Berlin 2008 – scientific programme
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CPP: Fachverband Chemische Physik und Polymerphysik
CPP 8: POSTERS Dynamics and Diffusion
CPP 8.6: Poster
Monday, February 25, 2008, 16:45–19:00, Poster A
The short time self diffusion coefficient of a sphere in a suspension of rigid rods — •Jan Guzowski1, Bogdan Cichocki2, Eligiusz Wajnryb2, and Gustavo Abade2 — 1Max Planck Institute fo Metals Research, Stuttgart — 2Warsaw University
The short--time self diffusion coefficient of a sphere in a suspension of rigid rods is calculated in first order in the rod volume fraction $\phi$. For low rod concentrations the correction to the Einstein diffusion constant of the sphere due to the presence of rods is a linear function of $\phi$ with the slope $\alpha$ proportional to the equilibrium averaged mobility diminution trace of the sphere interacting with a single freely translating and rotating rod. The two--body hydrodynamic interactions are calculated using the so--called bead model in which the rod of aspect ratio $p$ is replaced by a stiff linear chain of touching spheres. The interactions between spheres are calculated using the multipole method with the accuracy controlled by a multipole truncation order and limited only by the computational power. A remarkable accuracy is obtained already for the lowest truncation order, which enables calculations for very long rods, up to $p=1000$. Additionally, the bead model is checked by filling the rod with smaller spheres. This procedure shows that for longer rods the basic model provides reasonable results varying less than $5\%$ from the model with filling. An analytical expression for $\alpha$ as a function of $p$ is derived in the limit of very long rods. The higher order corrections depending on the applied model are computed numerically. An approximate expression is provided, valid for a wide range of aspect ratios.