Hydrodynamic Equations for Space-Inhomogeneous Aggregating Fluids with First-Principle Kinetic Coefficients

Area of Science:

• Physical Chemistry
• Fluid Dynamics
• Statistical Mechanics

Background:

• Current phenomenological models for aggregation kinetics in space-inhomogeneous fluids with fluxes often lack microscopic accuracy.
• Existing models may not fully capture the complex transport and reaction dynamics governing cluster formation.
• There is a need for a more rigorous theoretical framework derived from fundamental principles.

Purpose of the Study:

• To derive novel, first-principle hydrodynamic equations for aggregation kinetics.
• To develop microscopic expressions for aggregation rates and novel kinetic coefficients.
• To validate the new theoretical framework against atomistic simulations.

Main Methods:

• Derivation of Smoluchowski-Euler equations from Boltzmann equations.
• Microscopic calculation of aggregation rates and kinetic coefficients.
• Numerical solution of Smoluchowski-Euler equations.
• Validation using direct simulation Monte Carlo (DSMC) for aggregation after explosion and particle sedimentation.

Main Results:

• Microscopic expressions for aggregation rates differ significantly from phenomenological rates.
• Novel kinetic coefficients, combining transport and reaction properties, were identified and expressed microscopically.
• The derived Smoluchowski-Euler equations show excellent agreement with DSMC results.
• Phenomenological theories exhibit noticeable discrepancies compared to DSMC and the new first-principle approach.

Conclusions:

• The newly derived Smoluchowski-Euler equations provide a more reliable description of aggregation kinetics in inhomogeneous fluids.
• The findings highlight the limitations of current phenomenological theories.
• First-principle derivations are essential for accurate modeling of complex aggregation phenomena.