Impurity in a granular gas under nonlinear Couette flow

We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors [Vega Reyes F et al. 2007 Phys. Rev. E 75 061306]. Two routes have been considered. First, a hydrodynamic or normal solution is found by exploiting a formal mapping between the kinetic equations for the gas particles and for the impurity. We show that the transport properties of the impurity are characterized by the ratio between the temperatures of the impurity and gas particles and by five generalized transport coefficients: three related to the momentum flux (a nonlinear shear viscosity and two normal stress differences) and two related to the heat flux (a nonlinear thermal conductivity and a cross coefficient measuring a component of the heat flux orthogonal to the thermal gradient). Second, by means of a Monte Carlo simulation method we numerically solve the kinetic equations and show that our hydrodynamic solution is valid in the bulk of the fluid when realistic boundary conditions are used. Furthermore, the hydrodynamic solution applies to arbitrarily (inside the continuum regime) large values of the shear rate, of the inelasticity, and of the rest of parameters of the system. Preliminary simulation results of the true Boltzmann description show the reliability of the nonlinear hydrodynamic solution of the kinetic model. This shows again the validity of a hydrodynamic description for granular flows, even under extreme conditions, beyond the Navier-Stokes domain.Comment: 23 pages, 11 figures; v2: Preliminary DSMC results from the Boltzmann equation included, Fig. 11 is ne

Computer simulations of an impurity in a granular gas under planar Couette flow

We present in this work results from numerical solutions, obtained by means of the direct simulation Monte Carlo (DSMC) method, of the Boltzmann and Boltzmann--Lorentz equations for an impurity immersed in a granular gas under planar Couette flow. The DSMC results are compared with the exact solution of a recent kinetic model for the same problem. The results confirm that, in steady states and over a wide range of parameter values, the state of the impurity is enslaved to that of the host gas: it follows the same flow velocity profile, its concentration (relative to that of the granular gas) is constant in the bulk region, and the impurity/gas temperature ratio is also constant. We determine also the rheological properties and nonlinear hydrodynamic transport coefficients for the impurity, finding a good semi-quantitative agreement between the DSMC results and the theoretical predictions.Comment: 23 pages, 11 figures; v2: minor change

An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux

In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special class of states exists where the viscous heating and the inelastic cooling exactly compensate each other at every point, resulting in a uniform heat flux. In this state the (reduced) shear rate is enslaved to the coefficient of restitution $\alpha$, so that the only free parameter is the (reduced) thermal gradient $\epsilon$. It turns out that the reduced moments of order $k$ are polynomials of degree $k-2$ in $\epsilon$, with coefficients that are nonlinear functions of $\alpha$. In particular, the rheological properties ($k=2$) are independent of $\epsilon$ and coincide exactly with those of the simple shear flow. The heat flux ($k=3$) is linear in the thermal gradient (generalized Fourier's law), but with an effective thermal conductivity differing from the Navier--Stokes one. In addition, a heat flux component parallel to the flow velocity and normal to the thermal gradient exists. The theoretical predictions are validated by comparison with direct Monte Carlo simulations for the same model.Comment: 16 pages, 4 figures,1 table; v2: minor change

Subtoxic levels of some heavy metals cause differential root-shoot structure, morphology and auxins levels in Arabidopsis thaliana

