Résumé
The nature of the interface between two fluids has been the subject of an extensive investigation for more than two centuries [1]. From a mechanical point of view, surface tension can be calculated as an integral of unbalanced tangential stresses over the interface thickness [2] and it is thus of no surprise that, within the assumption of temporal and local equilibrium, such a tension can be ascribed to an interface between two miscible fluids [3] and assumes a nonzero value. The idea that there are capillary forces at work in the layer between miscible liquids goes back at least to an 1871 report of J. Bosscha, cited in a paper of Korteweg [1901], who was the first [4] to introduce stresses due to concentration inhomogeneities in the Navier-Stokes equation, aiming to mimic capillarity effects between two miscible liquids. Only much more recently experimental effort has been made to investigate the existence and the nature (the sign) of such off-equilibrium tension [5-11]. In all cases the authors have pointed out that such interfacial stresses mimic a positive interfacial tension. In analogy with the surface tension of an equilibrium interface between immiscible fluids, the effective surface tension has been rationalized within an approximation of small concentration gradients via the so called square gradient model [6,8,9]. The latter predicts a quadratic dependence of such tension on the compositional mismatch between two miscible fluids.Only very recently colloids and polymer suspensions in contact with a reservoir of solvent have been considered as a model two-fluid system to study off-equilibrium surface tensions [11, 12]: indeed, diffusion is much slower in colloids and polymers as compared to atomic systems, leaving a wider temporal window for probing the transient interface between miscible fluids. In a recent work [11] we have investigated off-equilibrium surface tension between microgel suspensions and their solvent (water) showing that equation (1) holds for low concentration gradients. On the other hand we have also pointed out that the square gradient model is far to catch the volume fraction dependence of the tension for compact hard sphere-like particles [12] up to concentrations close to the maximum packing for spheres. The scenario is then currently controversial.By visualizing viscous fingering instability (VF), appearing when a solvent displaces a suspension in radial Hele-Shaw geometry, we measure interfacial tensions in function of the volume fraction of the suspended colloids or polymers, showing that the internal degrees of freedom of the particles drive the low volume fraction behavior. Our results support the existence of a positive tension between miscible fluids, confirm the quadratic scaling predicted by Korteweg [4] for long linear and crosslinked polymers and show a positive rapidly growing tension for hard sphere suspensions, whose description necessitates a theoretical framework going beyond the classic square gradient model. We rationalize our findings assuming the suspension/solvent interface in local thermodynamic equilibrium, computing explicitly the square gradient contribution to the interfacial tension for polymer/solvent and simple molecular liquid mixtures and proposing a new phenomenological model capturing the compositional dependence of the interfacial tension for large concentration gradients. In addition to that we include and analyze data reported in literature and obtained via spinning drop tensiometry, validating our approach. We conclude proposing very generally the analysis of hydrodynamic instabilities as a new tool to measure interfacial stresses in complex fluids and characterize transient interfacial tensions.