Shear-induced quench of long-range correlations in a liquid mixture

A static correlation function of concentration fluctuations in a (dilute) binary liquid mixture subjected to both a concentration gradient and uniform shear flow is investigated within the framework of fluctuating hydrodynamics. It is shown that a well-known $|\nabla c|^2/k^4$ long-range correlation at large wave numbers $k$ crosses over to a weaker divergent one for wave numbers satisfying $k<(\dot{\gamma}/D)^{1/2}$, while an asymptotic shear-controlled power-law dependence is confirmed at much smaller wave numbers given by $k\ll (\dot{\gamma}/\nu)^{1/2}$, where $c$, $\dot{\gamma}$, $D$ and $\nu$ are the mass concentration, the rate of the shear, the mass diffusivity and the kinematic viscosity of the mixture, respectively. The result will provide for the first time the possibility to observe the shear-induced suppression of a long-range correlation experimentally by using, for example, a low-angle light scattering technique.Comment: 8pages, 2figure

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

Phase Transitions in Aqueous Tri-block Co-polymers: NMR Relaxation Studies.

Longitudinal NMR relaxation times were used to investigate the thermal transitions occurring in an aqueous triblock copolymer of the poly(oxyethylene)-poly(oxypropylene)-poly(oxyethylene) family. In such a system molecule-micelle and micelle-liquid crystal transitions are observed, depending on temperature and composition. The longitudinal relaxation time, R-1, significantly changes when the aforementioned phase transitions take place. In the case of molecule-micelle equilibrium, changes in R-1 values of the methyl (and methynic) group signal, located in the lipophilic portion of block copolymers, are observed. The effect is ascribed to a significant dehydration of the poly(oxypropylene) chains, as a consequence of micelle formation. Conversely, the thermal transitions from micelles to liquid-crystalline phases are associated with significant changes in the relaxation time of poly(oxyethylene) units. The latter effect is tentatively ascribed to a partial dehydration and/or interdigitation of the poly(oxyethylene) moieties in the block copolymer