Short-time dynamics of partial wetting

When a liquid drop contacts a wettable surface, the liquid spreads over the solid to minimize the total surface energy. The first moments of spreading tend to be rapid. For example, a millimeter-sized water droplet will wet an area having the same diameter as the drop within a millisecond. For perfectly wetting systems, this spreading is inertially dominated. Here we identify that even in the presence of a contact line, the initial wetting is dominated by inertia rather than viscosity. We find that the spreading radius follows a power-law scaling in time where the exponent depends on the equilibrium contact angle. We propose a model, consistent with the experimental results, in which the surface spreading is regulated by the generation of capillary waves.     

Macroscopic phase-field model of partial wetting: bubbles in a capillary tube

Drops and bubbles are nonspreading, local, compactly supported features. They are also equilibrium configurations in partial wetting phenomena. Yet, current macroscopic theories of capillary-dominated flow are unable to describe these systems. We propose a framework to model multiphase flow in porous media with nonspreading equilibrium configurations. We illustrate our approach with a one-dimensional model of two-phase flow in a capillary tube. Our model allows for the presence of compactons: nonspreading steady-state solutions in the absence of external forces. We show that local rate dependency is not needed to explain globally rate-dependent displacement patterns, and we interpret dynamic wetting transitions as the route from equilibrium, capillary-dominated configurations, towards viscous-dominated flow. Mathematically, these transitions are possible due to nonclassical shock solutions and the role of bistability and higher-order terms in our model.     

微纳复合结构表面稳定润湿状态及转型过程的热力学分析

自然界中的微纳复合结构超疏水表面由于其独特的润湿性质引起了人们的广泛关注, 大量实验研究表明了仿生人工微纳复合结构表面润湿性能的优越性, 然而液滴在微纳复合结构表面的润湿状态和转型过程的理论研究还并不完善. 本文首先用热力学方法分析了液滴在微纳复合结构表面可能存在的所有状态(四种稳定润湿状态和五种亚稳态到稳定态转型中的过渡态), 推导出了相应的能量表达式及表观接触角方程; 基于最小能量原理, 确定液滴在微纳复合结构表面的稳定状态, 较以往模型相比, 能够更好的预测已有的实验结果; 其次研究了微纳结构尺寸对稳定润湿状态和亚稳态到稳定态转型过程的影响; 最后提出了微纳复合结构表面设计原则, 即确定“超疏水稳定区”尺寸范围, 为超疏水表面的制备提供理论依据.     

Dynamic modelling of the deformed contact line under partial wetting conditions: Quasi-static approach

We study numerically the motion of contact lines in the context of the “Wilhelmy plate" experiment: a vertical solid plate is withdrawn at constant velocity from a bath of liquid. We apply the contact line dissipation quasi-static model to the relaxation of an initially periodically deformed contact line. The obtained numerical data are compared to the experimental results [1] showing a good agreement.     

Morphological stability analysis of the epitaxial growth of a circular island: Application to nanoscale shape control

In this paper, we present a comprehensive morphological stability analysis of a single, epitaxially growing, perturbed circular island by using a Burton-Cabrera-Frank (BCF) island dynamics model. We show that there exists a critical deposition flux for which a single mode perturbation remains unchanged. In the absence of an additional far-field mass flux, there exists a naturally stabilizing radius, so that beyond this radius, growth is always stable. Up to this radius, taking fluxes larger than the critical flux results in instability. The presence of kinetics makes sufficiently small islands grow stably, even without line tension or surface diffusion. The presence of desorption further introduces a range of parameters and island radii for which both stable and unstable shrinkage may occur. The presence of a far-field mass flux in the BCF model can eliminate the naturally stabilizing radius and unstable growth may be achieved for a wide range of island radii. We then demonstrate how these results may be exploited to control the shape of the island using the deposition flux and far-field mass flux as control parameters.     

Soliton solutions and stability analysis for some conformable nonlinear partial differential equations in mathematical physics

This research presents soliton solutions and stability analysis to some conformable nonlinear partial differential equations (CNPDEs). The CNPDEs equations in this paper are conformable Cahn–Allen and conformable Zoomeron equations. The powerful sine-Gordon method is used to carry out the soliton solutions for these equations. The aspects of stability analysis for the considered equations is investigated using the linear stability technique. The sine-Gordon method proves to be efficient and effective for the extraction of soliton solutions for different types of CNPDEs.     

Bonn-Gatchina partial wave analysis

The present status of the Bonn-Gatchina partial wave analysis of the photoproduction and pion induced data is presented. An observation of signals which can be associated with new baryon resonances and possible interpretations of the baryon spectrum is discussed.     

