Theory Of Capillarity Research Articles

Limit of accuracy in laser fabrication with metal powder

The research presented in this paper focuses on the laser-powder interaction. Through the experiment with metal powder in micrometers, we found that, in an invariable laser power density, the thickness of the final fabricated thin wall was similar to the geometrical dimension of the powder line, but could be much greater than the laser focus spot, even greater than two orders of magnitude. Furthermore, this paper showed that, the unmelted and semi-fused particles were concentrated. Thus, in this paper, combining the optical scattering theory with capillarity and infiltration theory pointed out the inducement effect of laser and the self-melting of powder. Based on the experimental phenomena and theory, we get our own ideas on the laser micro-fabrication.

Hybrid modeling of interfacial region thermophysics and intrinsic stability of thin free liquid films

The film rupture process that dictates merging of adjacent bubbles is particularly important in nucleate boiling heat transfer, bubbly two-phase flow in small tubes, and the mechanisms that dictate the Leidenfrost transition. To understand the mechanisms of bubble merging in nanostructured boiling surfaces and in nanotubes, it is useful to explore film stability and onset of rupture at the molecular level. This paper reports the results of such an investigation using a hybrid analysis scheme that combines a new formulation of capillarity theory for free liquid films with molecular dynamics (MD) simulations that use similar interaction potentials. Two forms of our molecular film capillarity theory are developed here: one for non-polar fluids based on a Lennard-Jones interaction potential, and a second specifically for water using a modified treatment of the SPC/E interaction potential that accounts for water dipole interactions. The hybrid model has the advantage that the capillarity theory provides theoretical relationships among parameters that govern film structure and thermophysical behavior, while the companion MD simulations allow more detailed molecular level exploration of the film thermophysics. Results obtained with the hybrid model indicate that wave instability predominates as an onset of rupture mechanism for liquid films of macroscopic extent, but for free liquid films with nanoscale lateral extent (in, for example, nanostructured boiling surfaces), lack of core stability is more likely to be the mechanism. The implications of these predictions for film rupture and bubble merging in nanostructured surfaces and nanotubes are examined in detail.

Capillarity theory for the fly-casting mechanism

Biomolecular folding and function are often coupled. During molecular recognition events, one of the binding partners may transiently or partially unfold, allowing more rapid access to a binding site. We describe a simple model for this fly-casting mechanism based on the capillarity approximation and polymer chain statistics. The model shows that fly casting is most effective when the protein unfolding barrier is small and the part of the chain which extends toward the target is relatively rigid. These features are often seen in known examples of fly casting in protein-DNA binding. Simulations of protein-DNA binding based on well-funneled native-topology models with electrostatic forces confirm the trends of the analytical theory.

Extension of the Neoclassical Theory of Capillarity to Advanced Cubic Equations of State

The neoclassical Redlich–Kwong (RK) theory of capillarity is extended to the Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) equations of state. Use of the SRK and PR fluid models results in poorer predictions of interfacial tension compared to the RK model because the RK overpredicts vapor densities to a greater extent than SRK or PR, reducing the corresponding RK interfacial tension predictions to be in better agreement with accepted values. The limits of the theory applied to cubic equations are reached by proposing modified SRK and PR fluid models based on a known interfacial tension datum and knowledge of the fluid molecular structure. These modified fluid models provide improved accuracy in interfacial tension predictions of 6% (SRK) and 10% (PR) for the fluid set in this study when compared to applying the RK model (17%). These modified fluid models also provide improved predictions of bulk liquid density, but sacrifice accuracy in pressure and vapor density predictions.

Translation-rotation correction factor in the theory of homogeneous nucleation

An analytical formula for the correction factor which is to multiply the classical expression for the nucleation rate to account the translation and rotation of the critical nucleus is proposed. The formula is based on the Reiss approach considering the contribution from the clusters translational degrees of freedom, Frenkel's kinetic theory of liquids, and Kusaka's theory. Using this formula we determined the correction factor for argon vapor-to-liquid phase nucleation for the temperature range 80-110 K. These evaluations are in a good agreement with the correction factor calculated numerically by Kusaka (2006). Basing on the Gibbs theory of capillarity it is also shown that for the case of ideal gas-to-liquid nucleation the exponent in the classical formula for the rate of nucleation is strictly equal to the reversible work of drop formation.

Concentration profile of vapor—liquid interface for spherical drops

The modified lattice-gas model is used to construct the model and the concentration profiles of the liquid—vapor for spherical drops of different size. A monotonic character of the temperature dependence of the width of the transition layer between the liquid and the vapor is demonstrated. The dependence of the surface tension on the drop size was studied. The calculation was carried out in the quasichemical approximation, which takes into account the correlation effects of the neighboring interacting molecules. The results are in qualitative agreement with earlier density functional theory calculations and calculations by the van der Waals theory of capillarity. The numerical analysis of the molecular model of the spherical drop gives two types of solution, which correspond to equilibrium and metastasble states of the drop.

