The analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape are derived. The reference center is arbitrary, and the reference frame is such that th
e rotational-rotational diffusion tensor is diagonal.
Dynamics of flexible non-Brownian fibers in shear flow at low-Reynolds-number are analyzed numerically for a wide range of the ratios A of the fiber bending force to the viscous drag force. Initially, the fibers are aligned with the flow, and later t
hey move in the plane perpendicular to the flow vorticity. A surprisingly rich spectrum of different modes is observed when the value of A is systematically changed, with sharp transitions between coiled and straightening out modes, period-doubling bifurcations from periodic to migrating solutions, irregular dynamics and chaos.
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equatio
n. The role of the particle mobility center is determined and discussed.
Systems of spherical particles moving in Stokes flow are studied for a different particle internal structure and boundaries, including the Navier-slip model. It is shown that their hydrodynamic interactions are well described by treating them as soli
d spheres of smaller hydrodynamic radii, which can be determined from measured single-particle diffusion or intrinsic viscosity coefficients. Effective dynamics of suspensions made of such particles is quite accurately described by mobility coefficients of the solid particles with the hydrodynamic radii, averaged with the unchanged direct interactions between the particles.
Rotne-Prager-Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation is that it includes all long-ra
nge terms (i.e. decaying as R^-3 or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne-Prager-Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne-Prager-Yamakawa approximation can be generalized for other geometries and boundary conditions.
