The structure and dynamics of confined suspensions of particles of arbitrary shape is of interest in multiple disciplines, from biology to engineering. Theoretical studies are often limited by the complexity of long-range particle-particle and particle-wall forces, including many-body fluctuating hydrodynamic interactions. Here, we report a computational study on the diffusion of spherical and cylindrical particles confined in a spherical cavity. We rely on an Immersed-Boundary General geometry Ewald-like method to capture lubrication and long-range hydrodynamics, and include appropriate non-slip conditions at the confining walls. A Chebyshev polynomial approximation is used to satisfy the fluctuation-dissipation theorem for the Brownian suspension. We explore how lubrication, long-range hydrodynamics, particle volume fraction and shape affect the equilibrium structure and the diffusion of the particles. It is found that once the particle volume fraction is greater than $10\%$, the particles start to form layered aggregates that greatly influence particle dynamics. Hydrodynamic interactions strongly influence the particle diffusion by inducing spatially dependent short-time diffusion coefficients, stronger wall effects on the particle diffusion towards the walls, and a sub-diffusive regime --caused by crowding-- in the long-time particle mobility. The level of asymmetry of the cylindrical particles considered here is enough to induce an orientational order in the layered structure, decreasing the diffusion rate and facilitating a transition to the crowded mobility regime at low particle concentrations. Our results offer fundamental insights into the diffusion and distribution of globular and fibrillar proteins inside cells.
We study the transport of Brownian particles through a corrugated channel caused by a force field containing curl-free (scalar potential) and divergence-free (vector potential) parts. We develop a generalized Fick-Jacobs approach leading to an effective one-dimensional description involving the potential of mean force. As an application, the interplay of a pressure-driven flow and an oppositely oriented constant bias is considered. We show that for certain parameters, the particle diffusion is significantly suppressed via the property of hyrodynamically enforced entropic particle trapping.
Recently, many interesting features of the hydrodynamically coupled motions of the Brownian particles in a viscous fluid have been reported which are impossible for the uncoupled motions of the similar particles. However, it is expected that those physics in a viscoelastic fluid is much more interesting due to the presence of the additional frequency dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive aspects. In…
We measure the energy exchanged between two hydrodynamically coupled micron-sized Brownian particles trapped in water by two optical tweezers. The system is driven out of equilibrium by random forcing the position of one of the two particles. The forced particle behaves as it has an "effective temperature" higher than that of the other bead. This driving modifies the equilibrium variances and cross-correlation functions of the bead positions: we measure an energy flow between the particles and an instantaneous cross-correlation, proportional to the effective temperature difference between the …
We experimentally study the statistical properties of the energy fluxes between two trapped Brownian particles, interacting through dissipative hydrodynamic coupling, submitted to an effective temperature difference $ΔT$, obtained by random forcing the position of one trap. We identify effective heat fluxes between the two particles and show that they satisfy an exchange fluctuation theorem (xFT) in the stationary state. We also show that after the sudden application of a temperature gradient $ΔT$, \resub{the total} hot-cold flux satisfies \resub{a} transient xFT for any integration time where…
Using our generalized Fick-Jacobs approach [Martens et al., PRL 110, 010601 (2013); Martens et al., Eur. Phys. J. Spec. Topics 222, 2453-2463 (2013)] and extensive Brownian dynamics simulations, we study particle transport through three-dimensional periodic channels of different height. Directed motion is caused by the interplay of constant bias acting along the channel axis and a pressure-driven flow. The tremendous change of the flow profile shape in channel direction with the channel height is reflected in a crucial dependence of the mean particle velocity and the effective diffusion coeffi…
We describe direct imaging measurements of a colloidal sphere's diffusion between two parallel surfaces. The dynamics of this deceptively simple hydrodynamically coupled system have proved difficult to analyze. Comparison with approximate formulations of a confined sphere's hydrodynamic mobility reveals good agreement with both a leading-order superposition approximation as well as a more general all-images stokeslet analysis.
