B. U. Felderhof

Friction and mobility of many spheres in Stokes flow

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.

Concentration dependence of the rate of diffusion‐controlled reactions

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.

Fluctuations of polarization and magnetization in dielectric and magnetic media

We consider thermal fluctuations of polarization, magnetization, and the associated electromagnetic fields in dielectric magnetic media which are allowed to be anisotropic and spatially nonhomogeneous. The theory is purely macroscopic and is based on an application of the fluctuation–dissipation theorem. It is shown that the correlation functions can be elegantly expressed in terms of the Green functions for Maxwell’s equations.

Competitive effects in diffusion‐controlled reactions

We study diffusion‐controlled reactions in a system of static sinks reacting with diffusing molecules and investigate the competitive effects due to the global distribution of sinks. We also study the effect of competition on growth or shrinkage of droplets in coagulation or burning.

Diffusion and absorption in a medium with spherical sinks

We consider particles diffusing in a uniform medium and being absorbed by statistically distributed spherical sinks. We study the average diffusion–absorption equation, as derived to first order in the sink density by multiple‐scattering theory. We show that for perfect sinks this equation must be modified to take proper account of instantaneous absorption of particles created inside the sinks.

Frequency‐dependent rate coefficient in diffusion‐controlled reactions

Diffusion‐controlled reactions between particles and a nondilute system of sinks are studied. It is shown that in time‐dependent situations it is necessary to take account of retardation effects in the building‐up of correlations between competing sinks. The retardation leads to a frequency dependence of the rate coefficient. We derive corrections to the dilute limit value of the rate coefficient in the low concentration, low frequency regime. As an application we consider the effect on the time dependence of a quenching process.

Hydrodynamic friction coefficients of coated spherical particles.

The complete set of hydrodynamic friction coefficients for a spherical particle coated with a porous layer and immersed in a viscous fluid is evaluated in analytic form. The coefficients allow the calculation of the flow disturbance caused by the coated particle for any incident flow which satisfies the creeping flow equations. The coefficients may be used for the evaluation of hydrodynamic pair interactions between coated spheres, as well as for the numerical calculation of many-sphere hydrodynamic interactions, and the calculation of transport properties of suspensions of coated spherical particles.

Fluctuation theory of single-file diffusion

In a one-dimensional suspension of Brownian particles, which cannot pass each other, the mean square displacement of a selected particle grows at long times with the square root of time, rather than linearly. It is shown that the coefficient of the square root, the so-called single-file mobility, can be derived from fluctuation theory, involving the velocity time scale and the fluctuation-dissipation theorem. The single-file mobility is expressed in terms of the collective diffusion coefficient and the isothermal osmotic compressibility, in agreement with the result derived earlier by Kollmann on the basis of the generalized Smoluchowski equation [M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)].

Reduced description of electric multipole potential in Cartesian coordinates

The electrostatic potential due to a multipole moment of order l is expressed in terms of 2l+1 independent Cartesian multipole components. The multipole expansion of the electrostatic interaction energy between two charge distributions is reduced correspondingly to the minimum number of Cartesian components.

Diffusion and velocity relaxation of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls

The diffusion tensor and velocity correlation function of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls are calculated in point approximation. The fluid is assumed to satisfy stick boundary conditions at the walls. It is found that the velocity correlation function decays asymptotically with a negative t(-2) long-time tail due to coupling to overdamped sound waves. The coefficient of the long-time tail is calculated and shown to be independent of fluid viscosity.