Brownian Fluid Research Articles

Large N two-dimensional Yang–Mills fields for the spectral behavior of Brownian particles and relativistic many-body systems

This work explores the spectral behavior of interacting many-body systems — gravitating dust solutions (galaxy formations and black hole clusters) and Brownian fluids. The eigenvalue dynamics of these systems are then represented by the two-dimensional Yang–Mills field (i.e. spectral projection). The interacting particles in the many-body systems are associated with random matrices of dimensions, N. The Painlevé II dynamical system is shown to surface at large N ([Formula: see text]); when the mentioned Yang–Mills field is configured in a specific way. Critical phenomena (Douglas–Kazakov phase transition) of the interacting many-body systems at large N were attained via the spectral projection of the mentioned physical systems. In addition, the existence of instantons (spectral Dirac monopoles) in the strong coupling phase was shown during phase transition.

Tracking the vortex motion by using Brownian fluid particles

In this paper, we propose a simple yet powerful vortex method to numerically approximate the dynamics of an incompressible flow. The idea is to sample the distribution of the initial vortices of the fluid flow in question and then follow vortex dynamics along Taylor's Brownian fluid particles. The weak convergences of this approximation scheme are obtained for both two-dimensional (2D) and three-dimensional (3D) fluid flows, though only for small time in 3D case. Based on our method, the simulation results are quite attracting.

The role of dimensionality and geometry in quench-induced nonequilibrium forces

We present an analytical formalism, supported by numerical simulations, for studying forces that act on curved walls following temperature quenches of the surrounding ideal Brownian fluid. We show that, for curved surfaces, the post-quench forces initially evolve rapidly to an extremal value, whereafter they approach their steady state value algebraically in time. In contrast to the previously-studied case of flat boundaries (lines or planes), the algebraic decay for curved geometries depends on the dimension of the system. Specifically, steady-state values of the force are approached in time as t −d/2 in d-dimensional spherical (curved) geometries. For systems consisting of concentric circles or spheres, the exponent does not change for the force on the outer circle or sphere. However, the force exerted on the inner circles or sphere experiences an overshoot and, as a result, does not evolve to the steady state in a simple algebraic manner. The extremal value of the force also depends on the dimension of the system, and originates from curved boundaries and the fact that particles inside a sphere or circle are locally more confined, and diffuse less freely than particles outside the circle or sphere.

Dynamic transition in a Brownian fluid: role of fluctuation–dissipation constraints

In this paper we study equations of fluctuating non-linear hydrodynamics (FNH) for a liquid in which the constituent particles follow Brownian dynamics (BD). Here the microscopic-level dynamics are dissipative as compared to the case of fluids with reversible Newtonian dynamics (ND). The implications of non-linearities in FNH equations for an ND liquid on its long-time dynamics and the possibility of an ideal ergodicity–non-ergodicity (ENE) transition at high density have been widely investigated in literature. It is known that in an ND fluid, dynamics described by FNH equations do not support a sharp ENE transition. In the present paper we demonstrate that, as a consequence of the fluctuation–dissipation constraints, an ideal ENE transition is also not supported from the FNH equations for BD fluid.

Tagged particle correlations in a dense fluid: Role of microscopic dynamics

We study the self diffusion process in a dense fluid in two cases for which the individual fluid particles follow respectively deterministic Newtonian dynamics (ND) and stochastic Brownian dynamics (BD). The role of correlated motion of fluid particles on the single particle diffusion is taken in to account here using mode coupling models. We demonstrate the subtle difference present in the corresponding mode coupling corrections to diffusion constants for fluids with BD and ND by carefully analysing the equations of fluctuating nonlinear hydrodynamics (FNH) in the respective cases. Finally, we use recently developed model for dynamics of binary mixtures to model a BD fluid in terms of a ND mixture whose species have a very large mass ratio. Here the high inertia larger particles are identified as Brownian and a mechanical interpretation of the noise in a Brownian fluid is made in terms of the smaller particles randomly colliding with them.

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory.

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

Dynamic equivalences in the hard-sphere dynamic universality class

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).

Single and multi-particle passive microrheology of low-density fluids using sedimented microspheres

We present a technique of passive microrheology based on tracking micron-sized particles which are denser than the surrounding fluid and therefore they sediment into a quasi two-dimensional layer. Theoretical corrections for the diffusion coefficient of polystyrene, magnetic, and melamine resin microspheres, situated at different average heights above the bottom of the container cell, allow to unify the corresponding results for the zero-shear viscosity and the dynamic modulus on low-density fluids, such as low-concentration mixtures of glycerol and poly(ethylene oxide) in water and 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid. Limitations of the experimental and data analysis methodology are discussed by developing experimental-like simulations of Brownian fluids.

