1,766 research outputs found
Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions
Simple bimolecular reactions are analyzed
within the framework of the Boltzmann equation in the initial stage of a
chemical reaction with the system far from chemical equilibrium. The
Chapman-Enskog methodology is applied to determine the coefficients of the
expansion of the distribution functions in terms of Sonine polynomials for
peculiar molecular velocities. The results are applied to the reaction
, and the influence of the non-Maxwellian
distribution and of the activation-energy dependent reactive cross sections
upon the forward and reverse reaction rate coefficients are discussed.Comment: 11 pages, 5 figures, to appear in vol.42 of the Brazilian Journal of
Physic
Polydispersity and optimal relaxation in the hard sphere fluid
We consider the mass heterogeneity in a gas of polydisperse hard particles as
a key to optimizing a dynamical property: the kinetic relaxation rate. Using
the framework of the Boltzmann equation, we study the long time approach of a
perturbed velocity distribution toward the equilibrium Maxwellian solution. We
work out the cases of discrete as well as continuous distributions of masses,
as found in dilute fluids of mesoscopic particles such as granular matter and
colloids. On the basis of analytical and numerical evidence, we formulate a
dynamical equipartition principle that leads to the result that no such
continuous dispersion in fact minimizes the relaxation time, as the global
optimum is characterized by a finite number of species. This optimal mixture is
found to depend on the dimension d of space, ranging from five species for d=1
to a single one for d>=4. The role of the collisional kernel is also discussed,
and extensions to dissipative systems are shown to be possible.Comment: 20 pages, 8 figures, 3 table
Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids
In this review, we describe and analyze a mesoscale simulation method for
fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now
called multi-particle collision dynamics (MPC) or stochastic rotation dynamics
(SRD). The method consists of alternating streaming and collision steps in an
ensemble of point particles. The multi-particle collisions are performed by
grouping particles in collision cells, and mass, momentum, and energy are
locally conserved. This simulation technique captures both full hydrodynamic
interactions and thermal fluctuations. The first part of the review begins with
a description of several widely used MPC algorithms and then discusses
important features of the original SRD algorithm and frequently used
variations. Two complementary approaches for deriving the hydrodynamic
equations and evaluating the transport coefficients are reviewed. It is then
shown how MPC algorithms can be generalized to model non-ideal fluids, and
binary mixtures with a consolute point. The importance of angular-momentum
conservation for systems like phase-separated liquids with different
viscosities is discussed. The second part of the review describes a number of
recent applications of MPC algorithms to study colloid and polymer dynamics,
the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of
viscoelastic fluids
A fast spectral method for the Boltzmann equation for monatomic gas mixtures
Although the fast spectral method has been established for solving the Boltzmann equation for single-species monatomic gases, its extension to gas mixtures is not easy because of the non-unitary mass ratio between the di↵erent molecular species. The conventional spectral method can solve the Boltzmann collision operator for binary gas mixtures but with a computational cost of the order m3rN6, where mr is the mass ratio of the heavier to the lighter species, and N is the number of frequency nodes in each frequency direction. In this paper, we propose a fast spectral method for binary mixtures of monatomic gases that has a computational cost O(pmrM2N4 logN), where M2 is the number of discrete solid angles. The algorithm is validated by comparing numerical results with analytical Bobylev- Krook-Wu solutions for the spatially-homogeneous relaxation problem, for mr up to 36. In spatially-inhomogeneous problems, such as normal shock waves and planar Fourier/Couette flows, our results compare well with those of both the numerical kernel and the direct simulation Monte Carlo methods. As an application, a two-dimensional temperature-driven flow is investigated, for which other numerical methods find it difficult to resolve the flow field at large Knudsen numbers. The fast spectral method is accurate and elective in simulating highly rarefied gas flows, i.e. it captures the discontinuities and fine structures in the velocity distribution functions
Fast spectral solution of the generalised Enskog equation for dense gases
We propose a fast spectral method for solving the generalized Enskog equation for dense gases. For elastic collisions, the method solves the Enskog collision operator with a computational cost of O(Md-1Nd logN), where d is the dimension of the velocity space, and Md-1 and Nd are the number of solid angle and velocity space discretizations, respectively. For inelastic collisions, the cost is N times higher. The accuracy of this fast spectral method is assessed by comparing our numerical results with analytical solutions of the spatially homogeneous relaxation of heated granular gases. We also compare our results for force driven Poiseuille flow and Fourier flow with those from molecular dynamics and Monte Carlo simulations. Although it is phenomenological, the generalized Enskog equation is capable of capturing the flow dynamics of dense granular gases, and the fast spectral method is accurate and efficient. As example applications, Fourier and Couette flows of a dense granular gas are investigated. In additional to the temperature profile, both the density and the high-energy tails in the velocity distribution functions are found to be strongly influenced by the restitution coefficient
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