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We perform a static analysis of a circular cylinder that forms a barrier between surfactant-laden and surfactant-free portions of a liquid–gas interface. In addition to determining the general implications of the balances for forces and torques, we quantify how the imbalance$\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}=\unicode[STIX]{x1D6FE}_{a}-\unicode[STIX]{x1D6FE}_{b}$between the uniform surface tension$\unicode[STIX]{x1D6FE}_{a}$of the surfactant-free portion of the interface and the uniform surface tension$\unicode[STIX]{x1D6FE}_{b}$of the surfactant-laden portion of the interface influences the load-bearing capacity of a hydrophobic cylinder. Moreover, we demonstrate that the difference between surface tensions on either side of a cylinder with a cross-section of arbitrary shape induces a horizontal force component$f^{h}$equal to$\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}$in magnitude, when measured per unit length of the cylinder. With an energetic argument, we show that this relation also applies to a rod-like barrier with cross-sections of variable shape. In addition, we apply our analysis to amphiphilic Janus cylinders and we discuss practical implications of our findings for Marangoni propulsion and surface pressure measurements.

The equations that govern, away from equilibrium and accounting for dissipation, the evolution of the contact line of an evaporating or condensing sessile drop on a rigid, planar substrate are derived. Aside from the normal and tangential components of the standard (Newtonian) force balance, these include a configurational force balance. At equilibrium, the normal component of the standard force balance reduces to the modified Young’s equation first mentioned by Gibbs. The remaining balances are purely dissipative and hence are vacuous in equilibrium. A complete description of contact-line dynamics generally involves all three equations. The theory is embedded in a thermodynamic framework that ensures consistency of all constitutive relations with the second law. In the linearly dissipative case, these involve six contact-line viscosities. When viscous coupling is neglected, only three viscosities remain. One is associated with stretching of the fluid along the contact line. The remaining two are related to dissipation that accompanies mass transfer between liquid and vapour phases during evaporation or condensation.

We use a newly developed set of interface conditions to revisit the problem of an evaporating thin liquid film. In particular, instead of the conventional Hertz–Knudsen–Langmuir equation for the evaporation mass flux, we impose a more general equation expressing the balance of configurational momentum. This balance, which supplements the conventional conditions enforcing the balances of mass, momentum and energy on the film surface, arises from a consideration of configurational forces within a thermodynamical framework. We study the influence of two newly introduced terms on the evolution of the liquid film. One of these terms accounts for the transport of energy within the liquid–vapour interface. The other term, which we refer to as the effective pressure, accounts for vapour recoil. Both new terms are found to be stabilizing. Furthermore, the effective pressure is found to affect a time-dependent base state of the evaporating film and to be an important factor in applications involving liquid films with thicknesses of one or two monolayers. Specifically, we demonstrate that consideration of the effective pressure makes it possible to observe the influence of the van der Waals interactions on film evolution close to the instant of rupture. Dimensional considerations indicate that one of the most significant influences of these effects occurs for molten metals.

We develop a complete set of equations governing the evolution of a sharp interface separating two fluid phases undergoing transformation. In addition to the conventional balances for mass, linear momentum and energy these equations include also a counterpart of the Gibbs–Thomson equation familiar from theories for crystal growth. This additional equation arises from a consideration of configurational forces within a thermodynamical framework. Although the notion of configurational forces is well-developed and understood for the description of materials, such as crystalline solids, that possess natural reference configurations, little has been done regarding their role in materials, such as viscous fluids, that do not possess preferred reference states. We therefore provide a comprehensive discussion of configurational forces, the balance of configurational momentum, and configurational thermodynamics that does not require a choice of reference configuration. The general evolution equations arising from our theory account for the thermodynamic structure of the bulk phases and the interface and for viscous and thermal dissipation in the bulk phases and for viscous dissipation on the interface. Because of the complexity of these equations, we provide a reduced system of equations based on simplified constitutive assumptions and approximations common in the literature on phase transformations. Using these reduced equations, we apply the theory to the radially symmetric problem for the condensation of a liquid drop into the vapour phase.

A linear stability analysis of the Rayleigh–Taylor problem for an incompressible fluid undergoing a liquid–liquid phase transformation is presented. Both inviscid and linearly viscous fluids are considered and interfacial tension is taken into account. Instability is possible only when the phase with the higher density is above that with the lower density. Study of the inviscid case shows that the exchange of mass between the phases decreases significantly both the range of unstable wavenumbers and the maximum growth rate for unstable perturbations as compared to those arising classically. For a linearly viscous fluid, the shear and dilational viscosities of the interface are taken into account as are the migrational viscosities associated with the motion of the interface relative to the underlying fluid. When no mass exchange occurs between the phases in the base state and the interfacial viscosities are neglected, the growth rates exceed by at least an order of magnitude those for the classical Rayleigh–Taylor problem. The various interfacial viscosities slow the growth rates of disturbances, but do not influence the range of unstable wavenumbers. For both the inviscid and viscous cases, interfacial tension plays the same stabilizing role as it does classically.

We establish transport relations for integrals over evolving fluid interfaces. These relations make it possible to localize integral balance laws over non-material interfaces separating fluid phases and, therefore, obtain associated interface conditions in differential form.