First correction to surface tension for the curvature of an interface

Tolman parameter δT, which determines the first correction to surface tension for the interface curvature, is calculated in molecular-dynamic experiments performed for Lennard-Jones fluid within the temperature range from the critical to the triple point (and slightly below). It is shown that parameter δT is positive and slightly depends on temperature; its absolute magnitude is no larger than 0.1–0.2 molecular diameters and does not coincide with the distance between the equimolecular dividing surface and the surface of tension in a flat interfacial layer, as calculated through the first moment of the pressure tensor. The results of the moleculardynamic experiments are compared with the δT values calculated in terms of the extended version of the van der Waals theory of capillarity. It is established that taking into account terms of higher orders than the squared density gradient in the expansion of the free energy of an inhomogeneous system does not reverse the negative sign at δT and slightly affects its value.

Wetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field model

We present a phase field approach to wetting problems, related to the minimization of capillary energy. We discuss in detail both the Γ-convergence results on which our numerical algorithm are based, and numerical implementation. Two possible choices of boundary conditions, needed to recover Young's law for the contact angle, are presented. We also consider an extension of the classical theory of capillarity, in which the introduction of a dissipation mechanism can explain and predict the hysteresis of the contact angle. We illustrate the performance of the model by reproducing numerically a broad spectrum of experimental results: advancing and receding drops, drops on inclined planes and superhydrophobic surfaces.

Dynamics of extrusion landslides on bank slopes

The mathematical models proposed in this work based on concepts and methods of the mechanics of solid bodies, continuous medium mechanics, and the theory of capillarity and surface processes make it possible to describe quantitatively these processes and determine the parameters of “extrusion” landslides at all their development stages.

Propagating wave patterns for the ‘resonant’ Davey–Stewartson system

The resonant nonlinear Schrödinger (RNLS) equation exhibits the usual cubic nonlinearity present in the classical nonlinear Schrödinger (NLS) equation together with an additional nonlinear term involving the modulus of the wave envelope. It arises in the context of the propagation of long magneto-acoustic waves in cold, collisionless plasma and in capillarity theory. Here, a natural (2 + 1) (2 spatial and 1 temporal)-dimensional version of the RNLS equation is introduced, termed the ‘resonant’ Davey–Stewartson system. The multi-linear variable separation approach is used to generate a class of exact solutions, which will describe propagating, doubly periodic wave patterns.

Molecular-Dynamics Investigation of Phase Equilibrium and Surface Tension in Argon−Neon System

The molecular-dynamics method has been used for calculating the density profiles of the mixture argon−neon, surface tension, and adsorption in systems of 4096−8957 Lennard−Jones particles at a reduced temperature T* = kBT/εα≃0.7 ± 0.01 and a pressure up to p* = pσα3/εα = 0.6, where σα and εα are parameters of the argon potential. The results of calculating phase-equilibrium parameters are compared with data for a single-fluid model of a solution. The paper discusses the applicability of an extended version of the van der Waals capillarity theory to the description of the surface tension of a gas-saturated liquid.

Mesoscopic model of volume changes due to moisture variations in porous materials

Porous solids swell and shrink in dependence on air humidity. Based on the independent pore model, the extended theory of capillarity based on the augmented Young–Laplace equation is used to evaluate the swelling and shrinkage of porous solids. Assuming cylindrical pores, theoretical results on the volume changes are in a fairly good agreement with experimental data for vycor glass, but they do not describe the behaviour of hardened cement paste. Comparing experimental data and the theoretical evaluations, we suggest that the discrepancies result from a very broad pore size distribution and the occurrence of a large amount of slit pores in cementitious materials.

CMC capillary surfaces at reentrant corners

For a capillary graph in a vertical cylinder  ◊ R R 3 , the existence of a reentrant corner P 2 @ makes the determination of the continuity at P (or the behavior of the radial limits at P) of the solution problematic. Since continuity is the necessary consequence of the existence of a “central fan” of radial limits under certain conditions, the determination of necessary and sufficient conditions for the existence of a central fan is a very important open question in the mathematical theory of capillarity. Examples by Finn and Shi suggest that “central fans” may be very rare in the sense that arbitrarily small perturbations can eliminate them. In this note we obtain examples of capillary graphs (with zero mean curvature), each of which is continuous or has a central fan at a reentrant corner.

