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

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 atomistic simulations by 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.