Search Results

The energies associated with surfaces — surface energy, interfacial energy, surface tension, and work of adhesion — drive many surface phenomena including tribological ones such as adhesion and friction. This chapter discusses the physical origins of surface energies for liquids and solids, and how the concepts of capillary pressure, capillary condensation, wetting, and work of adhesion are derived from surface energy. Further, this chapter covers the different methods for measuring surface energies, including a thorough discussion of the most common method to measure the surface energy of solids: contact angle measurements of liquid droplets on surfaces. The chapter also introduces how surface energies and surface tensions lead to adhesion and adhesion hysteresis between contacting surfaces, which is followed up in the subsequent chapters on surface forces.

In this chapter the molecular theory of surface properties and of the properties of inhomogeneous fluids is described. Distribution functions and molecular order parameters that give the molecular alignment at interfaces are considered. This is followed by sections on the theory of surface tension and of the pressure tensor at an interface. Calculations of these properties for fluid–fluid interfaces are presented. Density functional theory of inhomogeneous fluids is introduced, with derivation of the fundamental theorems followed by more approximate treatments based on local and non-local approximations. Perturbation theory and integral equation theory treatments are described. Finally, experimental and simulation studies of the preferred orientation of molecules at surfaces and in biomembranes are discussed. Comparisons with molecular simulation and experiment are a common theme. Appendices review the mathematics of functionals and the Maxwell equations for macroscopic electrostatics.

This chapter deals with the discretization issues raised by multifluid magnetohydrodynamics problems. The additional difficulty compared to those in Chapter 3, is the presence of one (or many) free interface(s) separating the fluids. Numerically, one has also to resort to up-to-date techniques for the simulation of moving interfaces. In particular, the chapter presents a numerical method based on the Arbitrary Lagrangian Eulerian formulation, and lays emphasis on the stability of the time-advancing schemes. A short review of some other numerical methods to deal with moving interfaces is provided. Some numerical test cases illustrate the capabilities of the ALE method.

This chapter presents a pedagogical discussion of the surface tension and its manifestation in a number of fluid systems. Interfacial boundary conditions are derived and then applied in various settings. Particular attention is given to highlighting the role of curvature pressure in fluid statics, including fluid menisci and the floating of small bodies at interfaces. Dynamic settings influenced by capillary effects and capillary instability are also highlighted, including fluid jets, sheets, and hydraulic jumps. Marangoni flows (dominated by gradients of surface tension) are also considered, and the role of surface impurities in interfacial flows discussed. Simple mathematical developments are augmented with physical discussion with hopes of improving intuition for this class of problems.

This chapter discusses theoretical equations and models for analysing the surface tension of metallic liquids. It covers semi-empirical equations for the surface tension of liquid metallic elements; equations for the surface tension in terms of new dimensionless parameters; and temperature coefficients of the surface tension of liquid metallic elements. It also provides an assessment of surface tension models. It then looks at adsorption of solutes on liquid metallic surfaces; equations for the surface tension of binary liquid mixtures; methods of surface tension measurement; and experimental data for the surface tension of liquid metallic elements.

Capillarity reflects the action of interfacial tension and has been central to understanding intermolecular forces. When a liquid meets a solid surface (with contact angle θ‎) it forms a meniscus which is associated with the rise/depression of liquid in a capillary tube, hence the term capillarity. Interfacial tensions also determine how a liquid wets and adheres to a solid or another liquid. Liquid menisci are curved, and Young, Laplace, and Kelvin have all thrown light upon the properties of curved liquid surfaces. The Young–Laplace equation relates the pressure difference across a curved liquid interface to both the interfacial tension and curvature of the interface. Interfacial tension also gives rise to a dependence of the vapour pressure (and solubility) of a liquid on the curvature of its surface (e.g. drop radius), as expressed in the Kelvin equation. Common methods for measurement of interfacial tensions are described in an Appendix.

This chapter shows how thermodynamics can be applied to other types of system. It considers three examples in detail: the elastic rod, the surface tension in a liquid, and the assembly of magnetic moments in a paramagnet.

Surfaces, or more generally, interfaces, are important in soft matter by two reasons. The weak forces associated with surfaces, such as the surface tension and inter-surface forces, are important in the flow and deformation of soft matter. Many soft matter systems, especially colloidal dispersions, have large internal interfaces, and the properties of interfaces are crucial for bulk properties. This chapter first discusses the capillary phenomena in usual liquids, and provides thermodynamic definitions for surface tensions and surface adsorptions. Second, it describes surfactants, the materials which change the surface properties. Theory for the micelle formation of surfactants and its effect on surface tension are discussed. Third, the chapter explains the inter-surface force – the force acting between surfaces in close proximity – with reference to the stability of colloidal dispersions.

In this chapter we discuss the structure and stability of foams at equilibrium. We start with a qualitative description of foam physics before turning to very dry foam structures. We will show how equilibrium properties are affected by the presence of a non-negligible amount of liquid in the foam, and we will describe the spatial distribution of this liquid.

This chapter discusses the properties of ³He surfaces and its interfaces with other substances. It presents a selection of experiments and their interpretation is made under six headings: restricted geometry, surface tensions, nucleation, thermal boundary resistance, wetting transitions, and thin films.

