Granular mixtures modeled as elastic hard spheres subject to a drag force

Granular gaseous mixtures under rapid flow conditions are usually modeled by a multicomponent system of smooth inelastic hard spheres with constant coefficients of normal restitution. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. The Navier--Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman--Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.Comment: The title has been changed, 4 figures, and to be published in Phys. Rev.

System of elastic hard spheres which mimics the transport properties of a granular gas

The prototype model of a fluidized granular system is a gas of inelastic hard spheres (IHS) with a constant coefficient of normal restitution $\alpha$. Using a kinetic theory description we investigate the two basic ingredients that a model of elastic hard spheres (EHS) must have in order to mimic the most relevant transport properties of the underlying IHS gas. First, the EHS gas is assumed to be subject to the action of an effective drag force with a friction constant equal to half the cooling rate of the IHS gas, the latter being evaluated in the local equilibrium approximation for simplicity. Second, the collision rate of the EHS gas is reduced by a factor $(1+\alpha)/2$, relative to that of the IHS gas. Comparison between the respective Navier-Stokes transport coefficients shows that the EHS model reproduces almost perfectly the self-diffusion coefficient and reasonably well the two transport coefficients defining the heat flux, the shear viscosity being reproduced within a deviation less than 14% (for $\alpha\geq 0.5$). Moreover, the EHS model is seen to agree with the fundamental collision integrals of inelastic mixtures and dense gases. The approximate equivalence between IHS and EHS is used to propose kinetic models for inelastic collisions as simple extensions of known kinetic models for elastic collisionsComment: 20 pages; 6 figures; change of title; few minor changes; accepted for publication in PR

Uniform shear flow in dissipative gases. Computer simulations of inelastic hard spheres and (frictional) elastic hard spheres

In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor $(1+\alpha)/2$ (where $\alpha$ is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range $0.5\leq \alpha\leq 0.95$ and two values of the imposed shear rate $a$. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. The EHS results are in general hardly distinguishable from the IHS ones if $\alpha\gtrsim 0.7$, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipationsComment: 23 pages; 18 figures; Figs. 2 and 9 include new simulations; two new figures added; few minor changes; accepted for publication in PR

Identification and characterization of Rhodopseudomonas palustris TIE-1 hopanoid biosynthesis mutants

Hopanes preserved in both modern and ancient sediments are recognized as the molecular fossils of bacteriohopanepolyols, pentacyclic hopanoid lipids. Based on the phylogenetic distribution of hopanoid production by extant bacteria, hopanes have been used as indicators of specific bacterial groups and/or their metabolisms. However, our ability to interpret them ultimately depends on understanding the physiological roles of hopanoids in modern bacteria. Toward this end, we set out to identify genes required for hopanoid biosynthesis in the anoxygenic phototroph Rhodopseudomonas palustris TIE-1 to enable selective control of hopanoid production. We attempted to delete 17 genes within a putative hopanoid biosynthetic gene cluster to determine their role, if any, in hopanoid biosynthesis. Two genes, hpnH and hpnG, are required to produce both bacteriohopanetetrol and aminobacteriohopanetriol, whereas a third gene, hpnO, is required only for aminobacteriohopanetriol production. None of the genes in this cluster are required to exclusively synthesize bacteriohopanetetrol, indicating that at least one other hopanoid biosynthesis gene is located elsewhere on the chromosome. Physiological studies with the different deletion mutants demonstrated that unmethylated and C_30 hopanoids are sufficient to maintain cytoplasmic but not outer membrane integrity. These results imply that hopanoid modifications, including methylation of the A-ring and the addition of a polar head group, may have biologic functions beyond playing a role in membrane permeability

Non-Newtonian Couette-Poiseuille flow of a dilute gas

The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille flow is analyzed when the shear-rate Knudsen number and the scaled force are of the same order and terms up to second order are retained. In this way, the transition from the bimodal temperature profile characteristic of the pure force-driven Poiseuille flow to the parabolic profile characteristic of the pure Couette flow through several intermediate stages in the Couette-Poiseuille flow are described. A critical comparison with the Navier-Stokes solution of the problem is carried out.Comment: 24 pages, 5 figures; v2: discussion on boundary conditions added; 10 additional references. Published in a special issue of the journal "Kinetic and Related Models" dedicated to the memory of Carlo Cercignan

Identification of a methylase required for 2-methylhopanoid production and implications for the interpretation of sedimentary hopanes

The rise of atmospheric oxygen has driven environmental change and biological evolution throughout much of Earth’s history and was enabled by the evolution of oxygenic photosynthesis in the cyanobacteria. Dating this metabolic innovation using inorganic proxies from sedimentary rocks has been difficult and one important approach has been to study the distributions of fossil lipids, such as steranes and 2-methylhopanes, as biomarkers for this process. 2-methylhopanes arise from degradation of 2-methylbacteriohopanepolyols (2-MeBHPs), lipids thought to be synthesized primarily by cyanobacteria. The discovery that 2-MeBHPs are produced by an anoxygenic phototroph, however, challenged both their taxonomic link with cyanobacteria and their functional link with oxygenic photosynthesis. Here, we identify a radical SAM methylase encoded by the hpnP gene that is required for methylation at the C-2 position in hopanoids. This gene is found in several, but not all, cyanobacteria and also in α -proteobacteria and acidobacteria. Thus, one cannot extrapolate from the presence of 2-methylhopanes alone, in modern environments or ancient sedimentary rocks, to a particular taxonomic group or metabolism. To understand the origin of this gene, we reconstructed the evolutionary history of HpnP. HpnP proteins from cyanobacteria, Methylobacterium species, and other α-proteobacteria form distinct phylogenetic clusters, but the branching order of these clades could not be confidently resolved. Hence,it is unclear whether HpnP, and 2-methylhopanoids, originated first in the cyanobacteria. In summary, existing evidence does not support the use of 2-methylhopanes as biomarkers for oxygenic photosynthesis