Anisotropic Diffusion of an Isolated Hard Ellipse in a 2D Hard-Disk Bath

Using event-driven molecular dynamics, we investigate the diffusion of an isolated hard ellipse immersed in a two-dimensional bath of comparably sized hard disks, with a primary focus on establishing general expressions for its translational and rotational diffusion coefficients, as well as the hydrodynamic boundary conditions governing its diffusive behavior. Translational anisotropy, quantified by the ratio D_a/D_b (D is diffusion coefficient with subscripts a and b meaning along the semi-major axis a and semi-minor axis b) of diffusion along the major and minor axes, increases linearly with the aspect ratio k=a/b and exhibits insensitivity to the ratio k_\rm R (defined as the ellipse area to bath-disk area). This trend contradicts the Doi–Edwards no-slip prediction of k -independent D_a/D_b and instead supports free-slip hydrodynamics in the athermal hard-core limit. Axis-resolved translational frictions obey \gamma_a\propto (b/k)^1/2 and \gamma_b\propto a^1/2, which combine to yield a total translational friction \gamma_\rm T\propto a^1/2/(k+1) —a dependence not captured by classical no-slip theories (e.g., Happel–Brenner). The rotational friction exhibits the scaling \gamma_\theta\propto b(a^2+b^2)(\ln k)^2 , consistent with qualitative expectations of the Hu–Zwanzig theory under slip conditions yet incompatible with the Perrin no-slip expression \gamma_\theta\propto (a^3+b^3)/(a+b) . Together, these results identify slip boundary conditions as the appropriate hydrodynamic description for anisotropic particles in this model system and provide quantitative benchmarks linking shape-dependent friction to anisotropic diffusion.