Capillarity Phenomena Research Articles

The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions

We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation−div(∇u/1+|∇u|2)=−au+b/1+|∇u|2, where a,b>0 are given parameters and Ω is a bounded Lipschitz domain in RN. This equation appears in the modeling theory of capillarity phenomena for compressible fluids and in the description of the geometry of the human cornea.

Vibration of structures containing compressible liquids with surface tension and sloshing effects. Reduced-order model

This paper deals with the development of the linear vibration of a general viscoelastic structure, with a local wall acoustic impedance, containing an inviscid compressible liquid (but with an additional volume dissipative term), with surface tension (capillarity) and sloshing effects, and neglecting the effects of internal gravity waves and the elastogravity operator. The sloshing problems of incompressible liquids with capillarity effects in elastic structures exhibit a major difficulty induced by the boundary contact conditions on the triple line because the capillarity forces are forces per unit length while the elastic forces are forces per unit surface. The proposed framework has the following novel features: (i) introducing a new appropriate boundary condition for the contact angle condition compatible with a deformable structure considered here as viscoelastic, (ii) considering a compressible liquid while incompressibility hypothesis is generally used for FSI problems including capillarity phenomena, and (iii) constructing a reduced-order model for the computational coupled problem.

Cobalt capping on WC–Co hardmetals. Part I: A mechanism explaining the presence or absence of cobalt layers on hardmetal articles during sintering

A reason for the presence or absence of Co thin layers on a surface of WC–Co hardmetals during sintering has been a riddle for a long time. As a result of sintering, such thin shiny Co layers are sometimes present on the surface of WC–Co articles and their formation is referred to as “Co capping” in the literature. Although the cobalt capping phenomenon is discussed in the literature, its mechanism is not well understood and there is no information on its technological implementations. Here we propose a new mechanism explaining the presence or absence of cobalt layers on hardmetal articles during sintering. The proposed mechanism is based on considering wetting phenomena of WC by liquid Co on the surface of hardmetal articles and capillarity phenomena acting on the liquid Co in narrow channels between WC grains in the hardmetal near-surface layer. The mechanism explains all the phenomena of the Co layer formation during sintering of various hardmetal grades followed by either fast or slow cooling.

A continuum model for deformable, second gradient porous media partially saturated with compressible fluids

In this paper a general set of equations of motion and duality conditions to be imposed at macroscopic surfaces of discontinuity in partially saturated, solid-second gradient porous media are derived by means of the Least Action Principle. The need of using a second gradient (of solid displacement) theory is shown to be necessary to include in the model effects related to gradients of porosity. The proposed governing equations include, in addition to balance of linear momentum for a second gradient porous continuum and to balance of water and air chemical potentials, the equations describing the evolution of solid and fluid volume fractions as supplementary independent kinematical fields. The presented equations are general in the sense that they are all written in terms of a macroscopic potential Ψ which depends on the introduced kinematical fields and on their space and time derivatives. These equations are suitable to describe the motion of a partially saturated, second gradient porous medium in the elastic and hyper-elastic regime. In the second part of the paper an additive decomposition for the potential Ψ is proposed which allows for describing some particular constitutive behaviors of the considered medium. While the potential associated to the solid matrix deformation is chosen in the form proposed by Cowin and Nunziato (1981) and Nunziato and Cowin (1979) and the potentials associated to water and air compressibility are chosen to assume a simple quadratic form, the macroscopic potentials associated to capillarity phenomena between water and air have to be derived with some additional considerations. In particular, two simple examples of microscopic distributions of water and air are considered: that of spherical bubbles and that of coalesced tubes of bubbles. Both these cases are suitable to describe capillarity phenomena in porous media which are close to the saturation state. Finally, an example of a simple microscopic distribution of water and air giving rise to a macroscopic capillary potential depending on the second gradient of fluid displacement is presented, showing the need of a further generalization of the proposed theoretical framework accounting for fluid second gradient effects.

Ni-Serrin type equations arising from capillarity phenomena with non-standard growth

In the present paper, in view of the variational approach, we discuss a Ni-Serrin type equation involving non-standard growth condition and arising from the capillarity phenomena. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.

