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

A I Osinsky1,2, N V Brilliantov1,3

  • 1<a href="https://ror.org/03f9nc143">Skolkovo Institute of Science and Technology</a>, 121205 Moscow, Russia.

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This study introduces new Smoluchowski-Euler equations for fluid aggregation kinetics, offering more accurate microscopic rates than current phenomenological models. These first-principle equations improve predictions, especially when validated with direct simulation Monte Carlo (DSMC) methods.

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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.