Adhesive contact of a fluid-filled membrane driven by electrostatic forces

Adhesion of a particle with a substrate in presence of electrostatic interaction is an appealing area of research because of its significance in many biological and industrial applications. In this work, we study an interesting problem in which a charged flexible particle located in an electrolytic environment adheres to an oppositely charged rigid substrate due to the electrostatic attraction between them. The particle is a membrane filled with incompressible fluid and can undergo large deformation. Continuum theories are used to model the mechanics of the membrane and the electric potential in the electrolytic solution. The developed model allows us to examine the nature of the coupling between the electrostatic interaction and the deformation of the membrane. In particular, the deformation of the membrane causes non-uniform distribution of charges on its surface and significant electrostatic repulsion between these charges. This repulsion is most pronounced within and near the contact zone and provides a source of resistance to its further deformation and contact formation. As a result, the coupling between electrostatics and deformation is most significant for moderate deformation and becomes weaker for very large deformation. The relation between the total electrostatic adhesive force and the contact area shows similar scaling $(F～a^n$, where $n=3)$ to the classical Hertz theory of contact at small deformation, but the value of n increases as deformation increases. The dependence of this relation on the Debye length of the solution and the initial fluid pressure in the membrane is also investigated.     

Asymptotic analysis of layered elastic beams

We consider an elastic beam formed by three layers, fixed at one end and loaded at the free end. We call adherents the upper and lower layers ${\Omega }_{+}^{?}$ and ${\Omega }_{?}^{?}$ and an adhesive layer ${\Omega }_m^{?}$. We denote by $?h_{\pm ,m}$ the thickness of each layer and we suppose that the stiffness of the adhesive layer is ${?}^2$, with respect to that of the adherents. By an asymptotic analysis we obtain the zeroth order limit problem and the form of the second order displacements. To cite this article: M. Serpilli, C. R. Mecanique 333 (2005).     

Instability of Navier slip flow of liquidsInstabilité des écoulements glissant de liquides.

We investigate the stability problem related to the basic slip flows of liquids in plane microchannels by using the Navier slip concept. We found that if the Navier slip parameter ($N_s$) equals 0.06, the critical Reynolds number (${\mathit{Re}}_{\mathrm{cr}}$) becomes 213.6. There are short-wave instabilities, however, when we further increase $N_s$ to 0.07 or 0.08. ${\mathit{Re}}_{\mathrm{cr}}$ becomes 132.9 for $N_s=0.08$ if we neglect the short-wave instability. To cite this article: A.K.-H. Chu, C. R. Mecanique 332 (2004).     

Déformation cumulée tensorielle dans le référentiel en rotation logarithmiqueCumulated tensorial strain measure in the logarithmic rotating frame.

The time integration of strain rate tensor $\stackrel{?}{\mathit{D}}$ is a central problem in large transformations even if it is often an underlying one. The cumulated tensorial strains, obtained by the time integration of strain rate tensor $\stackrel{?}{\mathit{D}}$, allow the tackling of this problem from a geometrical point of view, and independently of material behaviour considerations. The time integration here takes place in the local objective frame defined by the logarithmic spin proposed by Lehmann et al. and Xiao et al. The numerical results obtained in a closed deformation path are presented here. The advantages and drawbacks of this novel integration for the development of behaviour laws are described. To cite this article: V. Mora et al., C. R. Mecanique 332 (2004).     

Truth: non-additive measures for the determination of relative density of sands using CPT measurements

In this Note, a fuzzy-integral based approach is developed for aggregating some of the available correlations that are commonly used for determining relative density $D_r$, from cone penetration test (CPT) data, in which non-additive measures are used as fuzzy measures to relate the actual compressibility measured by the friction ratio of sands to the base correlations. The results of the case studied show that fuzzy measures and the fuzzy integral can be utilized for a new approach in geo-technical engineering. To cite this article: C. Tran, C. R. Mecanique 333 (2005).     

Stabilité de l'écoulement de Hartmann chauffé par le basStability of the Hartmann flow heated from below

A numerical study is conducted in order to determine the influence of a vertical magnetic field, the Reynolds number and a temperature stratification on the instabilities occurring in the Hartmann flow heated from below. For $\mathit{Pr}=0.001$ and $\mathit{Ha}?2.5$, the results show that the vertical magnetic field has a stabilizing effect on both transverse oscillatory travelling waves $(T)$ and longitudinal stationary rolls $(L)$. The temperature stratification is responsible of a destabilization of the transverse $(T)$ modes and the appearance of longitudinal $(L)$ modes non-existent for the isothermal Hartmann flow. Moreover, the extent of the domains of Re where the transverse modes $(T)$ prevail is found to narrow when Ha increases and to widen when Ra increases for a given value of Ha. On the other hand, for the $(L)$ modes, the extent of the domains of Re where they prevail increases when Ha grows. To cite this article: W. Fakhfakh et al., C. R. Mecanique 334 (2006).     

