Increasing temperature of cooling granular gases

Abstract

The kinetic energy of a force-free granular gas decays monotonously due to inelastic collisions of the particles. For a homogeneous granular gas of identical particles, the corresponding decay of granular temperature is quantified by Haff’s law. Here, we report that for a granular gas of aggregating particles, the granular temperature does not necessarily decay but may even increase. Surprisingly, the increase of temperature is accompanied by the continuous loss of total gas energy. This stunning effect arises from a subtle interplay between decaying kinetic energy and gradual reduction of the number of degrees of freedom associated with the particles’ dynamics. We derive a set of kinetic equations of Smoluchowski type for the concentrations of aggregates of different sizes and their energies. We find scaling solutions to these equations and a condition for the aggregation mechanism predicting growth of temperature. Numerical direct simulation Monte Carlo results confirm the theoretical predictions.

Size-polydisperse dust in molecular gas: Energy equipartition versus nonequipartition

“…Usually, in granular mixtures, the energy equipartition between particles of different sizes is violated. This has been predicted theoretically [7][8][9][10][11] and confirmed in experiments [12,13] and computer simulations [11,14,15]. The same is true for such natural systems as Saturn rings, which are essentially granular gas mixtures of particles with a size ranging from 10 −3 m to 1m [16,17].…”

Steady oscillations in aggregation-fragmentation processes

“…(21) it follows that τ = (3 + ν + μ)/2, then substituting τ = (3 + ν + μ)/2 into Eq. (16) we conclude that the generation functions C ν (z 0 ) converges only for ν − μ = θ < 1 (recall that ν μ). Hence Eq.…”

“…For thermodynamically closed systems, the temperature commonly decreases with time (see the discussion in Ref. [16]).…”

“…Equations (3) and (4) describe spatially homogeneous systems. The kernels K i,j may be obtained from the microscopic analysis of the aggregation and fragmentation processes (see, e.g., [10,13,16] and the Appendix). In applications, K i,j are usually homogeneous functions of the masses i and j of merging clusters.…”

“…Namely, we consider systems of particles that suffer ballistic aggregation and fragmentation. We chose such systems since the corresponding microscopic rates K ij and F ij are available [10,13,16]; see the Appendix.…”