Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems.

Area of Science:

• Mesoscopic physics
• Computational chemistry
• Biophysics

Background:

• Simulating mesoscopic systems with advection-diffusion-reaction (ADR) processes is computationally challenging.
• Existing methods often struggle with accurate boundary condition implementation and complex reaction dynamics.

Purpose of the Study:

• To introduce a novel transport dissipative particle dynamics (tDPD) model for mesoscopic ADR simulations.
• To develop and validate a methodology for implementing Dirichlet and Neumann boundary conditions within the tDPD framework.
• To demonstrate the model's capability in simulating complex biological systems.

Main Methods:

• Extended the classic dissipative particle dynamics (DPD) framework with additional variables for concentration fields.
• Modeled concentration transport using Fickian and random fluxes, with advection implicitly handled by particle movement.
• Developed an analytical formula to link tDPD parameters to the effective diffusion coefficient.
• Implemented and validated Dirichlet and Neumann boundary conditions through 1D and 2D simulations.
• Applied the tDPD model to simulate a 25-species blood coagulation system.

Main Results:

• tDPD simulations showed excellent agreement with theoretical solutions for 1D diffusion problems.
• 2D ADR simulations using tDPD closely matched results from the spectral element method.
• The tDPD model efficiently simulated a complex 25-species blood coagulation process.
• Computational cost for tDPD simulation of blood coagulation was only twice that of conventional DPD for hydrodynamics alone.

Conclusions:

• The presented tDPD model provides an accurate and efficient method for simulating mesoscopic ADR processes.
• The implemented boundary condition methodology enhances the model's applicability.
• tDPD offers a significant advantage over continuum solvers for complex biological dynamics simulations at the mesoscale.