Microrheological consequences of attractive colloid-colloid potentials in a two-dimensional Brownian fluid

By using microrheological methods commonly employed in videomicroscopy experiments, we study the rheology of a two-dimensional computational fluid formed by Brownian disks with the aim of exploring the influence of some effective colloid-colloid attractive interactions. The model of fluid is developed by Brownian dynamics simulations without hydrodynamical interactions, and it is characterized by calculating its equation of state from the pair distribution function. Micromechanical properties, relative and intrinsic viscosity and freezing are discussed. Then, we include attractive forces such a Asakura-Oosawa depletion force or an empiric expression proposed by Grier and Hal (GH) for an anomalous electrostatic potential observed in confined and charged colloids. By using both potentials, viscosity is clearly increased, but when the GH potential is included, viscoelastic gel state is reached for intermediate values of surface concentration. Finally, we analyse the influence of the attractive potentials in the breaking-up by thermal fluctuations of linear chains formed by 2D particles, finding that the GH potential reduces the characteristical time at which the disks can be considered as disaggregated. In this work, we employ an experimental-like methodology for the study of a Brownian hard-disk fluid, providing a very useful link with experimental procedures.

Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?

We aim to clarify confusions in the literature as to whether or not dynamical density functional theories for the one-body density of a classical Brownian fluid should contain a stochastic noise term. We point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified, depending on how the fluid one-body density is defined -- i.e. whether it is an ensemble averaged density distribution or a spatially and/or temporally coarse grained density distribution.

Dynamic equivalence between soft- and hard-core Brownian fluids.

In this work, we demonstrate the dynamic equivalence between the members of the family of Brownian fluids whose particles interact through strongly repulsive radially symmetric soft-core potentials. We specifically consider pair potentials proportional to inverse powers of (r/sigma). This equivalence is the dynamic extension of the static equivalence between all these pair potentials and the hard-sphere fluid, assumed in the treatment of soft-core reference potentials in the classical (Weeks-Chandler-Andersen or Barker-Henderson) perturbation theories of simple liquids. In contrast with the strict hard-sphere Brownian system, in the case of soft-sphere potentials the conventional Brownian dynamics algorithm is indeed well defined. We find that, except for small values of nu, and/or very short times, the dynamic properties of all these systems collapse into a single universal curve, upon a well-defined rescaling of the time and distance variables. This family of systems includes the hard-sphere limit. This observation permits a conceptually simple, new, and accurate Brownian dynamics algorithm to simulate the dynamic properties of the hard-sphere model dispersion without hydrodynamic interactions. Such an algorithm consists of the straightforward rescaling of the Brownian-dynamics simulated properties of any of the dynamically equivalent soft-sphere systems.

Self-consistent generalized Langevin equation for colloid dynamics.

We present a general self-consistent theory of colloid dynamics which, for a system without hydrodynamic interactions, allows us to calculate F(k,t), and its self-diffusion counterpart F(S)(k,t), given the effective interaction pair potential u(r) between colloidal particles, and the corresponding equilibrium static structural properties. This theory is build upon the exact results for F(k,t) and F(S)(k,t) in terms of a hierarchy of memory functions, derived from the application of the generalized Langevin equation formalism, plus the proposal of Vineyard-like connections between F(k,t) and F(S)(k,t) through their respective memory functions, and a closure relation between these memory functions and the time-dependent friction function Delta zeta(t). As an illustrative application, we present and analyze a selection of numerical results of this theory in the short- and intermediate-time regimes, as applied to a two-dimensional repulsive Yukawa Brownian fluid. For this system, we find that our theory accurately describes the dynamic properties contained in F(k,t) in a wide range of conditions, including strongly correlated systems, at the longest times available from our computer simulations.

Overdamped van hove function of colloidal suspensions

The generalized-hydrodynamic theory for collective diffusion of a monodisperse colloidal suspension is developed in the framework of the Onsager-Machlup theory of time-dependent fluctuations. The time evolution of the intermediate scattering function F(k,t) is derived as a contraction of the description involving the instantaneous particle number concentration, the particle current, and the stress tensor of the Brownian fluid as state variables. We show that the proper overdamped limit of this equation requires the explicit separation of the stress tensor in its mutually orthogonal kinetic and configurational contributions. Analogous results also follow for the self-intermediate scattering function F(s)(k,t). We show that neglecting the non-Markovian part of the configurational stress tensor memory, one recovers the single exponential memory approximation (based on sum rules derived from the Smoluchowski equation) for both F(s)(k,t) and F(k,t). We suggest simple approximate manners to relate the collective and the self-memory functions, leading to Vineyard-like approximate relations between F(s)(k,t) and F(k,t).

Vineyard-like approximations for colloid dynamics

In this paper we propose a hierarchy of higher-order Vineyard-like approximations for colloidal systems. These consist of approximate expressions for the intermediate scattering function F(k,t) in terms of the self-intermediate scattering function F(s)(k,t) (or some memory function associated with it), and of other static structural properties of the suspension. In order to assess the accuracy of the proposed approximations, we perform Brownian dynamics simulations in a simple model system (a two-dimensional Yukawa Brownian fluid), in which we determine F(k,t), F(s)(k,t), and the required static structural properties. We study proposals for "second-order" and "third-order" Vineyard-like approximations. We find that the detailed structure of the relationship between the corresponding collective and self-memory functions turns out to be most important, as quantified by our simulation results.