Contamination of soil by heavy metals severely affects plant growth and causes soil pollution. While effects on plant growth have been investigated for metals taken individually or in groups, less is known about their comparative effects. In this study Arabidopsis thaliana seedlings were grown for 14 days in Petri dishes containing medium contaminated by six common heavy metals (Hg, Cd, Pb, Cu, Ni and Zn), at the minimum concentrations defined as toxic by the most recent EU legislation on contamination of agricultural soils. (a) Root structure and morphology, (b) metal composition and translocation, and (c) the levels of indole-3-acetic acid (IAA) and indole-3-butyric acid (IBA) were analyzed. Metals accumulated more in roots than in shoots, with concentrations that differed by several orders of magnitude depending on the metal: Cd (ca. 700 × and ca. 450 × in roots and shoots, respectively), Hg (150 ×, 80 × ), Ni (50 ×, 20 × ), Cu (48 ×, 20 × ), Zn (23 ×, 6 × ), and Pb (9 ×, 4 × ). Responses were significant for at least nine of the ten root parameters (with the exception of Hg), and five of the six shoot parameters (with the exception of Zn). Cu and Zn induced respectively the strongest responses in root hormonal (up to ca. 240% the control values for IBA, 190% for IAA) and structural parameters (up to 210% for main root length, 330% for total lateral root length, 220% for number of root tips, 600% for total root surface, and from 2.5° to 26.0° of root growth angle). Regarding the shoots, the largest changes occurred for shoot height (down to 60% for Ni), rosette diameter (down to 45% for Hg), leaf number (up to 230% for Zn) and IBA (up to 240% for Pb and Cu). A microscope analysis revealed that shape and conformation of root hairs were strongly inhibited after Cd exposure, and enhanced under Hg and Pb. The results could have positive applications such as for defining toxicity thresholds (in phytoremediation) and acceptable concentration levels (for policies) for some of the most common heavy metals in agricultural soils

Subtoxic levels of some heavy metals cause differential root-shoot structure, morphology and auxins levels in Arabidopsis thaliana

Contamination of soil by heavy metals severely affects plant growth and causes soil pollution. While effects on plant growth have been investigated for metals taken individually or in groups, less is known about their comparative effects. In this study Arabidopsis thaliana seedlings were grown for 14 days in Petri dishes containing medium contaminated by six common heavy metals (Hg, Cd, Pb, Cu, Ni and Zn), at the minimum concentrations defined as toxic by the most recent EU legislation on contamination of agricultural soils. (a) Root structure and morphology, (b) metal composition and translocation, and (c) the levels of indole-3-acetic acid (IAA) and indole-3-butyric acid (IBA) were analyzed. Metals accumulated more in roots than in shoots, with concentrations that differed by several orders of magnitude depending on the metal: Cd (ca. 700 × and ca. 450 × in roots and shoots, respectively), Hg (150 ×, 80 × ), Ni (50 ×, 20 × ), Cu (48 ×, 20 × ), Zn (23 ×, 6 × ), and Pb (9 ×, 4 × ). Responses were significant for at least nine of the ten root parameters (with the exception of Hg), and five of the six shoot parameters (with the exception of Zn). Cu and Zn induced respectively the strongest responses in root hormonal (up to ca. 240% the control values for IBA, 190% for IAA) and structural parameters (up to 210% for main root length, 330% for total lateral root length, 220% for number of root tips, 600% for total root surface, and from 2.5° to 26.0° of root growth angle). Regarding the shoots, the largest changes occurred for shoot height (down to 60% for Ni), rosette diameter (down to 45% for Hg), leaf number (up to 230% for Zn) and IBA (up to 240% for Pb and Cu). A microscope analysis revealed that shape and conformation of root hairs were strongly inhibited after Cd exposure, and enhanced under Hg and Pb. The results could have positive applications such as for defining toxicity thresholds (in phytoremediation) and acceptable concentration levels (for policies) for some of the most common heavy metals in agricultural soils

The magnetorotational instability across the dead zone of protoplanetary disks

We examine the linear stability of a flow threaded by a weak, vertical magnetic field in a disk with a keplerian rotation profile and a vertical stratification of the ionization degree as that predicted for vast portions of protoplanetary disks. A quasi-global analysis is carried out, where the form of the perturbations in the vertical direction is determined. Considering the ohmic magnetic diffusivity of the gas, the conditions leading to the magnetorotational instability are analyzed as a function of the diffusivity at the disk surfaces, its vertical profile and the strength of the unperturbed magnetic field. For typical conditions believed to prevail in protoplanetary disks at radial distances between 0.1 and 10 AU, where the so-called dead zone is proposed to exist, we find that generally the instability is damped. This implies that, if the MRI is considered the only possible source of turbulence in protoplanetary disks, no viscous angular momentum transport occursat those radii.Comment: 33 pages, 8 figure