# Hydrodynamic equations for space-inhomogeneous aggregating fluids with first-principle kinetic coefficients Source: [Hydrodynamic equations for space-inhomogeneous aggregating fluids with first-principle kinetic coefficients]() Collection index: [llms.txt]() Data updated: 2025-10-27T04:33:06.473Z Authors: Alexander Osinsky, Nikolay Brilliantov Published: 2023-12-05T14:24:04.000Z ## Abstract We derive from the first principles new hydrodynamic equations -- Smoluchowski-Euler equations for aggregation kinetics in space-inhomogeneous fluids with fluxes. Starting from Boltzmann equations, we obtain microscopic expressions for aggregation rates for clusters of different sizes and observe that they significantly differ from currently used phenomenological rates. Moreover, we show that for a complete description of aggregating systems, novel kinetic coefficients are needed. They share properties of transport and reaction-rate coefficients; for them we report microscopic expressions. For two representative examples -- aggregation of particles at sedimentation and aggregation after an explosion we numerically solve Smoluchowski-Euler equations and perform Direct Simulation Monte Carlo (DSMC). We find that while the new theory agrees well with DSMC results, a noticeable difference is observed for the phenomenological theory. This manifests the unreliability of the currently used phenomenological theory and the need to apply new, first-principle equations. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()