arXiv subjects

David S. Dean

Publications and source records attributed to David S. Dean.

At least 19 recordsLinked to original sources

arXiv2026

Dielectric response as a source of viscosity in polar liquids

Transport coefficients and dielectric relaxation in liquids are often treated as distinct manifestations of molecular dynamics. We show that, in polar liquids, orientational dipolar fluctuations generate a substantial contribution to the shear viscosity that can be expressed in terms of dielectric response parameters. Using a Green-Kubo approach formulated in terms of dipolar body-force correlations, we derive an explicit relation linking the viscosity contribution to the static permittivity and the Debye relaxation time. With a single microscopic cutoff length fixed from one temperature, the theory predicts the temperature dependence of the viscosity for water and several alcohols using independently measured dielectric data. The results identify a general mechanism by which slow polarization dynamics generate an additional, and in strongly polar liquids often dominant, contribution to the viscosity, providing a quantitative bridge between dielectric spectroscopy and rheology.

cond-mat.stat-mech↗

arXiv2026

Self-phoretic oscillatory motion in a one-dimensional channel

We study a simple model for a particle that is active due to self-phoresis and that has been proposed to model symmetric camphor grains. The particle generates a concentration field through the continuous emission of a chemical substance, and its motion is driven by gradients of this field as it diffuses within a confined channel whose ends perfectly reflect the chemical. The reflection of the chemical field leads to an effective confinement of the particle, which itself is reflected before encountering the channel ends. The system displays a transition from a passive state, where the particle rests at the channel midpoint, to an active state characterized by highly regular, non-chaotic oscillations. We analytically construct the phase diagram and derive the oscillation frequency and amplitude in the vicinity of the transition. A perturbative analysis perfectly describes the dynamics of the particle even for oscillations as large as half the channel size. Furthermore, we develop an analysis which explains the mechanism of particle reflection close to the channel edges in the regime of large activity.

cond-mat.stat-mech↗

arXiv2025

Brownian motion near a soft surface

Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional colloid in an arbitrary external potential and near a soft surface. The latter is minimally modelled by a Winkler's foundation, and we restrict the study to the colloidal motion in the direction perpendicular to the surface. We start from deterministic hydrodynamic considerations, by invoking the already-established leading-order soft-lubrication forces acting on the particle. Importantly, a negative softness-induced and position-dependent added mass is identified. We then incorporate thermal fluctuations in the description. In particular, an effective Hamiltonian formulation is introduced and a temperature-dependent generalized potential is constructed in order to ensure equilibrium properties for the colloidal position. From these considerations and the Fokker-Planck equation, we then derive the relevant Langevin equation, which self-consistently allows to recover the deterministic equation of motion at zero temperature. Interestingly, besides an expected multiplicative-noise feature, the noise correlator appears to be modified by the surface softness. Moreover, a softness-induced temperature-dependent spurious drift term has to be incorporated within the Ito prescription. Finally, using numerical simulations with various initial conditions and parameter values, we statistically analyze the trajectories of the particle when placed within a harmonic trap and in presence of the soft surface. This allows us to: i) quantify further the influence of surface softness, through the added mass, which enhances the velocity fluctuations; and ii) show that intermediate-time diffusion is unaffected by softness, within the assumptions of the model.

cond-mat.soft↗

arXiv2025

Two dimensional Coulomb gas in a non-conservative trap

We study the nonequilibrium steady state of a two dimensional Coulomb gas under the action of an anisotropic harmonic trapping potential along with a non-conservative rotational force. In the case without rotation, the equilibrium (zero temperature) steady state has a uniform density supported over a a static elliptical droplet. The addition of a rotational force drives the system into a nonequilibrium steady state where the density is still uniform inside an ellipse, but the ellipse gets tilted by a a fixed angle compared to the non-rotational case. In addition, a nonzero current is generated inside the droplet which run concentrically to the droplet boundary. For large rotational force, the droplet develops a purely circular form. Our results are predicted by a simple hydrodynamic calculation and are confirmed by numerical simulations and provide a full understanding of a novel driven non-equilibrium state in a strongly interacting system.

