An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

Nonlinear evolution of thin liquid films dewetting near soft elastomeric layers

The nonlinear evolution of thin liquid films dewetting near soft elastomeric layers is examined in this work. Evolution equations are derived by applying the lubrication approximation and assuming that van der Waals forces in the liquid cause the dewetting and that the solid can be described as a linear viscoelastic material. Two cases are examined: (i) a liquid layer resting on an elastomer bounded from below by a rigid substrate, and (ii) an elastomer overlying a thin liquid film bounded from below by a rigid substrate. Linear stability analysis is carried out to obtain asymptotic relations which are then compared against solutions of the full characteristic equations. In the liquid-on-solid case, numerical solutions of the evolution equations show that van der Waals forces cause thinning of the liquid film and thickening of the elastomeric solid beneath film depressions. Inclusion of a short-range repulsive force suggests that regular patterns may form in which ridges of fluid rest on depressions in the solid. In the solid-on-liquid case, the van der Waals forces cause the solid layer to break up before the liquid film can dewet. The results presented here support the idea that the dewetting of thin liquid films might be exploited to create topographically patterned surfaces on soft polymeric solids.     

Interplay of Electronic Structure and Bulk Properties in 2D and 3D Ternary Carbonitrides from First Principles

The changes in electronic structure and hardness as inferred from the bulk modulus are investigated for model structures of ternary compounds XC₃N₃ (X = B, Al, P, As, Ga) within the framework of density functional theory (DFT). The optimisations of the proposed two‐ (2D) and three‐dimensional (3D) structures and the calculations of the bulk moduli are performed by a pseudo potential method. The electronic structures are calculated with the augmented sphere wave method (ASW). The obtained hardness for 2D BC₃N₃ system (B₀ ～ 220 GPa) points to a magnitude close to that of graphitic C₃N₄. For heavier X atoms it decreases rapidly. This is equally observed for the 3D systems examined in the β‐C₃N₄ structure for which B₀(β‐BC₃N₃) amounts to ～330 GPa. Within the magnitude of the well known hard material cubic BN, the BC₃N₃ phases can be predicted as candidates for ultra hard materials. The electronic effect induced by the chemical nature of the X substitutional was examined according to its position in the periodic table i.e. X_III or X_V. Both, band structures and the electron localisation function (ELF) were used for this analysis. The ELF plots show a decreasing covalency with heavier X‐atoms. Potential applications of the devised systems are proposed such as dopings with atoms (Li, rare gas) and molecules (N₂).     

Compressive advection and multi‐component methods for interface‐capturing

This paper develops methods for interface‐capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi‐component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P₁DG‐P₂(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface‐capturing scheme based on compressive control volume advection methods and high‐order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many‐material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows. Copyright © 2015 John Wiley & Sons, Ltd.     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

Contact phase modulation method for acoustic nonlinear parameter measurement in solid

In this work, a new method to measure in contact the nonlinearity parameter beta of solid plates is presented. A high frequency (HF) tone-burst signal of 20 MHz is inserted in the material by a contact-transducer (with a suitable coupling). A low frequency (LF) pulse (2.5 MHz) is applied to the other face, in the opposite direction, so that the nonlinear interaction of the two waves takes place during the back propagation toward the HF transducer. This collinear interaction creates a phase modulation of the HF tone-burst which is proportional to the beta coefficient and the particle velocity of the LF wave. To determine this particle velocity, in time domain, an extended self-reciprocity calibration of the contact LF transducer is used. A numeric phase demodulation is then performed, giving the beta coefficient of the sample. The proposed method is validated by nonlinearity parameter measurements in Fused Silica. The nonlinear parameter of Fused Silica measured is found to be in good agreement with the literature, and specially the negative sign of this parameter.     

Dewetting behavior of aqueous cationic surfactant solutions on liquid films

Previous experimental work has shown that the spreading of a drop of aqueous anionic surfactant solution on a liquid film supported by a negatively charged solid substrate may give rise to a fingering instability (Afsar-Siddiqui, A. B.; Luckham P, F.; Matar, O. K. Langmuir 2003, 19, 703-708). However, upon deposition of a cationic surfactant on a similarly charged support, the surfactant will adsorb onto the solid-liquid interface rendering it hydrophobic. Water is then expelled from the hydrophobic regions, causing film rupture and dewetting. In this paper, experimental results are presented showing how the surfactant concentration and film thickness affect the dewetting behavior of aqueous dodecyltrimethylammonium bromide solutions. At low surfactant concentrations and large film thicknesses, the film ruptures at a point from which dewetting proceeds. At higher concentrations and smaller film thicknesses, the ruptured region is annular in shape and fluid moves away from this region. At still higher concentrations and smaller film thicknesses, the deposited surfactant forms a cap at the point of deposition that neither spreads nor retracts. This variation in dewetting mode is explained by considering the relative Marangoni and bulk diffusion time scales as well as the mode of assembly of the surfactant adsorbed on the solid surface.