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Register a new userLong-range fluctuation-induced forces in driven electrolytes
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We study the stochastic dynamics of an electrolyte driven by a uniform external electric field and show that it exhibits generic scale invariance despite the presence of Debye screening. The resulting long-range correlations give rise to a Casimir-like fluctuation-induced force between neutral boundaries that confine the ions; this force is controlled by the external electric field, and it can be both attractive and repulsive with similar boundary conditions, unlike other long-range fluctuation-induced forces. This work highlights the importance of nonequilibrium correlations in electrolytes and shows how they can be used to tune interactions between uncharged biological or synthetic structures at large separations.
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Understanding how electrolyte solutions behave out of thermal equilibrium is a long-standing endeavor in many areas of chemistry and biology. Although mean-field theories are widely used to model the dynamics of electrolytes, it is also important to characterize the effects of fluctuations in these systems. In a previous work, we showed that the dynamics of the ions in a strong electrolyte that is driven by an external electric field can generate long-ranged correlations manifestly different from the equilibrium screened correlations; in the nonequilibrium steady state, these correlations give rise to a novel long-range fluctuation-induced force (FIF). Here, we extend these results by considering the dynamics of the strong electrolyte after it is quenched from thermal equilibrium upon the application of a constant electric field. We show that the asymptotic long-distance limit of both charge and density correlations is generally diffusive in time. These correlations give rise to long-ranged FIFs acting on the neutral confining plates with long-time regimes that are governed by power-law temporal decays toward the steady-state value of the force amplitude. These findings show that nonequilibrium fluctuations have nontrivial implications on the dynamics of objects immersed in a driven electrolyte, and they could be useful for exploring new ways of controlling long-distance forces in charged solutions.
We consider a model for periodic patterns of charges constrained over a cylindrical surface. In particular we focus on patterns of chiral helices, achiral rings or vertical lamellae, with the constraint of global electroneutrality. We study the dependence of the patterns size and pitch angle on the radius of the cylinder and salt concentration. We obtain a phase diagram by using numerical and analytic techniques. For pure Coulomb interactions, we find a ring phase for small radii and a chiral helical phase for large radii. At a critical salt concentration, the characteristic domain size diverges, resulting in macroscopic phase segregation of the components and restoring chiral symmetry. We discuss possible consequences and generalizations of our model.
We discuss fluctuation-induced forces in a system described by a continuous Landau-Ginzburg model with a quenched disorder field, defined in a $d$-dimensional slab geometry $mathbb R^{d-1}times[0,L]$. A series representation for the quenched free energy in terms of the moments of the partition function is presented. In each moment an order parameter-like quantity can be defined, with a particular correlation length of the fluctuations. For some specific strength of the non-thermal control parameter, it appears a moment of the partition function where the fluctuations associated to the order parameter-like quantity becomes long-ranged. In this situation, these fluctuations become sensitive to the boundaries. In the Gaussian approximation, using the spectral zeta-function method, we evaluate a functional determinant for each moment of the partition function. The analytic structure of each spectral zeta-function depending on the dimension of the space for the case of Dirichlet, Neumann Laplacian and also periodic boundary conditions is discussed in a unified way. Considering the moment of the partition function with the largest correlation length of the fluctuations, we evaluate the induced force between the boundaries, for Dirichlet boundary conditions. We prove that the sign of the fluctuation-induced force for this case depend in a non-trivial way on the strength of the non-thermal control parameter.
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold may depend also on the profiles of the perturbation in the particle directions. Specifically, we perform mean-field, linear stability, perturbative and numerical analyses on an approximated form of the Fokker-Planck equation describing the system. We find that if an angular perturbation to an initially homogeneous system is large in magnitude and highly localized in space, it will be amplified and thus serves as an indication of the onset of collective motion. Our results also demonstrate that high particle speed promotes collective motion.
We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations at zero wavenumber. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature ${bf 503}$, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability
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