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As it is more practical to measure the forces acting between two contacting surfaces then the energies of surfaces, this chapter covers those surface forces that are derived from surface energies. The starting point is Derjaguin's approximation, which relates the energy between two flat surfaces to other geometries: sphere/flat, sphere/sphere, and crossed cylinders. Next is a discussion of the surface forces in dry contacts with no liquid menisci around the contact points. This discussion covers the cases where adhesion causes deformation (JKR theory) and where deformation is insignificant (DMT theory). The second half of this chapter deals with how liquid menisci around contacts contribute to adhesion forces, both for sphere on flat geometries and for contacting rough surfaces.

This chapter focuses on the two experimental techniques — the surface force apparatus (SFA) and the atomic force microscope (AFM) — that are commonly used for measuring molecular level forces that act between two surfaces at small separation distances. The first part of this chapter covers the fundamental principles of SFA and AFM design. The second half of this chapter illustrates the application of AFM to measuring surface forces with examples the measurement of van der Waals forces, meniscus forces from liquid films and from capillary condensation, and electrostatic double-layer forces.

This chapter describes how W. H. Wollaston’s expertise in linear optics led him to design and patent in 1804 meniscus lenses for improved eye glasses which he called periscopic spectacles. He also suggested improvements to the camera lucida and microscopes that took advantage of curved lenses. He designed and patented in 1806 a novel and compact drawing aid he named a camera lucida, which was used by the sculptor Francis Chantrey to make preliminary drawings of his subjects. The device remained in wide use for sketching until well into the 20^th century. The chapter also discusses Wollaston’s1805 paper on the forces of moving bodies in which he placed emphasis on the work potential of a body supplying energy to another over a finite distance. Wollaston’s move into new social and scientific networks in London, such as the Chemistry Club and the Geological Society, is described.

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.

As it more practical to measure the forces acting between two contacting surfaces then the energies of surfaces, this chapter covers those surface forces that are derived from surface energies. The starting point is Derjaguin’s approximation, which relates the energy between two flat surfaces to the force in other geometries: sphere/flat, sphere/sphere, and crossed cylinders. Next is a discussion of the surface forces in dry contacts with no liquid menisci around the contact points. This discussion covers the cases where adhesion causes significant deformation (JKR theory), where deformation is insignificant (DMT theory), and the cases in between. How surface roughness impacts adhesion is also discussed. The second half of this chapter deals with how liquid menisci around contacts contribute to adhesion forces, both for the sphere-on-flat geometry and for contacting rough surfaces.

This chapter focuses on the two experimental techniques—the surface force apparatus (SFA) and the atomic force microscope (AFM)—that are commonly used for measuring molecular level forces that act between two surfaces at small separation distances. The first part of this chapter covers the fundamental principles of SFA and AFM design. The second half of this chapter illustrates the application of AFM to measuring surface forces with examples the measurement of van der Waals forces, atomic level repulsive forces, frictional forces, electrostatic double-layer forces, and meniscus forces from liquid films and from capillary condensation.

The mathematical study of flow in porous media is typically based on the 1856 empirical result of Henri Darcy. This result, known as Darcy’s law, states that the velocity of a single-phase flow through a porous medium is proportional to the hydraulic gradient. The publication of Darcy’s work has been referred to as “the birth of groundwater hydrology as a quantitative science” (Freeze and Cherry, 1979). Although Darcy’s original equation was found to be valid for slow, steady, one-dimensional, single-phase flow through a homogeneous and isotropic sand, it has been applied in the succeeding 140 years to complex transient flows that involve multiple phases in heterogeneous media. To attain this generality, a modification has been made to the original formula, such that the constant of proportionality between flow and hydraulic gradient is allowed to be a spatially varying function of the system properties. The extended version of Darcy’s law is expressed in the following form: qα=-Kα. Jα (2.1) where qα is the volumetric flow rate per unit area vector of the α-phase fluid, Kα is the hydraulic conductivity tensor of the α-phase and is a function of the viscosity and saturation of the α-phase and of the solid matrix, and Jα is the vector hydraulic gradient that drives the flow. The quantities Jα and Kα account for pressure and gravitational effects as well as the interactions that occur between adjacent phases. Although this generalization is occasionally criticized for its shortcomings, equation (2.1) is considered today to be a fundamental principle in analysis of porous media flows (e.g., McWhorter and Sunada, 1977). If, indeed, Darcy’s experimental result is the birth of quantitative hydrology, a need still remains to build quantitative analysis of porous media flow on a strong theoretical foundation. The problem of unsaturated flow of water has been attacked using experimental and theoretical tools since the early part of this century. Sposito (1986) attributes the beginnings of the study of soil water flow as a subdiscipline of physics to the fundamental work of Buckingham (1907), which uses a saturation-dependent hydraulic conductivity and a capillary potential for the hydraulic gradient.

Tearing is a common presenting complaint in infants referred to an ophthalmologist and may be the first sign of something as benign as an impermanent anatomic defect or as grave as congenital glaucoma. When tearing is chronic, parents of an affected infant are often frustrated by the persistent accumulation of fluid and mucopurulent material in the eye and on the eyelids and anxious that the condition may be a sign of a more serious problem. The best initial management of tearing in an infant is to take a detailed history, which often provides important clues as to the cause of tearing, and then to perform a thorough, systematic ophthalmic examination. Tears serve four main functions: (1) they form a tear film to keep the eye moist, (2) they lubricate the eye, (3) they keep the eye clear of particulate matter and debris, and (4) they provide a refractive surface on the corneal epithelium. The tear film comprises three layers: a thin inner layer of proteinaceous mucin coats and protects the eye, an aqueous layer keeps the eye moist and lubricated, and an outer lipid layer slows evaporation of the aqueous layer. Basal tears are produced by the accessory lacrimal glands located in the conjunctiva and keep the eye moist under steady-state conditions; normal patients have a tear meniscus (or “tear lake”) visible along the inner lower eyelid as a result of basal tear production. Irritation or emotional extremes can trigger reflex tear production by the main lacrimal gland in the superotemporal quadrant of the orbit, “flooding” the tear lake. The level of the tear lake is highest when the rate of tear production by the lacrimal glands exceeds the rate of tear drainage into the nasolacrimal system. Tears normally drain out of the eye through puncta located on the nasal portion of the upper and lower eyelids. They then enter the upper and lower canaliculi, which run inferiorly and medially before joining to form the common canaliculus, which conducts tears through the valve of Rosenmuller and into the lacrimal sac.