Bonn-Gatchina partial wave analysis

The present status of the Bonn-Gatchina partial wave analysis of the photoproduction and pion induced data is presented. An observation of signals which can be associated with new baryon resonances and possible interpretations of the baryon spectrum is discussed.     

A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio

This paper reports a new numerical scheme of the lattice Boltzmann method for calculating liquid droplet behaviour on particle wetting surfaces typically for the system of liquid–gas of a large density ratio. The method combines the existing models of Inamuro et al. [T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198 (2004) 628–644] and Briant et al. [A.J. Briant, P. Papatzacos, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion in a liquid–gas system, Philos. Trans. Roy. Soc. London A 360 (2002) 485–495; A.J. Briant, A.J. Wagner, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: I. Liquid–gas systems. Phys. Rev. E 69 (2004) 031602; A.J. Briant, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: II. Binary fluids, Phys. Rev. E 69 (2004) 031603] and has developed novel treatment for partial wetting boundaries which involve droplets spreading on a hydrophobic surface combined with the surface of relative low contact angles and strips of relative high contact angles. The interaction between the fluid–fluid interface and the partial wetting wall has been typically considered. Applying the current method, the dynamics of liquid drops on uniform and heterogeneous wetting walls are simulated numerically. The results of the simulation agree well with those of theoretical prediction and show that the present LBM can be used as a reliable way to study fluidic control on heterogeneous surfaces and other wetting related subjects.     

H2O on Pt(111): structure and stability of the first wetting layer

We study the structure and stability of the first water layer on Pt(111) by variable-temperature scanning tunneling microscopy. We find that a high Pt step edge density considerably increases the long-range order of the equilibrium √37 × √37R25.3°- and √39 × √39R16.1°-superstructures, presumably due to the capability of step edges to trap residual adsorbates from the surface. Passivating the step edges with CO or preparing a flat metal surface leads to the formation of disordered structures, which still show the same structural elements as the ordered ones. Coadsorption of Xe and CO proves that the water layer covers the metal surface completely. Moreover, we determine the two-dimensional crystal structure of Xe on top of the chemisorbed water layer which exhibits an Xe-Xe distance close to the one in bulk Xe and a rotation angle of 90° between the close-packed directions of Xe and the close-packed directions of the underlying water layer. CO is shown to replace H(2)O on the Pt(111) surface as has been deduced previously. In addition, we demonstrate that tunneling of electrons into the antibonding state or from the bonding state of H(2)O leads to dissociation of the molecules and a corresponding reordering of the adlayer into a √3 × √3R30°-structure. Finally, a so far not understood restructuring of the adlayer by an increased tunneling current has been observed.     

Morphological stability of two-dimensional new phase precipitate located at the grain boundary

The diffusion growth of two-dimensional new phase precipitate located at the grain boundary of a finite thickness is considered taking into account diffusion fluxes of impurity atoms from the bulk of a grain depth to the grain boundary. The stability of the growing precipitate of a relatively small radius to small random perturbations of its shape is analyzed taking into account the surface kinetics of the impurity atoms on the grain boundary-precipitate interface. The threshold radii of the precipitate are found, above which the amplitude of the shape distortion and the amplitude of the relative shape deformation of the precipitate rise.     

A new model for thermodynamic analysis on wetting behavior of superhydrophobic surfaces

Superhydrophobic surfaces have shown inspiring applications in microfluidics, and self-cleaning coatings owing to water-repellent and low-friction properties. However, thermodynamic mechanism responsible for contact angle hysteresis (CAH) and free energy barrier (FEB) have not been understood completely yet. In this work, we propose an intuitional 3-dimension (3D) droplet model along with a reasonable thermodynamic approach to gain a thorough insight into the physical nature of CAH. Based on this model, the relationships between radius of three-phase contact line, change in surface free energy (CFE), average or local FEB and contact angle (CA) are established. Moreover, a thorough theoretical consideration is given to explain the experimental phenomena related to the superhydrophobic behavior. The present study can therefore provide some guidances for the practical fabrications of the superhydrophobic surfaces.     

The non-linear stability of front solutions for parabolic partial differential equations

For the Ginzburg-Landau equation and similar reaction-diffusion equations on the line, we show convergence ofcomplex perturbations of front solutions towards the front solutions, by exhibiting a coercive functional.     

Elastic stability of columns on partial elastic foundations under subtangential loading

Divergence and flutter instability of a cantilevered beam on a partial elastic foundation subjected to a subtangential load at the free end are investigated. The dependence of divergence and flutter critical loads on the tangency coefficient is studied parametrically to illustrate the effects of the extent, position, and modulus of the partial foundation. Particular attention is paid to the stabilizing and destabilizing effects of the various parameters.