arXiv subjects

Michael Benzaquen

Publications and source records attributed to Michael Benzaquen.

95 records · Page 6Linked to original sources

arXiv2014

Capillary levelling of a cylindrical hole in a viscous film

The capillary levelling of cylindrical holes in viscous polystyrene films was studied using atomic force microscopy as well as quantitative analytical scaling arguments based on thin film theory and self-similarity. The relaxation of the holes was shown to consist of two different time regimes: an early regime where opposing sides of the hole do not interact, and a late regime where the hole is filling up. For the latter, the self-similar asymptotic profile was derived analytically and shown to be in excellent agreement with experimental data. Finally, a binary system of two holes in close proximity was investigated where the individual holes fill up at early times and coalesce at longer times.

cond-mat.soft↗

arXiv2013

Relaxation and Intermediate Asymptotics of a Rectangular Trench in a Viscous Film

The surface of a thin liquid film with nonconstant curvature flattens as a result of capillary forces. While this leveling is driven by local curvature gradients, the global boundary conditions greatly influence the dynamics. Here, we study the evolution of rectangular trenches in a polystyrene nanofilm. Initially, when the two sides of a trench are well separated, the asymmetric boundary condition given by the step height controls the dynamics. In this case, the evolution results from the leveling of two noninteracting steps. As the steps broaden further and start to interact, the global symmetric boundary condition alters the leveling dynamics. We report on full agreement between theory and experiments for: the capillary-driven flow and resulting time dependent height profiles; a crossover in the power-law dependence of the viscous energy dissipation as a function of time as the trench evolution transitions from two noninteracting to interacting steps; and the convergence of the profiles to a universal self-similar attractor that is given by the Green's function of the linear operator describing the dimensionless linearized thin film equation.

cond-mat.soft↗

arXiv2013

From adhesion to wetting of a soft particle

Using a thermodynamical approach, we calculate the deformation of a spherical elastic particle placed on a rigid substrate, under zero external load, and including an ingredient of importance in soft matter: the interfacial tension of the cap. In a first part, we limit the study to small deformation. In contrast with previous works, we obtain an expression for the energy that precisely contains the JKR and Young-Dupré asymptotic regimes, and which establishes a continuous bridge between them. In a second part, we consider the large deformation case, which is relevant for future comparison with numerical simulations and experiments on very soft materials. Using a fruitful analogy with fracture mechanics, we derive the exact energy of the problem and thus obtain the equilibrium state for any given choice of physical parameters.

cond-mat.soft↗

arXiv2012

Wave Resistance for Capillary Gravity Waves: Finite Size Effects

We study theoretically the capillary-gravity waves created at the water-air interface by an external surface pressure distribution symmetrical about a point and moving at constant velocity along a linear trajectory. Within the framework of linear wave theory and assuming the fluid to be inviscid, we calculate the wave resistance experienced by the perturbation as a function of its size (compared to the capillary length). In particular, we analyze how the amplitude of the jump occurring at the minimum phase speed $c_{\rm min}=(4 g γ/ρ)^{1/4}$ depends on the size of the pressure distribution ($ρ$ is the liquid density, $γ$ is the water-air surface tension, and $g$ is the acceleration due to gravity). We also show how for pressure distributions broader than a few capillary lengths, the result obtained by Havelock for the wave resistance in the particular case of pure gravity waves (i.e., $γ= 0$) is progressively recovered.

physics.flu-dyn↗

arXiv2011

Capillary-Gravity Waves on Depth-Dependent Currents: Consequences for the Wave Resistance

We study theoretically the capillary-gravity waves created at the water-air interface by a small two-dimensional perturbation when a depth-dependent current is initially present in the fluid. Assuming linear wave theory, we derive a general expression of the wave resistance experienced by the perturbation as a function of the current profile in the case of an inviscid fluid. We then analyze and discuss in details the behavior of the wave resistance in the particular case of a linear current, a valid approximation for some wind generated currents.

cond-mat.soft↗