Reactions, diffusion, and volume exclusion in a conserved system of interacting particles

Area of Science:

• Multiphysics modeling
• Chemical kinetics
• Statistical mechanics

Background:

• Transport processes involve interacting particles, with excluded volume effects well-studied.
• The combined effects of volume exclusion and heterogeneous particle reactions are less understood.
• Existing models often lack direct parametrization to experimental data.

Purpose of the Study:

• Develop a framework for reaction-diffusion processes incorporating volume exclusion.
• Derive a macroscopic model from a microscopic individual-based model.
• Investigate a hybrid model of chemotaxis with volume exclusion.

Main Methods:

• Off-lattice microscopic individual-based modeling.
• Fokker-Planck equation and matched asymptotic expansions.
• Derivation of nonlinear partial differential equations.

Main Results:

• A low-dimensional macroscopic model for particle evolution was derived.
• Reaction terms for contact-dependent reactions are of lower order than diffusion terms.
• Higher-order reaction terms are necessary for accurate simulation agreement.

Conclusions:

• The developed macroscopic model effectively incorporates volume exclusion in reaction-diffusion systems.
• The model offers improved parametrization capabilities for experimental data.
• This framework advances the study of complex particle interactions in biological and physical systems.