Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics

We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the oscillations with respect to fluctuations and noise.Comment: 19 pages, 2 figures, 4 table

Exact solutions of temperature-dependent Smoluchowski equations

We report a number of exact solutions for temperature-dependent Smoluchowski equations. These equations quantify the ballistic agglomeration, where the evolution of densities of agglomerates of different size is entangled with the evolution of the mean kinetic energy (partial temperatures) of such clusters. The obtained exact solutions may be used as a benchmark to assess the accuracy and computational efficiency of the numerical approaches, developed to solve the temperature-dependent Smoluchowski equations. Moreover, they may also illustrate the possible evolution regimes in these systems. The exact solutions have been obtained for a series of model rate coefficients, and we demonstrate that there may be an infinite number of such model coefficient which allow exact analysis. We compare our exact solutions with the numerical solutions for various evolution regimes; an excellent agreement between numerical and exact results proves the accuracy of the exploited numerical method

Smolchowski-Euler equations

We derive from the first principles Smoluchowski-Euler equations, describing aggregation kinetics in space-inhomogeneous systems with fluxes. Starting from Boltzmann equations, we obtain microscopic expressions for the aggregation rates for clusters of different size, and observe that they significantly differ from the currently used phenomenological rates. Moreover, we show that for a complete description of aggregating systems, novel kinetic coefficients are needed. These may be called ``flux-reaction'' and ``energy-reaction'' rates, as they appear, respectively, in the equations for fluxes and energy. We report microscopic expressions for these coefficients. We solve numerically the Smoluchowski-Euler equations for two representative examples -- aggregation of particles at sedimentation, and aggregation after an explosion. The solution of the novel equations is compared with the solution of currently used phenomenological equations, with phenomenological rate coefficients. We find a noticeable difference between these solutions, which manifests unreliability of the phenomenological approach and the need of application of new, first-principle equations.Comment: Submitted to Physical Review Letter

Electrification in granular gases leads to constrained fractal growth

The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from the early stages of planetesimal formation to aerosols. However, the collective effects of Coulomb forces on the nonequilibrium dynamics and aggregation process in a granular gas – a model representative of the above physical processes – have so far evaded theoretical scrutiny. Here, we establish a hydrodynamic description of aggregating granular gases that exchange charges upon collisions and interact via the long-ranged Coulomb forces. We analytically derive the governing equations for the evolution of granular temperature, charge variance, and number density for homogeneous and quasi-monodisperse aggregation. We find that, once the aggregates are formed, the granular temperature of the cluster population, the charge variance of the cluster population and the number density of the cluster population evolve in such a way that their non-dimensional combination obeys a physical constraint of nearly constant dimensionless ratio of characteristic electrostatic to kinetic energy. This constraint on the collective evolution of charged clusters is confirmed both by our theory and our detailed molecular dynamics simulations. The inhomogeneous aggregation of monomers and clusters in their mutual electrostatic field proceeds in a fractal manner. Our theoretical framework is extendable to more precise charge exchange mechanisms, a current focus of extensive experimentation. Furthermore, it illustrates the collective role of long-ranged interactions in dissipative gases and can lead to novel designing principles in particulate systems

Dust coagulation in equilibrium molecular gas

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