In this work, the authors present a cellular automata model in two dimensions to study mass transfer by diffusion of molecules in single and binary solvent systems. The method builds on the probabilistic cellular automata (PCA) of Vanag, in which diffusion is simulated through the stochastic exchange of molecules between neighbouring cells.
While the original framework effectively models the diffusion of a single component driven by gradients of concentration, it could not account for diffusion coefficients that vary. The authors address this limitation by generalising the approach to binary systems. The probability of an exchange between two cells now depends on the composition they share, so that the diffusion coefficient can change with the composition of the mixture.
Simulations for a single component reproduce the analytical solutions for diffusion from line and point sources, and a steady binary case agrees with the analytical solution for a diffusion coefficient that varies with concentration. For a mixture of ethanol and water, the exchange probabilities were derived from experimental diffusion data, and the simulation follows the mixing of the two liquids until a uniform composition is reached.
The extension enables the simulation of diffusion in heterogeneous materials with varied transport properties and broadens the applicability of methods based on cellular automata for capturing complex diffusion dynamics. The simulation code is openly available.
The study was carried out at the Institute of Thermal Separation Processes at Hamburg University of Technology, with funding from the German Research Foundation within the Collaborative Research Centre CRC 1615 (SMART Reactors) and the project GU 1842/6-1.
Preethi Aranala Gurumoorthi, Mansi Aliveli, Irina Smirnova, Pavel Gurikov (2026). A cellular automata framework to study the diffusion in single and binary solvent systems. Scientific Reports 16, 31485.