Hydrodynamically interacting active particles in an external harmonic potential form a self-assembled fluid pump at large enough Péclet numbers. Here, we give a quantitative criterion for the formation of the pump and show that particle orientations align in the self-induced flow field in surprising analogy to ferromagnetic order where the active Péclet number plays the role of inverse temperature. The particle orientations follow a Boltzmann distribution $Φ(\mathbf{p}) \sim \exp(A p_z)$ where the ordering mean field $A$ scales with active Péclet number and polar order parameter. The mean flow…
The conformational and dynamical properties of active self-propelled filaments/polymers are investigated in the presence of hydrodynamic interactions by both, Brownian dynamics simulations and analytical theory. Numerically, a discrete linear chain composed of active Brownian particles is considered, analytically, a continuous linear semiflexible polymer with active velocities changing diffusively. The force-free nature of active monomers is accounted for - no Stokeslet fluid flow induced by active forces - and higher order hydrodynamic multipole moments are neglected. The nonequilibrium chara…
We have calculated the probability distribution function G(R,L|R',0) of the end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a cylinder, a cone and a curved torus in 3-D. We showed that: surface curvature induces a geometrical localization area; at short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at large scales, (R-R')^2 is constant for the sphere, it is linear in L for the cylinder and reaches different constant values for the torus. The cone vertex induces (funct…
Miniaturized, self-propelled locomotors use chemo-mechanical transduction mechanisms to convert fuel in the environment to autonomous motion. Recent experimental and theoretical studies demonstrate that these autonomous engines can passively follow the contours of solid boundaries they encounter. Boundary guidance, however, is not necessarily stable: Mechanical disturbances can cause the motor to hydrodynamically depart from the passively guided pathway. Furthermore, given the scaled-down size of micromotors (typically 100 nm -10 $μ$m), Brownian thermal fluctuation forces are necessarily impor…
We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions "on the fly". Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically-correlated…
In this work, we report a new method to simulate active Brownian particles (ABPs) in molecular dynamics (MD) simulations. Immersed in a fluid, each ABP consists of a head particle and a spherical phantom region of fluid where the flagellum of a microswimmer takes effect. The orientation of the active particle is governed by a stochastic dynamics, with the orientational persistence time determined by the rotational diffusivity. To hydrodynamically drive the active particle as a pusher, a pair of active forces are exerted on the head particle and the phantom fluid region respectively. The active…
We introduce a Rigid-Body Fluctuating Immersed Boundary (RB-FIB) method to perform large-scale Brownian dynamics simulations of suspensions of rigid particles in fully confined domains, without any need to explicitly construct Green's functions or mobility operators. In the RB-FIB approach, discretized fluctuating Stokes equations are solved with prescribed boundary conditions in conjunction with a rigid-body immersed boundary method to discretize arbitrarily-shaped colloidal particles with no-slip or active-slip prescribed on their surface. We design a specialized Split--Euler--Maruyama tempo…
Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: Dynamical clustering, non-Gaussianity and hydrodynamic correlations
Technische Universität Berlin（柏林工业大学）；Forschungszentrum Jülich（于利希研究中心）；Heinrich-Heine Universität Düsseldorf（杜塞尔多夫海因里希·海涅大学）
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these nonequilibrium fluctuations is a very difficult problem, yet they are of great importance for a wide range of processes including pigment deposition in cosmetic or paint films, the transport of microfluidic droplets, ... All these samples concern rigidly confined fluids, which we consider in this paper. We address the collective dynamics of non-Brownian droplets cruisi…
Attractive colloidal dispersions, suspensions of fine particles which aggregate and frequently form a space spanning elastic gel are ubiquitous materials in society with a wide range of applications. The colloidal networks in these materials can exist in a mode of free settling when the network weight exceeds its compressive yield stress. An equivalent state occurs when the network is held fixed in place and used as a filter through which the suspending fluid is pumped. In either scenario, hydrodynamic instabilities leading to loss of network integrity occur. Experimental observations have sho…
Active motions of a biological membrane can be induced by non-thermal fluctuations that occur in the outer environment of the membrane. We discuss the dynamics of a membrane interacting hydrodynamically with an active wall that exerts random velocities on the ambient fluid. Solving the hydrodynamic equations of a bound membrane, we first derive a dynamic equation for the membrane fluctuation amplitude in the presence of different types of walls. Membrane two-point correlation functions are calculated for three different cases; (i) a static wall, (ii) an active wall, and (iii) an active wall wi…
Periodic arrays of micro- or nano-pillars constitute solid state matrices with excellent properties for DNA size separation. Nanofabrication technologies offer many solutions to tailor the geometry of obstacle arrays, yet most studies have been conducted with cylinders arranged in hexagonal lattices. In this report, we investigate the dynamics of single DNA collision with elliptical nanoposts using hydrodynamic actuation. Our data shows that the asymmetry of the obstacles has minor effect on unhooking dynamics, and thus confirms recent predictions obtained by Brownian dynamics simulations. In …
Biochemical reactions typically occur at low copy numbers, but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. However, while particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them oftentimes imply trade-offs between computationa…
