Nikolai V. Brilliantov

MODEL FOR COLLISIONS IN GRANULAR GASES

We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity. \textcopyright{} 1996 The American Physical Society.

Sodium salts in E-ring ice grains from an ocean below the surface of Enceladus

Saturns moon Enceladus emits plumes of water vapour and ice particles from fractures near its south pole, suggesting the possibility of a subsurface ocean. These plume particles are the dominant source of Saturn’s E ring. A previous in situ analysis of these particles concluded that the minor organic or siliceous components, identified in many ice grains, could be evidence for interaction between Enceladus’ rocky core and liquid water. It was not clear, however, whether the liquid is still present today or whether it has frozen. Here we report the identification of a population of E-ring grains that are rich in sodium salts (∼0.5–2% by mass), which can arise only if the plumes originate from liquid water. The abundance of various salt components in these particles, as well as the inferred basic pH, exhibit a compelling similarity to the predicted composition of a subsurface Enceladus ocean in contact with its rock core. The plume vapour is expected to be free of atomic sodium. Thus, the absence of sodium from optical spectra is in good agreement with our results. In the E ring the upper limit for spectroscopy is insufficiently sensitive to detect the concentrations we found.

Coefficient of restitution of colliding viscoelastic spheres.

We perform a dimension analysis for colliding viscoelastic spheres to show that the coefficient of normal restitution epsilon depends on the impact velocity g as epsilon=1-gamma(1)g(1/5)+gamma(2)g(2/5)-/+..., in accordance with recent findings. We develop a simple theory to find explicit expressions for coefficients gamma(1) and gamma(2). Using these and few next expansion coefficients for epsilon(g) we construct a Padé approximation for this function which may be used for a wide range of impact velocities where the concept of the viscoelastic collision is valid. The obtained expression reproduces quite accurately the existing experimental dependence epsilon(g) for ice particles.

Slow dust in Enceladus' plume from condensation and wall collisions in tiger stripe fractures.

One of the spectacular discoveries of the Cassini spacecraft was the plume of water vapour and icy particles (dust) originating near the south pole of Saturn’s moon Enceladus. The data imply considerably smaller velocities for the grains than for the vapour, which has been difficult to understand. The gas and dust are too dilute in the plume to interact, so the difference must arise below the surface. Here we report a model for grain condensation and growth in channels of variable width. We show that repeated wall collisions of grains, with re-acceleration by the gas, induce an effective friction, offering a natural explanation for the reduced grain velocity. We derive particle speed and size distributions that reproduce the observed and inferred properties of the dust plume. The gas seems to form near the triple point of water; gas densities corresponding to sublimation from ice at temperatures less than 260 K are generally too low to support the measured particle fluxes. This in turn suggests liquid water below Enceladus’ south pole.

Granular gas dynamics

Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy dissipation leads to a significant departure from the elastic case. Specifically, the velocity distributions have overpopulated high energy tails and different velocity components are correlated. In the freely cooling case, the velocity distribution develops an algebraic high-energy tail, with an exponent that depends sensitively on the dimension and the degree of dissipation. Moments of the velocity distribution exhibit multiscaling asymptotic behavior, and the autocorrelation function decays algebraically with time. In the forced case, the steady state velocity distribution decays exponentially at large velocities. An impurity immersed in a uniform inelastic gas may or may not mimic the behavior of the background, and the departure from the background behavior is characterized by a series of phase transitions.Part I: Kinetic Theory.- Asymptotic Solutions of the Nonlinear Boltzmann Equation for Dissipative Systems.- The Homogeneous Cooling State Revisited.- The Inelastic Maxwell Model.- Cooling Granular Gases: The Role of Correlations in the Velocity Field.- Self-Similar Asymptotics for the Boltzmann Equation With Inelastic Interactions.- Kinetic Integrals in the Kinetic Theory of Dissipative Gases.- Kinetics of Fragmenting Freely Evolving Granular Gases.- Part II: Granular Hydrodynamics.- Shock Waves in Granular Gases.- Linearized Boltzmann Equation and Hydrodynamics for Granular Gases.- Development of a Density Invesion in Driven Granular Gases.- Kinetic Theory for Inertia Flows of Dilute Turbulent Gas-Solids Two-Phase Mixtures.- Part III: Driven Gases and Structure Formation.- Driven Granular Gases.- Van der Waals-Like Transition in Fluidized Granular Matter.- Birth and Sudden Death of Granular Cluster.- Vibrated Granular Media as Experimentally Realized Granular Gases.

Chain Collapse and Counterion Condensation in Dilute Polyelectrolyte Solutions

A quantitative theory for polyelectrolytes in salt-free dilute solutions is developed. Depending on the electrostatic interaction strength, polyelectrolytes in solutions can undergo strong stretching (with polyelectrolyte dimension

Kinetics of Prion Growth

{R}_{\mathrm{g}}\ensuremath{\sim}{l}_{B}^{1/3}N

Rolling friction of a hard cylinder on a viscous plane

, where

Self-diffusion in granular gases

{l}_{B}

Velocity distribution in granular gases of viscoelastic particles

is the Bjerrum length and