arXiv subjects

Elie Raphael

Publications and source records attributed to Elie Raphael.

46 records · Page 3Linked to original sources

arXiv2002

Surface flows of granular materials: A short introduction to some recent models

We present a short review of recent theoretical descriptions of flows occuring at the surface of granular piles, and focus mainly on two models: the phenomenological ``BCRE'' model and the hydrodynamic model, based on Saint-Venant equations. Both models distinguish a ``static phase'' and a ``rolling'' phase inside the granular packing and write coupled equations for the evolutions of the height of each of these phases, which prove similar in both approaches. The BCRE description provides a very intuitive picture of the flow, whereas the Saint-Venant hydrodynamic description establishes a general and rigorous framework for granular flow studies.

cond-mat↗

arXiv2002

Roughening Transition in a Moving Contact Line

The dynamics of the deformations of a moving contact line on a disordered substrate is formulated, taking into account both local and hydrodynamic dissipation mechanisms. It is shown that both the coating transition in contact lines receding at relatively high velocities, and the pinning transition for slowly moving contact lines, can be understood in a unified framework as roughening transitions in the contact line. We propose a phase diagram for the system in which the phase boundaries corresponding to the coating transition and the pinning transition meet at a junction point, and suggest that for sufficiently strong disorder a receding contact line will leave a Landau--Levich film immediately after depinning. This effect may be relevant to a recent experimental observation in a liquid Helium contact line on a Cesium substrate [C. Guthmann, R. Gombrowicz, V. Repain, and E. Rolley, Phys. Rev. Lett. {\bf 80}, 2865 (1998)].

cond-mat.soft↗

arXiv2002

A Scaling Theory of the Competition between Interdiffusion and Cross-Linking at Polymer Interfaces

We study theoretically situations where competition arises between an interdiffusion process and a cross-linking chemical reaction at interfaces between pieces of the same polymer material. An example of such a situation is observable in the formation of latex films, where, in the presence of a cross-linking additive, colloidal polymer particles initially in suspension come at contact as the solvent evaporates, and, optimally, coalesce into a continuous coating. We considered the low cross-link density situation in a previous paper (A. Aradian, E. Raphael, P.-G. de Gennes, Macromolecules 33, 9444 (2000)), and presented a simple control parameter that determines the final state of the interface. In the present article, with the help of simple scaling arguments, we extend our description to higher cross-link densities. We provide predictions for the strength of the interface in different favorable and unfavorable regimes, and discuss how it can be optimized.

cond-mat.soft↗

arXiv2001

"Marginal pinching" in soap films

We discuss the behaviour of a thin soap film facing a frame element: the pressure in the Plateau border around the frame is lower than the film pressure, and the film thins out over a certain distance lambda(t), due to the formation of a well-localized pinched region of thickness h(t) and extension w(t). We construct a hydrodynamic theory for this thinning process, assuming a constant surface tension: Marangoni effects are probably important only at late stages, where instabilitites set in. We find lambda(t) ~ t^{1/4}, and for the pinch dimensions h(t) ~ t^{-1/2}$ and w(t) ~ t^{-1/4}. These results may play a useful role for the discussion of later instabilitites leading to a global film thinning and drainage, as first discussed by K. Mysels under the name ``marginal regeneration''.

cond-mat↗

arXiv2001

Dissipation in Dynamics of a Moving Contact Line

The dynamics of the deformations of a moving contact line is studied assuming two different dissipation mechanisms. It is shown that the characteristic relaxation time for a deformation of wavelength $2π/|k|$ of a contact line moving with velocity $v$ is given as $τ^{-1}(k)=c(v) |k|$. The velocity dependence of $c(v)$ is shown to drastically depend on the dissipation mechanism: we find $c(v)=c(v=0)-2 v$ for the case when the dynamics is governed by microscopic jumps of single molecules at the tip (Blake mechanism), and $c(v)\simeq c(v=0)-4 v$ when viscous hydrodynamic losses inside the moving liquid wedge dominate (de Gennes mechanism). We thus suggest that the debated dominant dissipation mechanism can be experimentally determined using relaxation measurements similar to the Ondarcuhu-Veyssie experiment [T. Ondarcuhu and M. Veyssie, Nature {\bf 352}, 418 (1991)].

cond-mat.soft↗

arXiv2000

Comb-like polymers inside nanoscale pores

A new method of polymer characterization, based on permeation studies using nanoscale pores, was recently proposed by Brochard and de Gennes. In the present paper, we study how this method, initially developped for star polymers can be extended to comb-like polymers.

cond-mat.soft↗

arXiv2000

Hysteretic behavior of a polymer molecule immersed in an incompatible melt

The radius of gyration of a polymer chain immersed in a low molecular weight solvent is known to vary monotonically with the solvent quality. Here, we consider the behavior of a chain immersed in a high molecular weight solvent (polymer melt). Unsurprisingly, we find that, as the incompatibility between the chain and the polymer melt is increased, the two limiting conformations of the chain are the ideal random coil (R = aN^1/2) and the dense globule (R = aN^1/3). We show, however, that between these two limits the radius of gyration of the chain presents a hysteretic behavior .

cond-mat.soft↗

arXiv2000

Relaxation of a Moving Contact Line and Landau-Levich Effect

The dynamics of the deformations of a moving contact line is formulated. It is shown that an advancing contact line relaxes more quickly as compared to the equilibium case, while for a receding contact line there is a corresponding slowing down. For a receding contact line on a heterogeneous solid surface, it is found that a roughening transition takes place which formally corresponds to the onset of leaving a Landau-Levich film.

cond-mat.soft↗

arXiv1999

Capillary-gravity waves: The effect of viscosity on the wave resistance

The effect of viscosity on the wave resistance experienced by a 2d perturbation moving at uniform velocity over the free surface of a fluid is investigated. The analysis is based on Rayleigh's linearized theory of capillary-gravity waves. It is shown in particular that the wave resistance remains bounded as the velocity of the perturbation approches the minimun phase speed, unlike what is predicted by the inviscid theory.

cond-mat.soft↗

arXiv1999

Thick surface flows of granular materials: The effect of the velocity profile on the avalanche amplitude

A few years ago, Bouchaud al. introduced a phenomenological model to describe surface flows of granular materials [J. Phys. Fr. I, 4, 1383 (1994)]. According to this model, one can distinguish between a static phase and a rolling phase that are able to exchange grains through an erosion/accretion mechanism. Boutreux et al. [Phys. Rev. E, 58, 4692 (1998)] proposed a modification of the exchange term in order to describe thicker flows where saturation effects are present. However, these approaches assumed that the downhill convection velocity of the grains is constant inside the rolling phase, a hypothesis that is not verified experimentally. In this article, we therefore modify the above models by introducing a velocity profile in the flow, and study the physical consequences of this modification in the simple situation of an avalanche in an open cell. We present a complete analytical description of the avalanche in the case of a linear velocity profile, and generalize the results for a power-law dependency. We show, in particular, that the amplitude of the avalanche is strongly affected by the velocity profile.

cond-mat↗