Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation

The linear integral equations defining the Navier-Stokes (NS) transport coefficients for polydisperse granular mixtures of smooth inelastic hard disks or spheres are solved by using the leading terms in a Sonine polynomial expansion. Explicit expressions for all the NS transport coefficients are given in terms of the sizes, masses, compositions, density and restitution coefficients. In addition, the cooling rate is also evaluated to first order in the gradients. The results hold for arbitrary degree of inelasticity and are not limited to specific values of the parameters of the mixture. Finally, a detailed comparison between the derivation of the current theory and previous theories for mixtures is made, with attention paid to the implication of the various treatments employed to date.Comment: 26 pages, to be published in Phys. Rev.

Tracer diffusion in granular shear flows

Tracer diffusion in a granular gas in simple shear flow is analyzed. The analysis is made from a perturbation solution of the Boltzmann kinetic equation through first order in the gradient of the mole fraction of tracer particles. The reference state (zeroth-order approximation) corresponds to a Sonine solution of the Boltzmann equation, which holds for arbitrary values of the restitution coefficients. Due to the anisotropy induced in the system by the shear flow, the mass flux defines a diffusion tensor $D_{ij}$ instead of a scalar diffusion coefficient. The elements of this tensor are given in terms of the restitution coefficients and mass and size ratios. The dependence of the diffusion tensor on the parameters of the problem is illustrated in the three-dimensional case. The results show that the influence of dissipation on the elements $D_{ij}$ is in general quite important, even for moderate values of the restitution coefficients. In the case of self-diffusion (mechanically equivalent particles), the trends observed in recent molecular dynamics simulations are similar to those obtained here from the Boltzmann kinetic theory.Comment: 5 figure

Diffusion of impurities in a granular gas

Diffusion of impurities in a granular gas undergoing homogeneous cooling state is studied. The results are obtained by solving the Boltzmann--Lorentz equation by means of the Chapman--Enskog method. In the first order in the density gradient of impurities, the diffusion coefficient $D$ is determined as the solution of a linear integral equation which is approximately solved by making an expansion in Sonine polynomials. In this paper, we evaluate $D$ up to the second order in the Sonine expansion and get explicit expressions for $D$ in terms of the restitution coefficients for the impurity--gas and gas--gas collisions as well as the ratios of mass and particle sizes. To check the reliability of the Sonine polynomial solution, analytical results are compared with those obtained from numerical solutions of the Boltzmann equation by means of the direct simulation Monte Carlo (DSMC) method. In the simulations, the diffusion coefficient is measured via the mean square displacement of impurities. The comparison between theory and simulation shows in general an excellent agreement, except for the cases in which the gas particles are much heavier and/or much larger than impurities. In theses cases, the second Sonine approximation to $D$ improves significantly the qualitative predictions made from the first Sonine approximation. A discussion on the convergence of the Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.

Effects of a 1-year randomised controlled trial of resistance training on blood lipid profile and chylomicron concentration in older men

© 2016 Springer-Verlag Berlin HeidelbergPurpose: Resistance exercise is promoted in older adults for its ability to improve muscle mass, strength and, hence, in reducing falls. However, its effects on blood lipids and CVD risk are less well established, particularly in this age group. This study aimed to investigate whether a 1-year resistance exercise program improves lipid profile and chylomicron concentration in older men. Methods: Participants were randomised to either three, 1 h resistance training sessions per week (RE) or an active control group [asked to undertake three 30 min walking sessions per week (AC)]. Fasting blood samples were collected at 0, 6, and 12 months for determination of lipid profile and glycaemic control. Diet, morphological and activity data were also collected at these time points. Results: Following 12 months, the RE intervention group had greater improvements in cholesterol profile; LDL-cholesterol concentration significantly decreased by 0.2 (0.2) mM [mean (SEM)] compared to control (P < 0.05). The RE group also exhibited a significant increase in lean body mass of 0.9 (1.3) kg after 12 months compared to the AC group (P < 0.05). There was no treatment or time effect on other anthropometric measures or fasting triacylglycerol, glucose, insulin or chylomicron concentrations. Conclusion: The observed improvements in lean body mass and cholesterol profile promote the implementation of a resistance exercise intervention in this population