Étude numérique du couplage de la convection naturelle avec le rayonnement de surfaces en cavité carrée remplie d'airNumerical study of natural convection-surface radiation coupling in air-filled square cavities

A numerical tool is developed for coupling natural convection in cavities with surface radiation and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Compared to the adiabatic case without radiation, the top wall is cooled, the bottom wall is heated, air flow along the horizontal walls are reinforced and thermal stratification in cavity core is reduced. Detailed analysis shows that net radiative heat flux is linear with ΔT if $\mathrm{\Delta }T?T_0$, which is the case at low Rayleigh number, and that radiative Nusselt number is a linear function of the cavity height. Surface radiation induces an early transition to time-dependent flows: for $?=0.2$ and a cavity height of 0.335 m the critical Rayleigh number is equal to $9.3\times {10}^6$ and the corresponding Hopf bifurcation is supercritical. Furthermore, multiple periodic solutions are observed between $\mathit{Ra}=1.2\times {10}^7$ and $1.3\times {10}^7$. To cite this article: H. Wang et al., C. R. Mecanique 334 (2006).     

Mouvements propres d'un système à 1 D.D.L. avec amortissement viscoélastique

In this note, one considers a 1-d.o.f. oscillator consisting of a mass and a viscoelastic spring, the rheology of which is represented by a generalized so-called Biot's model with $2n+1$ parameters. It is proved that its $n+2$ independent eigenmotions are of the following nature: two eigenmotions damped with or without oscillations (as in the case of classical viscous damping) and n eigenmotions damped without oscillations which are induced by the viscoelastic rheology. To cite this article: P. Muller, C. R. Mecanique 333 (2005).     

Estimation of aerodynamic noise generated by forced compressible round jetsEstimation du bruit d'origine aérodynamique rayonné par des jets ronds forcés compressibles

An acoustic numerical code based on Ligthill's analogy is combined with large-eddy simulations techniques in order to evaluate the noise emitted by subsonic $(M=0.7)$ and supersonic $(M=1.4)$ round jets. We show first that, for centerline Mach number $M=0.9$ and Reynolds number $\mathit{Re}=3.6\times {10}^3$, acoustic intensities compare satisfactorily with experimental data of the literature in terms of levels and directivity. Afterwards, high Reynolds number $(\mathit{Re}=3.6\times {10}^4)$ free and forced jets at Mach 0.7 and 1.4 are studied. Numerical results show that the jet noise intensity depends on the nature of the upstream mixing layer. Indeed, the subsonic jet is 4 dB quieter than the free jet when acting on this shear layer by superposing inlet varicose and flapping perturbations at preferred and first subharmonic frequency, respectively. The maximal acoustic level of the supersonic jet is, on the other hand, 3 dB lower than the free one with a flapping upstream perturbation at the second subharmonic. The results reported in this paper confirm previous works presented in the literature demonstrating that jet noise may be modified according to the inlet conditions. To cite this article: M. Maidi, C. R. Mecanique 334 (2006).     

Stress induced phase transitions in silicon

Silicon has a tremendous importance as an electronic, structural and optical material. Modeling the interaction of a silicon surface with a pointed asperity at room temperature is a major step towards the understanding of various phenomena related to brittle as well as ductile regime machining of this semiconductor. If subjected to pressure or contact loading, silicon undergoes a series of stress-driven phase transitions accompanied by large volume changes. In order to understand the material's response for complex non-hydrostatic loading situations, dedicated constitutive models are required. While a significant body of literature exists for the dislocation dominated high-temperature deformation regime, the constitutive laws used for the technologically relevant rapid low-temperature loading have severe limitations, as they do not account for the relevant phase transitions. We developed a novel finite deformation constitutive model set within the framework of thermodynamics with internal variables that captures the stress induced semiconductor-to-metal ($\mathrm{cd-Si}\to \mathrm{\beta }\mathrm{-Si}$), metal-to-amorphous ($\mathrm{\beta }\mathrm{-Si}\to \mathrm{a-Si}$) as well as amorphous-to-amorphous ($\mathrm{a-Si}\to \mathrm{hda-Si}$, $\mathrm{hda-Si}\to \mathrm{a-Si}$) transitions. The model parameters were identified in part directly from diamond anvil cell data and in part from instrumented indentation by the solution of an inverse problem. The constitutive model was verified by successfully predicting the transformation stress under uniaxial compression and load–displacement curves for different indenters for single loading–unloading cycles as well as repeated indentation. To the authors' knowledge this is the first constitutive model that is able to adequately describe cyclic indentation in silicon.     

Instabilité non linéaire dans un milieu en expansionNonlinear instability in a expanding medium

We consider nonlinear acoustical phenomena, explosive instabilities and a formation of localized structures in nonstationary environment. An example of such a medium is our Universe in expansion considered as a fluid submissive to a gravitational self-concorded force field and governed by the classical hydrodynamics equations. We show that the taking into account of the nonlinear effects allow us to understand the causes of the appearance of the specific nonlinear instability, which is calling explosive instability. This type of instability is more fast, $～\ln [{(t_0?t)}^{\mathrm{?1}}]$ for density fluctuation, that the habitual instability (exponential, $～{\mathrm{e}}^{\gamma t}$): at the end of a finite time, all spatial inhomogeneity of the initials conditions lead to a formation of singularities in the fields. This phenomena will be appear if certains conditions for the initials amplitudes and wavelengths of the fluctuations are observed. To cite this article: F. Henon, V. Pavlov, C. R. Mecanique 334 (2006).