Critical Capillary Absorption of Current‐Melted Silver Nanodroplets into Multiwalled Carbon Nanotubes

Capillarity phenomena at the nanometer scale are investigated by real-time experiments. The capillary absorption of a molten Ag droplet can occur only when the ratio of the droplet's size Di to the inner diameter Dt of a multiwalled carbon nanotube (CNT) goes below a critical value, and this value decreases as the CNT's inner diameter reduces.

Surface tension of γ-TiAl-based alloys

Within the Integrated Project IMPRESS, funded by the EU, a concerted action was taken to determine the thermophysical properties of a γ-TiAl-based alloys, suitable for casting of large turbine blades for aero-engines and stationary gas turbines. The challenge was to develop a castable alloy, free of grain refiners and susceptible to heat treatment. Owing to the high reactivity of this class of alloys, many difficulties were encountered to process the liquid phase in a crucible. This prevented also the measurements of specific heat, viscosity and electrical conductivity in the liquid phase. However, surface tension and density could be measured using container-less techniques. For the surface tension determination, both the oscillating droplet method by the electromagnetic levitation as well as a combined method using two methodologies in one test (i.e. the pendant drop and sessile drop) by an advanced experimental complex that has been designed for investigations of high temperature capillarity phenomena were applied. All the quantities have been obtained as a function of temperature, in some cases also in the undercooled liquid. In this article, we report a comparative discussion on the results obtained for the surface tension of Ti–Al–Nb and Ti–Al–Ta alloys, together with the corresponding theoretical values calculated by thermodynamic models.

Experimental complex for investigations of high temperature capillarity phenomena

The paper presents the description of an experimental complex that has been designed for investigations of high temperature capillarity phenomena by various testing methods (classical sessile drop, pendant drop, dispensed drop, sandwiched drop, transferred drop, drop sucking, drop pushing, drop smearing or rubbing) at a temperature of up to 2100 °C under vacuum of up to 10 −7 hPa or in protective atmosphere (static or flowing gas with controlled rate at required level of pressure). Several examples of high temperature wettability tests are discussed in order to demonstrate the wide testing possibilities of the new experimental complex.

Wetting and minimal surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface and then derive simple diagrammatic rules to calculate the nonlinear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasilocal--i.e., that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.

Migration of liquid phase in low temperature sintering of AlN

In the process of low-temperature sintering of AlN ceramics, the reaction of the sintering aids YF3 and CaF2 with superficial Al2O3, inherently contained in AlN lattice, results in formation of liquid phase. Nevertheless, the uniformly dispersed liquid phase is prone to migrate from the bulk to the surface of the samples, opposing densification. The analysis of the experimental results indicates that fresh liquid phase can continuously arrive from the bulk to the surface due to chemical reactions and crystallization which occur at the surface as well as wettalibilty and capillarity phenomena. The surface is depleted of liquid phase since the latter is consumed due crystallization and carbothermal reduction reactions with the elements of the atmosphere of the furnace N2 and C, resulting in formation of a dense layer of crystals of Al2Y4O9, CaYAl3O7 and Y2O3, grown perpendicularly to the surface. The chemical and structural features of this newly formed crystalline surface layer generate a significant difference of the wetting regimes and the capillary forces between the surface and the bulk, favouring pumping of the liquid from the bulk to the surface.

Statistical mechanics of fluids adsorbed in wedges and at edges

Some of the history and modern significance of wetting phenomena involving wedge and edge geometries is discussed. The adsorption of fluids onto structured surfaces or colloidal objects yields rich behaviour, including new classes of interfacial phase transitions and alternative ways to consider classical capillarity. I describe how the equilibrium properties of these systems can be described with exact virial theorems obtained from statistical mechanics, that are of immediate relevance to computer simulation procedures, density functional theories and experiments capable of measuring inhomogeneous fluid density profiles. In wedge geometry the physics behind these sum rules can be illustrated with the use of the Derjaguin approximation, familiar to colloidal science. Three specific examples of the utility of statistical mechanics to this field are described: (i) a sum rule analysis is provided of capillarity phenomena involving two-phase coexistence within a linear triangular wedge, whose walls could be chemically distinct, (ii) an example emphasizing that experimental systems will typically involve both wedge and edge geometries that cannot be readily separated and (iii) an example concerning adsorption within an annular wedge, taken from colloidal science.

