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The interfacial tension between immiscible fluids is responsible for a wealth of every-day phenomena, from the spherical shape of small drops and bubbles to the ability to walk on water of many insects.More than a century ago, physicist and mathematician D. Korteweg postulated the existence of an effective interface tension for miscible fluids, whenever a composition gradient exists, as encountered, e.g., in many flow geometries. In this mini-review, we discuss experimental work performed in the last decades that demonstrates the existence of a positive effective interface tension in a variety of systems, from molecular, near-critical liquids to complex fluids such as polymer solutions and colloidal suspensions. The various experimental strategies that have been deployed are discussed, together with their advantages and limitations. Finally, some of the key theoretical questions still open are outlined.

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Ising spin-glass models with bimodal, Gaussian, uniform, and Laplacian interaction distributions in dimension five are studied through detailed numerical simulations. The data are analyzed in both the finite-size scaling regime and the thermodynamic limit regime. It is shown that the values of critical exponents and of dimensionless observables at criticality are model dependent. Models in a single universality class have identical values for each of these critical parameters, so Ising spin-glass models in dimension five with different interaction distributions each lie in different universality classes. This result confirms conclusions drawn from measurements in dimension four and dimension two.

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Computer simulations give precious insight into the microscopic behavior of amorphous materials, but their typical timescales are orders of magnitude shorter than the experimentally relevant ones. We close this enormous gap for a class of polydisperse models, which we successfully equilibrate beyond experimental timescales by means of the swap Monte Carlo algorithm. This numerical advance allows us to address some crucial outstanding questions, such as the relationship between jamming and glass transitions and the relevance of an entropy crisis for glass formation.

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Classical particle systems characterized by continuous size polydispersity, such as colloidal materials, are not straightforwardly described using statistical mechanics, since fundamental issues may arise from particle distinguishability. Because the mixing entropy in such systems is divergent in the thermodynamic limit we show that the configurational entropy estimated from standard computational approaches to characterize glassy states also diverges. This reasoning would suggest that polydisperse materials cannot undergo a glass transition, in contradiction to experiments. We explain that this argument stems from the confusion between configurations in phase space and states defined by free energy minima, and propose a simple method to compute a finite and physically meaningful configurational entropy in continuously polydisperse systems. Physically, the proposed approach relies on an effective description of the system as an $M^*$-component system with a finite $M^*$, for which finite mixing and configurational entropies are obtained. We show how to directly determine $M^*$ from computer simulations in a range of glass-forming models with different size polydispersities, characterized by hard and soft interparticle interactions, and by additive and non-additive interactions. Our approach provides consistent results in all cases and demonstrates that the configurational entropy of polydisperse system exists, is finite, and can be quantitatively estimated.

Commentaires: 13 pages, 4 figures. v2: Published version. Réf Journal: J. Chem. Phys. 146, 014502 (2017)