cond-mat.stat-mech↗

arXiv2025

Exact height distribution in one-dimensional Edwards-Wilkinson interface with diffusing diffusivity

We study the height distribution of a one-dimensional Edwards-Wilkinson interface in the presence of a stochastic diffusivity $D(t)=B^2(t)$, where $B(t)$ represents a one-dimensional Brownian motion at time $t$. The height distribution at a fixed point is space is computed analytically. The typical height $h(x,t)$ at a given point in space is found to scale as $t^{3/4}$ and the distribution $G(H)$ of the scaled height $H=h/t^{3/4}$ is symmetric but with a nontrivial shape: while it approaches a nonzero constant quadratically as $H\to 0$, it has a non-Gaussian tail that decays exponentially for large $H$. We show that this exponential tail is rather robust and holds for a whole family of linear interface models parametrized by a dynamical exponent $z>1$, with $z=2$ corresponding to the Edwards-Wilkinson model.

cond-mat.stat-mech↗

arXiv2025

Effective description of Taylor dispersion in strongly corrugated channels

Taylor dispersion in periodic but highly corrugated channels is studied. Exact analytical expressions for the long-time diffusion constant and drift along the channel are derived to next-to-leading order in the limit of small channel period. Using these results we show how an effective model for Taylor dispersion in tortuous porous media can be framed in terms of dispersion in a uniform channel with absorption/desorption at its surface, an effective slip length for the flow at the surface and an effective, universal, diffusion constant on the surface. This work thus extends the concept of an effective slip-length for hydrodynamics flows to Taylor dispersion by those flows. The analytical results are confirmed by numerical calculations, and present a robust method to understand and upscale the transport properties of flows in porous media.

cond-mat.stat-mech↗

arXiv2025

Solving Lyapunov equations for electrically driven ternary electrolytes -- application to long-range van der Waals interactions

Stochastic density functional theory (SDFT) has been widely used to study the out of equilibrium properties of electrolyte solutions. Examples include investigations of electrical conductivity -- both within and beyond linear response -- and modifications of thermal van der Waals interactions in driven electrolytes. Within the approximation scheme derived from linearizing SDFT for fluctuations around mean densities, the steady state correlation functions between the $N$ ionic species are governed by linear Lyapunov equations of degree $N(N+1)/2$. Consequently, the system's complexity increases significantly when transitioning from binary to ternary electrolytes, and few analytical results exist for the latter. In this paper, we demonstrate how -- for the specific case of electrolytes -- the Lyapunov equations can be reduced to a system of $N$ linear equations. We apply this reduction to compute the long-range component of the van der Waals interaction between two slabs containing a ternary electrolyte under an applied electric field parallel to the slabs. Unlike the binary electrolyte case, we show that the resulting van der Waals interaction for a ternary electrolyte depends on the ionic species' diffusion coefficients, highlighting its inherently out of equilibrium nature.

cond-mat.soft↗

arXiv2025

Enhanced diffusion over a periodic trap by hydrodynamic coupling to an elastic mode

In many physical systems, degrees of freedom are coupled \emph{via} hydrodynamic forces, even in the absence of Hamiltonian interactions. A particularly important and widespread example concerns the transport of microscopic particles in fluids near deformable boundaries. In such a situation, the influence of elastohydrodynamic couplings on Brownian motion remains to be understood. Unfortunately, the temporal and spatial scales associated with the thermal fluctuations of usual surfaces are often so small that their deformations are difficult to monitor experimentally, together with the much slower and larger particle motion at stake. Here, we propose a minimal model describing the hydrodynamic coupling of a colloidal particle to a fluctuating elastic mode, in presence of an external periodic potential. We demonstrate that the late-time diffusion coefficient of the particle increases with the compliance of the elastic mode. Remarkably, our results reveal that, and quantify how: i) spontaneous microscopic transport in complex environnements can be affected by soft boundaries -- a situation with numerous practical implications in nanoscale and biological physics; ii) the effects of fast and tiny surface deformations are imprinted over the long-term and large-distance colloidal mobility -- and are hence measurable in practice.

