Steven R. Dahl

Kinetic temperatures for a granular mixture.

An isolated mixture of smooth, inelastic hard spheres supports a homogeneous cooling state with different kinetic temperatures for each species. This phenomenon is explored here by molecular dynamics simulation of a two component fluid, with comparison to predictions of the Enskog kinetic theory. The ratio of kinetic temperatures is studied for two values of the restitution coefficient alpha=0.95 and 0.80, as a function of mass ratio, size ratio, composition, and density. Good agreement between theory and simulation is found for the lower densities and higher restitution coefficient; significant disagreement is observed otherwise. The phenomenon of different temperatures is also discussed for driven systems, as occurs in recent experiments. Differences between the freely cooling state and driven steady states are illustrated.

Size segregation in rapid, granular flows with continuous size distributions

Two-dimensional (dissipative) molecular-dynamics simulations of particulate mixtures with Gaussian and lognormal particle size distributions are employed to gain insight on the segregation behavior of these mixtures when exposed to a granular temperature gradient. Simulations are performed for a collection of smooth, inelastic, hard disks (with constant material density and a constant coefficient of restitution) confined between two walls set to constant, though unequal, granular temperatures. As a result, a gradient in granular temperature develops across the domain. In general, particles of all sizes are found to move toward regions of low granular temperature (overall segregation). Species segregation is also observed. Specifically, large particles demonstrate a higher affinity for the low-temperature regions, and thus accumulate in these cool regions to a greater extent than their smaller counterparts. Furthermore, the local particle size distribution remains of the same form (Gaussian or lognormal) as the overall (including all particles) size distribution. In addition, the behaviors of Gaussian size distributions and narrow lognormal distributions are found to be quite similar.

The effects of continuous size distributions on the rapid flow of inelastic particles

Molecular-dynamics simulations are employed to investigate the stresses and granular energy in granular materials with Gaussian and lognormal size distributions. Specifically, smooth circular disks of uniform material density engaged in unbounded two-dimensional shear flow are simulated using an event-driven algorithm. Particle collisions are treated as hard-sphere collisions and all collisions have the same coefficient of restitution. The resulting stresses, when nondimensionalized with the root-mean-square diameter, are found to remain relatively constant as the widths of the particle size distributions are increased away from the monodisperse limit. As a consequence, the stresses predicted by monodisperse kinetic theory (using the root-mean-square diameter) are reasonably accurate in the Gaussian and lognormal systems studied herein. This width-independent nature of the total stresses is traced to an effective balancing of the stresses between the larger particles, which generate relatively high stresses, and smaller particles, which generate lower stresses. Moreover, similar to binary-sized systems, the granular energy in Gaussian and lognormal systems is found to be unequally distributed among the various sizes of particles, with large particles possessing more granular energy than their smaller counterparts (i.e., an equipartition of energy is not observed). This difference in granular energy between two particles increases with both inelasticity and the size difference.

Instabilities in the homogeneous cooling of a granular gas: A quantitative assessment of kinetic-theory predictions

Previous work has indicated that inelastic grains undergoing homogeneous cooling may be unstable, giving rise to the formation of velocity vortices, which may also lead to particle clustering. In this effort, molecular dynamics (MD) simulations are performed over a wide parameter space to determine the critical system size demarcating the stable and unstable regions. Specifically, a system of monodisperse, frictionless, inelastic hard spheres is simulated for restitution coefficients e ≥ 0.6 and solids fractions φ ≤ 0.4. Simulations for each e, φ pairing are then carried out over a range of system sizes to determine the critical dimensionless length scale LC/d (L is the system length and d is the particle diameter), above which velocity vortices appear (unstable system) and below which they are suppressed (stable system). The results show excellent agreement with the theoretical predictions obtained by Garzo [Phys. Rev. E 72, 021106 (2005)] using a linear stability analysis of kinetic-theory-based (contin...

Molecular simulation study of the assembly of DNA-functionalised nanoparticles: Effect of DNA strand sequence and composition

DNA functionalisation is a proven route to program an assembly of nanoparticles into a vast array of nanostructures. In this paper, we used coarse-grained molecular dynamics simulations to study DNA-functionalised nanoparticles and demonstrate the effect of grafted DNA strand composition, specifically the placement and number of contiguous G/C bases in the grafted DNA single strands, on the thermodynamics and structure of nanoparticle assembly at varying grafting densities and particle sizes. At a constant G/C content, nanoparticles assemble more readily when the G/C bases are placed on the outer or middle portions of the strands than on the inner portion. In addition, the number of neighbours within the assembled cluster decreases as the placement of the G/C bases goes from the outer to middle to inner sections of the strand. As the G/C content decreases, the cluster dissociation temperature, Td, decreases, as the enthalpic drive to assemble decreases. At a high G/C content (number of grafts and G/C placement are held constant), as particle size decreases, Td increases. This is because the smaller particles experience a lower entropic loss than do larger particles upon assembly. On the other hand, at a low G/C content, small changes in particle size lead to negligible changes in Td.

Molecular simulation study of assembly of DNA-grafted nanoparticles: effect of bidispersity in DNA strand length

In this paper, we use molecular dynamics simulations to study the assembly of DNA-grafted nanoparticles to demonstrate specifically the effect of bidispersity in grafted DNA strand length on the thermodynamics and structure of nanoparticle assembly at varying number of grafted single-stranded DNA (ssDNA) strands and number of guanine/cytosine (G/C) bases per strand. At constant number of grafted ssDNA strands and G/C nucleotides per strand, as bidispersity in strand lengths increases, the number of nanoparticles that assemble as well as the number of neighbours per particle in the assembled cluster increases. When the number of G/C nucleotides per strand in short and long strands is equal, the long strands hybridise with the other long strands with higher frequency than the short strands hybridise with short/long strands. This dominance of the long strands leads to bidisperse systems having similar thermodynamics to that in corresponding systems with monodisperse long strands. Structurally, however, as a result of long–long, long–short and short–short strand hybridisation, bidispersity in DNA strand length leads to a broader inter-particle distance distribution within the assembled cluster than seen in systems with monodisperse short or monodisperse long strands. The effect of increasing the number of G/C bases per strand or increasing the number of grafted DNA strands on the thermodynamics of assembly is similar for bidisperse and monodisperse systems. The effect of increasing the number of grafted ssDNA strands on the structure of the assembled cluster is dependent on the extent of strand bidispersity because the presence of significantly shorter ssDNA strands among long ssDNA strands reduces the crowding among the strands at high grafting density. This relief in crowding leads to larger number of strands hybridised and as a result larger coordination number in the assembled cluster in systems with high bidispersity in strands than in corresponding monodisperse or low bidispersity systems.