Molar surface energy and Eötvös’s law

The apparatus of classical capillarity theory does not explicitly contain the general dimensional equation of its own scalar variables. Introduction of such an equation permits the interpretation of experimental physical quantities characterizing the bulk phases from the point of view of the capillary interaction. Eotvos’s law is one of the basic empirical equations of capillarity relating to the molar-free energy of the free liquid surface. The extended theory also enables Eotvos’s Law to be deduced in a relatively simple way, proving that the heuristic potential of this parametric method goes beyond the limits of traditional theory.

Homogeneous nucleation: Classical formulas as asymptotic limits of the Cahn-Hilliard approach

Classical expressions for the critical cluster work of formation approximate the nonclassical expressions based in the density functional theory of capillarity for the limit of low supersaturation degrees. However, the ratio between classical and nonclassical expressions for nucleation rates grows as the supersaturation degree decreases. Here, with the aim to obtain simple and more accurate expressions that approximate the modern nucleation rate formulas, an asymptotic expansion of the Cahn-Hilliard expression of the critical work of formation is developed within the limit of low supersaturation. In such asymptotic expansion, terms up to third order are retained. The ratios between the corrected classical expressions and the nonclassical ones are now decreasing for supersaturation degrees tending to zero. However, the corrected approximate formulas are as difficult to handle as the exact Cahn-Hilliard expressions. When only the two first low-order terms of the asymptotic expansion are retained, a simpler corrected classical expression is obtained but it can only approximate nonclassical expressions up to order unity. Finally, using a Becker-Doring model of nucleation, the kinetic prefactor of the critical nuclei rate of formation is modeled consistently with the Cahn-Hilliard approach to the critical work of formation.

On the Capillary Problem for Compressible Fluids

Classical capillarity theory is based on a hypothesis that virtual motions of fluid particles distinct from those on a surface interface have no effect on the form of the interface. That hypothesis cannot be supported for a compressible fluid. A heuristic reasoning suggests that even small amounts of compressibility could have significant effect on surface behavior. In an earlier work, Finn took a partial account of compressibility, and formulated a variant of the classical capillarity equation for fluid surface height in a vertical capillary tube; he was led to a necessary condition for existence of a solution with prescribed mass in a tube closed at the bottom. For a circular tube, he proved that the condition also suffices, and that solutions are uniquely determined for any contact angle γ.

A Molecular Dynamics Study on Stability and Thermophysical Properties of Nanoscale Liquid Threads

The thermophysical properties and stability characteristics of liquid threads are investigated by molecular dynamics (MD) simulations. Density and pressure profiles are obtained, and properties such as equimolar dividing radius, radius of surface of tension, and surface tension are determined. The relationship between the surface tension and thread radius based on the Gibbs theory of capillarity is derived for the liquid thread, and compared with MD simulation results. It shows that the surface tension rapidly deceases as the radius approaches the molecular scale. The surface tension of a simple binary mixture is also considered. The surface tension relative to that of one-component fluid decreases with increasing the binary ratio of the solute with a strong affinity. For a given binary ratio, the surface tension increases gradually as the affinity coefficient reaches 1.6 and decreases rapidly as it gets larger. The critical wavelength of perturbation for the instability is shown to be smaller than is predicted by the classical theory.

The contact angle in capillarity

In 1805, Thomas Young gave a reasoning to support the view that the contact angle at a solid/liquid/gas interface is a physical constant depending only on the materials, and in no other way on the particular configuration considered. That conclusion has become one of the underpinnings of both classical and modern capillarity theory. The present paper raises some questions about the reasoning and some of its consequences, and offers partial answers.

On the theory of capillarity of three-phase disperse systems

The distribution of a liquid over the height of a vertical column (with the lower part immersed in a wetting liquid) of close-packed solid spherical particles is studied. For such a system, the equilibrium distribution of the liquid in the three-phase region with a high expansion ratio is shown to be described by the same formulas as for a two-phase disperse system (high-expansion monodisperse foam), but the radius of spherical particles is used in the three-phase case instead of the radius of polyhedral foam cells of equivalent volume. Linear, surface, and bulk capillary forces acting in model three-phase systems with liquid “collars” between close-packed spherical particles are considered. Specific forces of capillary adhesion are shown to be independent of the specific volume of the liquid if it is small enough, but they increase with decreasing size of the particles. In the two-dimensional case with hexagonal packing of particles, these forces are also independent of the particle size.

Properties of argon liquid-vapor interface

The short-wave cutoff boundary of the capillary wave spectrum is established. Effective thickness L b of the “bare” density profile in the interfacial layer is calculated according to experimental data on the ellipticity ratio of reflected light. The free parameters of the extended van der Waals theory of capillarity are determined. The positions of the equimolecular dividing surface and tension surface are calculated, as well as the temperature dependence of the Tolman parameter.