cond-mat.soft↗

arXiv2025

Correlation decoupling of Casimir interaction in an electrolyte driven by external electric fields

It has been established for a long time that the long range van der Waals or thermal Casimir interaction between two semi-infinite dielectrics separated by a distance $H$ is screened by an intervening electrolyte. Here we show how this interaction is modified when an electric field of strength $E$ is applied parallel to the dielectric boundaries, leading to a non-equilibrium steady state with a current. The presence of the field induces a long range thermal repulsive interaction, scaling just like the thermal Casimir interaction between dielectrics without the intervening electrolyte, {\em i.e.} as $1/H^3$. At small $E$ the effect is of order $E^2$ while at large fields it saturates to an $E$ independent value. We explain the results in terms of a decoupling mechanism between the charge density fluctuations of cations and anions at large applied fields.

cond-mat.stat-mech↗

arXiv2025

Repulsive thermal van der Waals interaction in multi-species asymmetric electrolytes driven by external electric fields

It is well established that the long-range component of the thermal van der Waals interaction between two semi-infinite dielectrics becomes short-range when an electrolyte is present between them, this is the well known phenomenon of screening. In Phys. Rev. Lett, 133, 238002 (2024) it was shown that for a binary symmetric electrolyte, an electric field parallel to the dielectric boundaries disrupts screening and a long-range thermal repulsive interaction appears. At large applied fields this long-range repulsive interaction can be explained by the fact that the cations and anions have differing average drifts moving in opposite directions, leading to the correlation of charge density fluctuations between the two species to decouple. Here we extend these results to binary electrolytes which are asymmetric as well as electrolytes with more than two ionic species.

cond-mat.soft↗

arXiv2024

Uphill drift in the absence of current in single-file diffusion

Single-file diffusion is a paradigmatic model for the transport of Brownian colloidal particles in narrow one-dimensional channels, such as those found in certain porous media, where the particles cannot cross each other. We consider a system where a different external uniform potential is present to the right and left of an origin. For example, this is the case when two channels meeting at the origin have different radii. In equilibrium, the chemical potential of the particles are equal, the density is thus lower in the region with the higher potential, and by definition there is no net current in the system. Remarkably, a single-file tracer particle initially located at the origin, with position denoted by $Y(t)$, exhibits an average up-hill drift toward the region of highest potential. This drift has the late time behavior $\langle Y(t)\rangle= C t^{1/4}$, where the prefactor $C$ depends on the initial particle arrangement. This surprising result is shown analytically by computing the first two moments of $Y(t)$ through a simple and physically-illuminating method, and also via extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2024

Singular viscoelastic perturbation to soft lubrication

Soft lubrication has been shown to drastically affect the mobility of an object immersed in a viscous fluid in the vicinity of a purely elastic wall. In this theoretical study, we develop a minimal model incorporating viscoelasticity, carrying out a perturbation analysis in both the elastic deformation of the wall and its viscous damping. Our approach reveals the singular-perturbation nature of viscoelasticity to soft lubrication. Numerical resolution of the resulting non-linear, singular and coupled equations of motion reveals peculiar effects of viscoelasticity on confined colloidal mobility, opening the way towards the description of complex migration scenarios near realistic polymeric substrates and biological membranes.

cond-mat.soft↗

arXiv2023

Single-file diffusion in spatially inhomogeneous systems

We study the effect of spatially-varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Non-interacting particles in such a system exhibit normal diffusion at late times, which is characterised by an effective diffusion constant $D_\mathrm{eff}$. Here we demonstrate the physically appealing result that the dispersion of single-file tracers in this system has the same long-time behavior as that for Brownian particles in a spatially-homogeneous system with constant diffusivity $D_\mathrm{eff}$. Our results are based on a late-time analysis of the Fokker-Planck equation, motivated by the mathematical theory of homogenization. The findings are confirmed by numerical simulations for both annealed and quenched initial conditions.