This relatively short chapter goes beyond the earlier description of a liquid and its vapor in thermal and mechanical equilibrium to consider the case of drop formation within a saturated vapor: the description now takes into consideration the surface tension of the drop, which in turn depends on the drop’s radius. An equation is then also obtained for the difference in vapor pressure across the surface of the drop. A further discussion of raindrops estimates the speed at which they fall in the atmosphere: two limiting cases are considered. The first is that of a very small drop whose limiting velocity is determined by viscosity and the second is of a very large drop for which aerodynamic drag is the limiting factor.

The interaction of electrons and positive ions with liquid helium is very strong and locally modifies the environment. Positive ions polarize the surrounding fluid. Electrostriction produces such a large pressure increase near the ion that the melting transition appears at a distance of a few Ångstroms from the ion. The ion is surrounded by a solvation shell of solid helium-ice called a snowball. On the other hand, electrons interact with the electronic clouds of the atoms of the liquid via short-range exchange repulsion forces. As a consequence, electrons are encompassed by an empty cavity of approximately 20 Ångstroms in diameter. This chapter describes how thermodynamics and quantum mechanics allows the researchers to calculate the charge structures.

The energies associated with surfaces—surface energy, interfacial energy, surface tension, and work of adhesion—drive many surface and interfacial phenomena including tribological ones such as adhesion and friction. This chapter discusses the physical origins of surface energies for liquids and solids, and how the concepts of capillary pressure, capillary condensation, wetting, and work of adhesion are derived from surface energy. Further, this chapter covers the different methods for measuring surface energies, including the most common method for solid surfaces: contact angle measurements of liquid droplets on surfaces. This chapter also introduces how surface energies and surface tensions lead to adhesion and adhesion hysteresis between contacting surfaces, which is followed up in the subsequent chapters on surface forces.

The thickness and hence material content of a surface is generally unknown, and there are two common definitions of a surface/interface. In one the surface is treated as a phase distinct from the surrounding bulk phases, and in the other, due to Gibbs, the Gibbs dividing surface is supposed to be a plane, parallel to the physical interface. The former model gives rise to the surface concentrationΓ‎^s of a surfactant, and the Gibbs model introduces the surface excess concentration, Γ‎^σ‎. Some thermodynamic quantities for surfaces (e.g. surface chemical potential and Gibbs free energy for surfaces) are defined. Adsorption lowers interfacial tension by an amount termed the surface pressure, and the Gibbs adsorption equation allows the calculation of Γ‎^s or Γ‎^σ‎ for a surfactant from the variation of interfacial tension of a liquid/fluid interface with surfactant concentration in bulk solution.

The fundamentals of thermodynamics are reviewed, focusing on the chemistry of high-temperature metals, oxides (slags), and salts. Thermochemical data are provided for important molten metals: the free energies of solution of alloy elements, and interaction coefficients. Standard free energies of reactions are also provided, so the reader may calculate important chemical equilibria. Example calculations are provided for the deoxidation of steel. The removal of sulfur and phosphorus are also described. The second half of the chapter considers fundamental aspects of important physical properties: viscosity, surface tension, diffusion, and thermal and electrical conductivity.

In this chapter, the special techniques needed to simulate and calculate properties for inhomogeneous systems are presented. The estimation of surface properties, such as the interfacial tension, may be accomplished by a variety of methods, including the calculation of the stress tensor profiles, the change in the potential energy on scaling the surface area at constant volume, the observation of equilibrium capillary wave fluctuations, or direct free energy measurement by cleaving. The structure within the interface is also of interest, and ways of quantifying this are described. Practical issues such as system size, preparation of a two-phase system, and equilibration time, are discussed. Special application areas, such as liquid drops, fluid membranes, and liquid crystals, are described.

The surface tension of metallic liquids is one of the most important thermophysical properties. In any and every liquid metallic processing operation, the behaviour of metallic liquids is closely related to its surface tension. This chapter discusses the modified Schytil model, which is used to calculate the melting point surface tension of liquid metallic elements.

This chapter examines how the physical properties of water influence and explain the great diversity of swimming performance and mechanisms - from the scale of spermatozoa on up to whales. The key parameters of inertia, viscosity and their manifestation in the critically important Reynolds number are explained and placed in the context of a range of swimming mechanisms, including undulatory movement and fin-based, jet-based, flagellar and ciliary propulsion. The air-water interface also presents an intriguing mechanical challenge for the many organisms that move on top of the water’s surface. The chapter concludes with a brief overview of the burgeoning field of biorobotic swimmers.

In this chapter it is shown that the differences between solids, liquids, and gases have to be explained at the level of the molecular structure. The continuum hypothesis makes it possible to characterise any fluid and ultimately analyse its response to pressure difference Δ‎p and shear stress τ‎ through macroscopic physical properties, dependent only upon absolute temperature T and pressure p, which can be defined at any point in a fluid. The most important of these physical properties are density ρ‎ and viscosity μ‎, while some problems are also influenced by compressibility, vapour pressure pV, and surface tension σ‎. It is also shown that the bulk modulus of elasticity Ks is a measure of fluid compressibility which determines the speed at which sound propagates through a fluid. The perfect-gas law is introduced and an equation derived for the soundspeed c.