Two-dimensional Diffusion with a Transverse Gravitational Force: Analytical, Numerical and Simulations Results

Using the Kalinay and Percus projection method a new effective diffusion coefficient is found. This diffusivity generalizes the well-known results previously reported in the literature. Specifically, it is a coefficient that can be applied to two-dimensional asymmetrical channels under an external gravitational-like potential. Furthermore, Brownian Dynamics simulations are performed, and their agreement with the theoretical results is shown. Also, the Mean First-Passage Time is studied for two-dimensional straight conical channels, where the analytical results are analyzed to understand its applicability range using numerical methods, which are compared with Brownian Dynamics simulations. A remarkable result is also presented: the Mean First-Passage Time assumes a minimum at finite values of the external potential amplitude.