode. A SiO_x shell is formed on the surface of the nanoparticles through the passivation process. SiO_x encapsulated FeSi₂–Si eutectic nanoparticles exhibit excellent capacity of 674.9 mAh/g after 500 charge/discharge cycles. The capacity retention rate is above 90% after the stabilization process. This work provides a new nanomaterial design for high performance silicon-based anode materials of lithium-ion batteries.     

Viscous waves and wave-structure interaction in a tank using adapting quadtree grids

Viscous waves and waves over a submerged cylinder in a stationary tank are simulated using a volume-of-fluid numerical scheme on adaptive hierarchical grids. A high resolution interface-capturing method is used to advect the free surface interface and the Navier–Stokes equations are discretised using finite volumes with collocated primitive variables and solved using a Pressure Implicit with Splitting of Operators (PISO) algorithm. The cylinder is modelled by using the technique of Cartesian cut cells. Results of flow of a single fluid past a cylinder at Reynolds number Re=100 are presented and found to agree well with experimental and other numerical data. Viscous free surface waves in a tank are simulated using uniform and quadtree grids for Reynolds numbers in the range from 2 to 2000, and the results compared against analytical solutions where available. The quadtree-based results are of the same accuracy as those on the equivalent uniform grids, and retain a sharp interface at the free surface while leading to considerable savings in both storage and CPU requirements. The nonlinearity in the wave is investigated for a selection of initial wave amplitudes. A submerged cylinder is positioned in the tank and its influence on the waves as well as the hydrodynamic loading on the cylinder is investigated.     

A parametric study of droplet deformation through a microfluidic contraction: Shear thinning liquids

Numerical simulations of a droplet passing through an axisymmetric microfluidic contraction are presented, focusing on systems where one of the two liquids present is shear thinning. The simulations are performed using a transient Volume of Fluid (VOF) algorithm. When the droplet is shear thinning and the surrounding phase Newtonian, droplets deform in a similar way to Newtonian droplets that have a viscosity equal to the average viscosity of the shear thinning fluid while it is within the contraction. When the surrounding phase is shear thinning and the droplet Newtonian, droplets deform in a similar way to droplets contained within a Newtonian liquid that has a viscosity that is lower than that of the droplet. In both cases the behaviour of the shear thinning fluid can be broadly described in terms of a ‘characteristic’ Newtonian viscosity: However, determining the exact value of this viscosity without performing a full shear thinning simulation is not possible.     

Rheological models with microstructural constraints

Rheological models of complex fluids with a physically restricted microstructure are analyzed to obtain general classes of dynamical evolution equations for these materials. These classes insure that the appropriate mathematical constraints, associated with each type of physical restriction, are consistently incorporated into the corresponding model development. Describing the microstructure of the complex fluid with a second-rank tensor variable, a general class of dynamical evolution equations is derived for three physically meaningful constraints associated with constancy of the invariants of this microstructural tensor. The physical rationale for each of these constraints is discussed, and a corresponding set of constrained dynamical evolution equations is derived in general terms. Abdellatif Ait-Kadi passed away suddenly during the course of this research. The surviving authors express their gratitude to Abdellatif for our many hours of productive work and companionship.     

Pulsatile flow between permeable beds

Pulsatile flow of a viscous fluid between two permeable beds is analyzed. The flow between and through the permeable beds are governed by the Navier-Stokes equations and Darcy's law, respectively. The velocity field and the volume flux are obtained for several cases and discussed. Further, when the permeability parameter k→0, the results agree with those of Wang (J. Appl. Mech. 38 (1971) 553).     

A variational approach to a micro-structured theory of solid-fluid mixtures

Summary In this paper, we present a micro-structured model for describing global deformations of heterogeneous mixtures. In particular, for a saturated solid-fluid mixture, we regard the solid volume fraction as a microstructural parameter so as to enlarge the space of admissible deformations with respect to the classical theory of mixtures. According to the variational approach, the governing equations are obtained as the stationarity of a suitable action functional. The micro-structured model is then forced to establish a second-gradient mixture theory, by introducing among the considered state parameters a suitable internal constraint. Finally, we determine under which (integrability) conditions the additional balance laws, typically employed to close the theory of porous media endowed with the volume fraction, can fit the variational framework. The authors wish to thank Prof. Francesco dell'Isola from University of Rome La Sapienza for his constructive criticism about the variational approach to continuum mechanics and the interpretation of the volume-fraction balance law.     

Determination of in situ parameters of sandy soils for off-road vehicle mobility

This study focuses on the development of a methodology for the determination of some in situ parameters for off-road vehicle mobility on sandy soils. The stress field in the vicinity of and at the interface between a wedge and soil was determined by solving the stress equations using the method of characteristics. The governing equations were solved numerically by using backward finite difference method. The proposed method allows the prediction of any two of the in situ soil parameters δ, φ, and γ (respectively, the interfacial friction angle between the material of a wedge penetrometer and the soil, the internal friction angle, and the unit weight of the soil), given the value of any one of them and the results of penetration tests of two different apex angle wedges. The predictions and the measured values are in agreement.     

A penalization method applied to the wave equation

In this Note we investigate the mathematical properties of the volume penalization method applied to the one-dimensional wave equation. Generally speaking, the penalization method allows one to handle complex geometries by simply adding a term to the equation to impose the boundary conditions. We study the convergence of the method with regards to the penalization parameter and we present error and stability analyses for the wave equation. Numerical simulations using a finite difference scheme illustrate the results. To cite this article: A. Paccou et al., C. R. Mecanique 333 (2005).     

Phase transition in polymer gels due to local heating by illumination of light

The volume phase transition in gels induced by visible light and its related properties are presented, the mechanism of which is based on local heating of a polymer network by illumination of light. The gels consist of a covalently cross-linked copolymer network of thermosensitive N-isopropylacrylamide and a chromophore. Without light illumination, the gel volume changes sharply, but continuously at approximately 34°C when the temperature is varied. At a fixed temperature of an appropriate value, a discontinuous volume transition is observed when the light intensity is gradually changed. The phase transitions can be understood in terms of the temperature increment at the immediate vicinity of polymer chains due to the local heating via light absorption and subsequent thermal dissipation of light by the chromophore. The results can be qualitatively described by the Flory-Huggins mean-field equation of state of gels. In order to make clear the mechanism of the light-induced phase transition in the present system, we measured the light transmitting properties and the swelling as well as shrinking kinetics. These preliminary results are described semi-qualitatively by making use of a simple phenomenological model.