Nonequilibrium Interfacial Tension in Simple and Complex Fluids

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.

Effective interfacial tension in flow-focusing of colloidal dispersions: 3-D numerical simulations and experiments

“…They carried out experimental measurements of the Saffman-Taylor instability in a Hele-Shaw cell with miscible complex fluids including colloidal dispersions. Their measurements went beyond confirming Korteweg's theory and showed that EIT is also a function of particle structure (basically size and shape) together with particleparticle and particle-solvent interactions (Truzzolillo et al 2016). Effective interfacial tension is expected to have relevance in many fields starting from material processing to multiphase complex fluid dynamic problems involving droplet and bubbles formation, jetting, coalescence and break-up of droplets (Truzzolillo & Cipelletti 2017).…”

Hydrodynamic instabilities in miscible fluids

“…Collectively these experiments show that the theory of Paterson captures the behavior of molecular newtonian liquids where interdiffusion rapidly smears the concentration profile, such that capillary forces can be neglected. On the other hand, we have recently shown [44] that the wavelength characterizing the onset of radial viscous fingering, does depend on the injection rate and, most importantly, on the physico-chemical nature of the two fluids in contact. These results were obtained with colloidal suspensions brought in contact with their own solvent, for which interdiffusion can be neglected on the time scale of the experiments.…”

“…A unified and solid framework allowing one to predict the onset and the evolution of viscous fingering in miscible fluids remains elusive unless transient capillary forces are invoked. The latter depend on the physicochemical nature of the fluids in contact [44] and are not negligible in the case of sharp compositional mismatches. Panel A: Viscous fingering created by water displacing a polysaccharide aqueous solution.…”

“…It has have been used very recently to measure interfacial stresses between colloidal suspensions and their own solvent [34,92,44]. We showed that the effective tension between the suspensions and their solvent is dramatically affected by the microstructural details of the fluids: a quadratic dependence on the concentration characterizes (linear or crosslinked) polymer suspensions, while a much sharper dependence on volume fraction has been observed for compact particles [44]. In the same work, we have proposed a new phase field formulation that is based on a frozen time approximation, valid when diffusion is slow with respect to the time of the experiments.…”

“…To take into account the various probabilities of AA, AB, and BB bonds within the three-layer region, it is convenient to indicate by z the number of neighbors of a site of the central layer that belongs to the adjacent layers i ± 1, where z may in general be different from the lattice coordination number z, so that the number of neighbors within the same layer is z − 2z . Neglecting terms of order O(|∇ϕ| 4 ) and after some algebra (see [44] for details) the full expression of the square gradient contribution to the interfacial tension reads:…”