Two-Phase Flow and the Capillarity Phenomenon in Porous Solids – A Continuum Thermomechanical Approach

Two-phase flow and capillarity phenomenon in porous solids, well known in physics and engineering, are treated from a rigorous continuum thermomechanical point of view for the first time. A ternary model, consisting of a porous solid phase, a liquid phase, and a gas phase, is investigated within the framework of thermodynamics. The main result of the evaluation of the entropy principle turns out to be that the interaction forces between the solid, gas, and liquid phases are dependent on the free Helmholtz energy functions of the corresponding phases and on the gradient of the liquid density. The classical result for the driving volume force for raising a water column in a narrow tube against the force of gravity is contained in the general investigation.

Multiphase flow in a capillary porous medium

Based on the theory of porous media, a calculation concept for the multiphase flow in a capillary porous medium will be presented. We will exclusively investigate the rise of liquids in porous bodies due to the capillarity phenomenon. The field equations used consist of the mechanical balance equations and the physical constraint conditions. The treatment of the capillary problem, based on thermomechanical investigations, yields the result that the capillarity force is a volume interaction force and depends on the free Helmholtz energy functions of the phases and the density gradient of the liquid. With respect to the aforementioned outcome, further constitutive relations for the ternary model are developed. The aim of this investigation is the numerical simulation of the behavior of liquid and gas phases in a rigid porous body at rest. Therefore, the needed weak formulations of the governing field equations, i.e. the balance equations of mass and the balance equations of momentum of the liquid and gas phases, will be given. The usefulness of the proposed theory will be demonstrated with an example.

Theoretical Approach for Determining Pore Characteristics Between Fibers

This theoretical work describes pores between fibers in general fiber assemblies. The basic idea is to treat the pores between fibers—under certain assumptions—as air fibers surrounded by fictional borders. Different pore characteristics are formulated from basic definitions of fiber assemblies. It is possible to find alternative theoretical definitions for pores of any shape by introducing the so-called fictive pore borders. Four different definitions of pores—conventional pores, pores with a constant shape factor, pores with a constant length, and generalized pores—are mathematically derived based on the geometric structural characteristics of any fiber assembly such as packing density, equiv alent pore diameter, pore length, and other variables. The well-known Hagen-Poiseuille law of flow and the Carmen-Kozeny equation are discussed in the course of deriving equations. Possible applications of these derived equations in the fields of capillarity phenomenon, fluid flow, and filtration are introduced.

Transport of fluids in capillary porous solids

AbstractCapillarity is a well known phenomenon in physics and engineering. The term denotes the transport of liquids and gas, against the force of gravity in narrow tubes, cracks and pores, caused by the intermolecular forces of cohesion and adhesion of the constituents involved. We will exclusively investigate the rise of liquids in porous bodies due to the capillarity phenomenon. Well‐known examples are the capillary rise in drying processes in soils with small pores and the moisture motion in walls consisting of bricks or concrete. The treatment of the capillary problem, based on thermomechanical investigations, yields the result that the capillarity force is a volume interaction force and depends on the free Helmholz energy functions of the solid phases and the density gradient of the liquid. The aim of this investigation is the numerical simulation of the behavior of liquid and gas phases in a rigid porous body at rest. An example will demonstrate the usefulness of the proposed theory.

Theoretical Prediction of the Soil Thermal Conductivity at Moderately High Temperatures

The theoretical model of the present paper assumes the unit cell of the porous medium as composed of a cubic space with a cubic solid particle at the center. The thermal conductivity is evaluated by solving the heat conduction equation with the assumption of parallel isotherms within the cubic space. The liquid water in the porous medium is distributed around the solid particle according to the phenomena of adsorption and capillarity. The thermal conductivity of the gas present within the pores takes into account the thermal conductivity of the water vapor and dry air, without enhanced vapor diffusion. The model simplifies the variation of the relative humidity, from dryness to the field capacity, with a linear increase. The predicted results, compared to experimental data, show the agreement is very good at the temperatures in the range (30–50°C) and acceptable at 70°C. At high temperature (90°C) the predictions are higher than the experiments and a better agreement could be obtained by decreasing the thermal conductivity of the gas phase. Besides, the trend of the theoretical predictions is in good agreement with the experiments also at high temperatures.

