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.

To investigate the interplay between microscopic dynamics and macroscopic rheology insoft matter, we couple a stress-controlled-rheometer equipped with a Couette cell to a lightscattering setup in the imaging geometry, which allows us to measure both the deformationfield and the microscopic dynamics. To validate our setup, we test two model systems. For anelastic solid sample, we recover the expected deformation field within 1 μm. For a pure viscousfluid seeded with tracer particles, we measure the velocity profile and the dynamics of thetracers, both during shear and at rest. The velocity profile is acquired over a gap of 5 mm witha temporal and spatial resolution of 1 s and 100 μm, respectively. At rest, the tracer dynamicshave the expected diffusive behavior. Under shear, the microscopic dynamics corrected for theaverage drift due to solid rotation scale with the local shear rate, demonstrating that our setupcaptures correctly the relative motion of the tracers due to the affine deformation.

Surface tension between immiscible fluids is a well-understood and well-characterized phenomenon. By contrast, much less is known about the effective, off-equilibrium surface tension that arises when a (transient) interface is created between miscible fluids.This effective surface tension plays a key role in many driven phenomena, from jetting and drop formation and coalescence to precipitation and deposition, as it was already recognized more than 100 years ago by Korteweg [1]. However, experimental investigations in this field remain scarce and the theoretical predictions by Korteweg have not quantitatively tested so far, to the best of our knowledge. We present a thorough experimental investigation of the Saffman-Taylor instability arising when a simple fluid (the solvent of a colloidal or polymer suspension) is pushed through a miscible, more viscous one (the colloidal or polymer suspension itself). We show [2] that the resulting interface pattern can be accounted for by the non-linear rheological properties of the suspension and an effective surface tension. By measuring the effective surface tension for suspensions at a variety of polymer volume fractions, we successfully test Korteweg's theory for free and cross-linked polymer suspensions. We moreover find that the effective surface tension increases with the size of polymers, a surprising result at odd with the typical behavior in atomic or colloidal systems at equilibrium, where the surface tension usually decreases as the squared particle size. Finally we present new data on the effective surface tension between suspensions of hard, compact particles and their own solvent showing that polymers and hard particles exhibit vastly different effective surface tension properties. We discuss this surprising result in view of available models for interfacial stresses.[1] D. Korteweg, Arch. Neerlandaises Sci. Exactes Naturelles, 6, 1 (1901).[2] D.Truzzolillo, S. Mora, C. Dupas, L. Cipelletti, Phys. Rev. Lett., 112, 208303 (2014).