Abstract
Interfacial tension between immiscible phases is a well-known phenomenon, which manifests itself in everyday life, from the shape of droplets and foam bubbles to the capillary rise of sap in plants or the locomotion of insects on a water surface. More than a century ago, Korteweg generalized this notion by arguing that stresses at the interface between two miscible fluids act transiently as an effective, nonequilibrium interfacial tension, before homogenization is eventually reached. In spite of its relevance in fields as diverse as geosciences, polymer physics, multiphase flows, and fluid removal, experiments and theoretical works on the interfacial tension of miscible systems are still scarce, and mostly restricted to molecular fluids. This leaves crucial questions unanswered, concerning the very existence of the effective interfacial tension, its stabilizing or destabilizing character, and its dependence on the fluid's composition and concentration gradients. We present an extensive set of measurements on miscible complex fluids that demonstrate the existence and the stabilizing character of the effective interfacial tension, unveil new regimes beyond Korteweg's predictions, and quantify its dependence on the nature of the fluids and the composition gradient at the interface. We introduce a simple yet general model that rationalizes nonequilibrium interfacial stresses to arbitrary mixtures, beyond Korteweg's small gradient regime, and show that the model captures remarkably well both our new measurements and literature data on molecular and polymer fluids. Finally, we briefly discuss the relevance of our model to a variety of interface-driven problems, from phase separation to fracture, which are not adequately captured by current approaches based on the assumption of small gradients.
Highlights
The spherical shape of soap bubbles and liquid droplets, the capillary forces responsible, e.g., for the sap rise in trees, the locomotion of water-strider insects, and the fractionation of a liquid jet exploited in the spray or automotive industry are only a few among the very numerous manifestations of the interfacial tension between immiscible phases
We present an extensive set of measurements on miscible complex fluids that demonstrate the existence and the stabilizing character of the effective interfacial tension, unveil new regimes beyond Korteweg’s predictions, and quantify its dependence on the nature of the fluids and the composition gradient at the interface
We study suspensions of colloidal particles (CP) and solutions of linear polymers (LP) of different chemistry, size, and molecular weight, at volume fractions φ ranging from 2.8 × 10−3 to 0.633, depending on the sample [57]
Summary
The spherical shape of soap bubbles and liquid droplets, the capillary forces responsible, e.g., for the sap rise in trees, the locomotion of water-strider insects, and the fractionation of a liquid jet exploited in the spray or automotive industry are only a few among the very numerous manifestations of the interfacial tension between immiscible phases. Deviations from Korteweg’s Δφ2 scaling have been clearly observed in molecular [13] and complex fluids alike [16,41], demonstrating the need for a more general theory Even for those systems where Korteweg’s law correctly captures the Δφ scaling of Γe, no predictions are available for the magnitude of the square gradient coefficient κ, with the exception of microgel colloidal particles [18]. The model proposed here provides a compact yet powerful description of the interface contribution to the (free) energy of a multiphase system, for arbitrary concentration gradients We expect it to be of use in the description of systems with sharp interfaces, namely within density-functional theory or phase field approaches
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