Surface tension

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The interfacial region between two homogeneous phases contains matter in a distinct physical state; that is to say, matter in the interfacial state exhibits properties different from those matters in the gaseous, liquid, or solid states. As a result, as soon as interfaces are considered explicitly, new variables – for example, interfacial surface tension – enter into the classical thermodynamic description of equilibrium systems. Interfaces in equilibrium systems need not be considered explicitly unless the surface-to-volume ratio is large, because the contribution of interfacial free energy to the total free energy is usually small. However, interfacial effects on the dynamic behavior of flow systems can be profound, even when the proportion of matter in interfacial regions is extremely small. Furthermore, motion may originate in an interface in systems that are not in thermal or compositional equilibrium.

When two adjacent fluids are at rest, their interface ordinarily behaves as if it is in a state of uniform tension. It is both possible and convenient to mathematically represent the interface as a geometric surface in tension. This representation is also appropriate for many flows with free boundaries; indeed, it is the basis of the treatment of capillarity in classical hydrodynamics. Considerations of equilibrium surface tension lead to the conclusion that the normal component of fluid stress, or pressure, is discontinuous at a curved interface, while the shear stress is continuous. Classical hydrodynamics also recognizes – in connection with the calming action of oil on water waves – that extension and contraction of a surface film produces longitudinal variations in surface tension. This in turn gives rise to discontinuities in the tangential components of fluid stress at the interface.

A design engineer must have some understanding of these and other phenomena to design effective devices. The field of interfacial phenomena has been the realm of researchers primarily in chemical and mechanical engineering, physical chemistry, and material science. Much of the analytical basis for their work comes from a subcontinuum view of the physical world. Models of molecular interaction and the use of statistical mechanics are typical in the literature. The earliest practical work on interfacial phenomena used equilibrium thermodynamics. Today, the ad hoc use of thermodynamics and simple molecular interaction models constitute the most useful treatment of two-phase heat transfer problems. However, a significant effort has been made to develop a unified approach via the extension of continuum mechanics using the conservation equations and some form of the flux laws. Direct solution methods for interfacial phenomena do not always follow from this type of investigation, but one frequently gains valuable insight into the behavior at the interface. The assumption is that one is not interested in the precise details of the interfacial region but rather in how it affects the bulk regions.


Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA.

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