The Romans and Their World: A Short Introduction. By Brian Campbell. (New Haven, CT: Yale University Press, 2011. Pp. xi, 288. $35.00.)

On a Boussinesq Capillarity System: Hamiltonian Reductions and Associated Quartic Geometries

“…A generalization of the associated "curvature free energy" has been adopted independently by Helfrich [26] which, in turn, has led via minimization to the celebrated "shape equation" of biomembrane physics (see [27] and references therein). In [28], the underlying idea of "curvature elasticity" has been used in the more general context of an extension of Gibbs' classical theory of capillarity [1]. Against this background, we now turn to the Boussinesq capillarity system in three spatial dimensions.…”

“…The classical theory of capillarity of Gibbs [1] assumes the two adjoining phases to be separated by a smooth geometric surface of zero thickness [2] and thereby avoids the complex problem of the structure of the liquid-vapor separation region. In [3], Antanovskii developed a phase field model of capillarity which accounts for the structure of the liquid-vapor region in a systematic manner and, importantly, provides an explicit expression for the capillarity stress tensor in terms of the free energy of the liquid-vapor system.…”

Phase Transitions in Soft Matter Induced by Selective Solvation

“…From Eqs. (3.26) and (3.28) σ g is expressed at small ion densities as 66 , the electrostatic contribution −σ e is neglected. However, it is crucial for antagonistic salt 24,29 and for ionic surfactant 35 .…”

Selective Solvation in Aqueous Mixtures: Interface Deformations and Instability

“…For a small amount of solute, most experimental interpretations have been based on the Gibbs formula [21,22] γ = γ 0 − k B T Γ, where γ 0 is the surface tension without solute and Γ represents the adsorption of solute per unit area. However, we have recently shown the presence of a negative electrostatic contribution γ el for a small amount of charged solute.…”