Analytic calculation of the diffusion coefficient for random walks on strips of finite width: Dependence on size and nature of boundaries

Two interacting diffusing particles on low-dimensional discrete structures

“…The solution of the random walks problem on the diffusion graph can be simplified by the following considerations. As already shown in [18] the diffusion problem on a ladder-like lattice can be mapped into that of a linear chain. This follows from the fact that we are interested only in the walker displacement in the unbounded direction, and not in its position on the upper or on the lower chain.…”

Fractal model for predicting the effective binary oxygen diffusivity of the gas diffusion layer in proton exchange membrane fuel cells

“…The lattice Boltzmann method [12] can also be used in continuous modeling. Discrete modeling methods include random walks [13], Monte Carlo methods [14,15], molecular gas dynamics [16] and particle tracing methods [17].…”

Exact calculation of the tortuosity in disordered linear pores in the Knudsen regime

“…2), while the time inside the dead ends increases the total time t of the walk without increasing x 2 . Quantitative considerations [18,19,22] show that D/D 0 = V x /V, with the volume V x of the x-channels and the system volume V (of channel plus dead ends).…”

“…Of particular interest is the tortuosity factor κ = √ D 0 /D that describes the relation between the diffusion coefficients D and D 0 of systems with and without geometrical disorder [8] and can be gained by studying either the transport-or the self diffusion problem, leading in both cases to the same diffusion coefficent D for a given geometry. Theoretical calculations of D on complex pores have mostly been based on numerical simulations of the transport- [9][10][11][12] or the self diffusion problem [11][12][13][14][15] and/or phenomenological or semi-analytical approaches [16], whereas exact analytical results of specific pore geometries have only been provided along loopless curved one-dimensional paths [17] and for systems with dead ends [18,19]. Whereas in loopless curved systems (see Fig.…”