Dynamic density functional theory for sedimentation processes on complex domains: Modelling, spectral elements, and...

Area of Science:

• Computational physics
• Chemical engineering
• Applied mathematics

Background:

• Accurate modeling of hard particle dynamics in complex domains is vital for processes like drug delivery and wastewater treatment.
• Capturing volume exclusion effects is essential for simulating sedimentation and driven flows.

Purpose of the Study:

• To develop and demonstrate a novel computational framework for simulating hard particle systems.
• To incorporate diffusion, external forces, particle interactions, and volume exclusion in dynamic simulations.
• To extend the methodology for control problems in industrial processes.

Main Methods:

• Dynamic Density Functional Theory (DDFT) applied to particle density evolution.
• A spectral element framework enabling simulations on complex domains.
• Implementation of various boundary conditions, including no-flux, non-local, and non-linear types.

Main Results:

• The developed method allows, for the first time, dynamic simulations of hard particles including all key effects on complex geometries.
• The incorporation of volume exclusion was found to be critical for simulation accuracy.
• The choice of boundary conditions significantly influences the simulated particle dynamics.

Conclusions:

• The novel spectral element DDFT approach provides a versatile tool for simulating complex particle systems.
• Accurate representation of volume exclusion and boundary conditions is paramount for reliable simulations in industrial applications.
• The methodology's extension to control problems offers potential for optimizing industrial processes.