Highlights in the Historical Development of the Porous Media Theory: Toward a Consistent Macroscopic Theory

First contributions to the theory of porous media were made by R Woltman in 1794 when he independently developed a more sophisticated earth pressure theory than C Coulomb, and surprisingly in another context introduced the concept of volume fractions. In the last century, further important contributions were published by A Delesse, A Fick, H Darcy, and J Stefan on the concept of surface fractions, the diffusion problem, ground-water flow, and the mixture theory, which are essential parts of the theory of porous media. In the twentieth century, the scientific discussion on porous media theories was opened by P Fillunger in 1913 in a paper about the uplift problem in saturated rigid porous solids. In subsequent articles, he investigated the phenomena of friction and capillarity and discovered the effect of effective stresses. In 1923, K von Terzaghi, founder of modern soil mechanics, started his investigations on saturated deformable porous solids within the framework of the calculation of the permeability coefficient of clay. In 1936, Fillunger founded the concept of the mechancial theory of liquid-saturated deformable porous solids. However, his substantial masterpiece was completely forgotten and ignored. The reason for this may lie in the fact that in the 1930’s deep hostility arose between Fillunger and von Terzaghi due to different scientific views on the porous media theory and soil mechanics, leading to a large controversy which ended very tragically. The works of von Terzaghi and Fillunger were continued by M Biot, G Heinrich, and I Frenkel in the next decades. Today, two important directions of the macroscopic porous media theory are commonly acknowledged. The first one is based on investigations by M Biot, and the second one proceeds from the mixture theory, restricted by the concept of volume fractions (porous media theory). In particular, the porous media theory has turned out to be an efficient tool to treat saturated and empty porous solids.

Steam Drying - Modelling and Applications

ABSTRACT The concept of steam drying originates from the mid of the last century. However, a broad industrial acceptance of the technique has so far not taken place. The paper deals with modelling the steam drying process and applications of steam drying with in certain industrial sectors where the technique has been deemed to hove special opponunities. In the modelling scction the mass and heat transfer proceases are described along with equilibrium, capillarity and sorption phenomena occurring in porous materials during the steam drying process. In addition existing models in the literslure are presented. The applications discussed involve drying of fuels with high moisture contcna, cattle feed exemplified by sugar beet pulp. lumber. paper pulp. paper and sludges. Steam drying is compared to flue gas drying of biofuels prior to combustion in a boiler. With reference to a current insrallation in Sweden. the exergy losses. as manifested by loss of co-generation cupacity. are discussed. The energy saving p...

Low cycle fatigue fracture limits of structural materials and structural elements: Yamada, M. Proc. Conf. Testing of Metals for Structures, Naples, Italy, 29–31 May 1990, pp 184–192

Functionally graded cemented carbides obtained on the basis of capillarity phenomena can be very important for numerous applications and are expected to substitute conventional WC–Co cemented carbides. Drifts of liquid Co-based binders in couples of model WC–Co alloys with different WC mean grain sizes sintered together were examined. Noticeable Co drifts occur from coarse-grain into fine-grain regions of the model alloys due to different capillary forces. The Co drifts become more pronounced when the difference between WC mean grains sizes of the coarse-grain region and fine-grain region increases.

Life predictions in fatigue taking into account material memory properties: Caligiana, G. Proc. Conf. Testing of Metals for Structures, Naples, Italy, 29–31 May 1990, pp 104–115

Functionally graded cemented carbides obtained on the basis of capillarity phenomena can be very important for numerous applications and are expected to substitute conventional WC–Co cemented carbides. Drifts of liquid Co-based binders in couples of model WC–Co alloys with different WC mean grain sizes sintered together were examined. Noticeable Co drifts occur from coarse-grain into fine-grain regions of the model alloys due to different capillary forces. The Co drifts become more pronounced when the difference between WC mean grains sizes of the coarse-grain region and fine-grain region increases.