A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker–Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution.

Brownian dynamics with hydrodynamic interactions

Differently from passive Brownian particles, active particles, also known as self-propelled Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy from their environment and converting it into directed motion. Because of this constant flow of energy, their behavior can be explained and understood only within the framework of nonequilibrium physics. In the biological realm, many cells perform directed motion, for example, as a way to browse for nutrients or to avoid toxins. Inspired by these motile microorganisms, researchers have been developing artificial particles that feature similar swimming behaviors based on different mechanisms. These man-made micromachines and nanomachines hold a great potential as autonomous agents for health care, sustainability, and security applications. With a focus on the basic physical features of the interactions of self-propelled Brownian particles with a crowded and complex environment, this comprehensive review will provide a guided tour through its basic principles, the development of artificial self-propelling microparticles and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.

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Active Particles in Complex and Crowded Environments

Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics.

Developments in the theory of Ostwald ripening since the classic work of I. M. Lifshitz and V. V. Slyozov (LS) are reviewed and directions for future work are suggested. Recent theoretical work on the role of a finite volume fraction of coarsening phase on the ripening behavior of two-phase systems is reformulated in terms of a consistent set of notation through which each of the theories can be compared and contrasted. Although more theoretical work is necessary, these theories are in general agreement on the effects of a finite volume fraction of coarsening phase on the coarsening behavior of two-phase systems. New work on transient Ostwald ripening is presented which illustrates the broad range of behavior which is possible in this regime. The conditions responsible for the presence of the asymptotic state first discovered by LS, as well as the manner in which this state is approached, are also discussed. The role of elastic fields during Ostwald ripening in solid-solid mixtures is reviewed, and it is shown that these fields can play a dominant role in determining the coarsening behavior of a solid-solid system.

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The Theory of Ostwald Ripening

Active Brownian particles, also referred to as microswimmers and nanoswimmers, are biological or manmade microscopic and nanoscopic particles that can self-propel. Because of their activity, their behavior can only be explained and understood within the framework of nonequilibrium physics. In the biological realm, many cells perform active Brownian motion, for example, when moving away from toxins or towards nutrients. Inspired by these motile microorganisms, researchers have been developing artificial active particles that feature similar swimming behaviors based on different mechanisms; these manmade micro- and nanomachines hold a great potential as autonomous agents for healthcare, sustainability, and security applications. With a focus on the basic physical features of the interactions of active Brownian particles with a crowded and complex environment, this comprehensive review will put the reader at the very forefront of the field of active Brownian motion, providing a guided tour through its basic principles, the development of artificial self-propelling micro- and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.

/pdf/active-brownian-particles-in-complex-and-crowded-3ym4we2m8l.pdf

Active Brownian Particles in Complex and Crowded Environments

An efficient scheme is presented for the numerical calculation of hydrodynamic interactions of many spheres in Stokes flow. The spheres may have various sizes, and are freely moving or arranged in rigid arrays. Both the friction and mobility matrix are found from the solution of a set of coupled equations. The Stokesian dynamics of many spheres and the friction and mobility tensors of polymers and proteins may be calculated accurately at a modest expense of computer memory and time. The transport coefficients of suspensions can be evaluated by use of periodic boundary conditions.

Friction and mobility of many spheres in Stokes flow

We evaluate the hydrodynamic interaction tensors for two spheres of unequal size and for general mixed slip-stick boundary conditions. A method of reflections leads to a series expansion for the diffusion tensors in powers of the inverse distance l−1 between sphere centers and explicit results are derived through terms of order l−7. It turns out that the series expansion for the diffusion tensors converges much more rapidly than that for the friction tensors.

Hydrodynamic interaction between two spheres

A theory for the concentration dependence of the rate of diffusion‐controlled reactions is formulated. One of the reacting partners is taken to be a collection of static sinks. The steady state situation for a random distribution of these sinks is studied. The rate coefficient is predicted to increase with concentration of sinks and the dependence on concentration is shown to be nonanalytic.

Concentration dependence of the rate of diffusion‐controlled reactions

We study the short‐time collective and self‐diffusion coefficients, the rotational self‐diffusion coefficient, and the high frequency effective viscosity of a suspension of spherical Brownian particles. At low volume fraction these transport coefficients are given by integrals of hydrodynamic pair interactions. Using exact series expansions in powers of the inverse distance between centers of a pair of particles, we obtain accurate values for the low density transport coefficients. We consider hard spheres with mixed slip–stick boundary conditions, as well as spherical liquid droplets with an internal viscosity different from the bulk. We show that the transport coefficients depend strongly on the particle model.

Short‐time diffusion coefficients and high frequency viscosity of dilute suspensions of spherical Brownian particles

We study the long‐time self‐diffusion coefficient and the zero‐frequency effective viscosity for a suspension of spherical Brownian particles. The correction to first order in the volume fraction to the self‐diffusion coefficient and the correction to second order in the volume fraction to the effective viscosity are given by integral expressions derived by Batchelor. Using exact series expansions of the hydrodynamic interaction functions in powers of the inverse distance between centers of a pair of particles we obtain accurate values for the correction terms. We consider hard spheres with mixed slip‐stick boundary conditions as well as spherical liquid droplets with a viscosity different from the bulk.

B. U. Felderhof

Papers

Friction and mobility of many spheres in Stokes flow

Hydrodynamic interaction between two spheres

Concentration dependence of the rate of diffusion‐controlled reactions

Short‐time diffusion coefficients and high frequency viscosity of dilute suspensions of spherical Brownian particles

Long-time self-diffusion coefficient and zero-frequency viscosity of dilute suspensions of spherical Brownian particles