10 research outputs found
Universality of temperature distribution in granular gas mixtures with a steep particle size distribution
Distribution of granular temperatures in granular gas mixtures is
investigated analytically and numerically. We analyze space uniform systems in
a homogeneous cooling state (HCS) and under a uniform heating with a
mass-dependent heating rate . We demonstrate that
for steep size distributions of particles the granular temperatures obey a
universal power-law distribution, , where the exponent
does not depend on a particular form of the size distribution, the
number of species and inelasticity of the grains. Moreover, is a
universal constant for a HCS and depends piecewise linearly on for
heated gases. The predictions of our scaling theory agree well with the
numerical results
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
A dissipative force between colliding viscoelastic bodies: Rigorous approach
A collision of viscoelastic bodies is analysed within a mathematically
rigorous approach. We develop a perturbation scheme to solve continuum
mechanics equation, which deals simultaneously with strain and strain rate in
the bulk of the bodies' material. We derive dissipative force that acts between
particles and express it in terms of particles' deformation, deformation rate
and material parameters. It differs noticeably from the currently used
dissipative force, found within the quasi-static approximation and does not
suffer from inconsistencies of this approximation. The proposed approach may be
used for other continuum mechanics problems where the bulk dissipation is
addressed.Comment: 6 pages, 1 figur
A model of ballistic aggregation and fragmentation
A simple model of ballistic aggregation and fragmentation is proposed. The
model is characterized by two energy thresholds, Eagg and Efrag, which
demarcate different types of impacts: If the kinetic energy of the relative
motion of a colliding pair is smaller than Eagg or larger than Efrag, particles
respectively merge or break; otherwise they rebound. We assume that particles
are formed from monomers which cannot split any further and that in a
collision-induced fragmentation the larger particle splits into two fragments.
We start from the Boltzmann equation for the mass-velocity distribution
function and derive Smoluchowski-like equations for concentrations of particles
of different mass. We analyze these equations analytically, solve them
numerically and perform Monte Carlo simulations. When aggregation and
fragmentation energy thresholds do not depend on the masses of the colliding
particles, the model becomes analytically tractable. In this case we show the
emergence of the two types of behavior: the regime of unlimited cluster growth
arises when fragmentation is (relatively) weak and the relaxation towards a
steady state occurs when fragmentation prevails. In a model with mass-dependent
Eagg and Efrag the evolution with a cross-over from one of the regimes to
another has been detected
A dissipative force between colliding viscoelastic bodies: Rigorous approach
Abstract -A collision of viscoelastic bodies is analysed within a mathematically rigorous approach. We develop a perturbation scheme to solve continuum mechanics equation, which deals simultaneously with strain and strain rate in the bulk of the bodies' material. We derive dissipative force that acts between particles and express it in terms of particles' deformation, deformation rate and material parameters. It differs noticeably from the currently used dissipative force, found within the quasi-static approximation and does not suffer from inconsistencies of this approximation. The proposed approach may be used for other continuum mechanics problems where the bulk dissipation is addressed