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 <i>D</i>_a/<i>D</i>_b of diffusion along the major and minor axes, increases linearly with the aspect ratio <i>k</i>=<i>a</i>/<i>b</i> and exhibits insensitivity to the ratio <i>k</i>_R between the ellipse area and bath-disk area. This trend contradicts the Doi–Edwards no-slip prediction of <i>k</i>-independent <i>D</i>_a/<i>D</i>_b and instead supports free-slip hydrodynamics in the athermal hard-core limit. Axis-resolved translational frictions obey <i>γ</i>_a ∝ (<i>b</i>/<i>k</i>)^1/2 and <i>γ</i>_b ∝ <i>a</i>^1/2, which combine to yield a total translational friction <i>γ</i>_T ∝ <i>a</i>^1/2/(<i>k</i>+1)—a dependence not captured by classical no-slip theories (\textite.g., Happel–Brenner). The rotational friction exhibits the scaling <i>γ</i>_θ ∝ <i>b</i>(<i>a</i>²+<i>b</i>²)(ln<i>k</i>)², consistent with qualitative expectations of the Hu–Zwanzig theory under slip conditions yet incompatible with the Perrin no-slip expression <i>γ</i>_θ ∝ (<i>a</i>³+<i>b</i>³)/(<i>a</i>+<i>b</i>). 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.