cond-mat.stat-mech↗

arXiv2023

Interactions enhance dispersion in fluctuating channels via emergent flows

Understanding particle motion in narrow channels is essential to guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of channel walls for fluid-filled channels can slow down or increase the dispersion of tracer particles. Entropic trapping in the wall bulges slows dispersion, and hydrodynamic flows induced by wall fluctuations enhance dispersion. Previous studies primarily concentrated on the case of a single Brownian tracer either embedded in an incompressible fluid or in the ideal case where the presence of fluid is ignored. Here we address the question of what happens when there is a large ensemble of interacting Brownian tracers -- a common situation in applications. Introducing repulsive interactions between the tracer particles, while ignoring the presence of a background fluid, leads to an effective flow field. This flow field enhances tracer dispersion, a phenomenon strongly reminiscent of that seen in incompressible background fluid. We characterise the dispersion by the long-time diffusion coefficient of a single tracer, numerically and analytically with a mean-field density functional analysis. We find a surprising effect where an increased particle density enhances the diffusion coefficient, challenging the notion that crowding effects tend to reduce diffusion. Here, inter-particle interactions push particles closer to the fluctuating channel walls. Then, interactions between the fluctuating wall and the now-nearby particles drive particle mixing. Our mechanism is sufficiently general that we expect it to apply to various systems. In addition, the perturbation theory we derive quantifies dispersion in generic advection-diffusion systems with arbitrary spatiotemporal drift.

cond-mat.soft↗

arXiv2023

Effusion of stochastic processes on a line

We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with uniform density and leaking into the positive half line is an example which has been extensively studied in the literature. Here we derive new results for the average number and variance of the number of leaked particles for arbitrary Gaussian processes initially confined to the negative half line and also derive its joint two-time probability distribution, both for the annealed and the quenched initial conditions. For the annealed case, we show that the two-time joint distribution is a bivariate Poisson distribution. We also discuss the role of correlations in the initial particle positions on the statistics of the number of particles on the positive half line. We show that the strong memory effects in the variance of the particle number on the positive real axis for Brownian particles, seen in recent studies, persist for arbitrary Gaussian processes and also at the level of two-time correlation functions.

cond-mat.stat-mech↗

arXiv2022

Non-Gaussian diffusion near surfaces

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a non-zero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.

cond-mat.soft↗

arXiv2022

How stickiness can speed up diffusion in confined systems

The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian tracers. Here, using a general adsorption desorption model with surface diffusion, we show analytically that making surfaces or obstacles attractive can accelerate dispersion. In particular, we show that this enhancement of diffusion can exist even when the surface diffusion constant is smaller than that in the bulk. Even more remarkably, this enhancement effect occurs when the effective diffusion constant, when restricted to surfaces only, is lower than the effective diffusivity with purely reflecting boundaries. We give analytical formulas for this intriguing effect in periodic arrays of spheres as well as undulating micro-channels. Our results are confirmed by numerical calculations and Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2021

Generalized Taylor dispersion for translationally invariant microfluidic systems

We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the walls become important. We provide a simple and general formula for the effective diffusion constant along the channel as well as the first non-trivial finite time correction for arbitrary flows along the channel, arbitrary interaction potentials with the walls and arbitrary expressions for the diffusion tensor. The formula are in particular amenable to a straightforward numerical implementation, rendering them extremely useful for comparison with experiments. We present a number of applications, notably for systems which have parabolically varying diffusivity profiles, to systems with attractive interactions with the walls as well as electroosmotic flows between plates with differing surface charges within the Debye-Hückel approximation.

physics.flu-dyn↗