Computer Simulation of Particle Suspensions

Particle suspensions are ubiquitous in our daily life, but are not well understood due to their complexity. During the last twenty years, various simulation methods have been developed in order to model these systems. Due to varying properties of the solved particles and the solvents, one has to choose the simulation method properly in order to use the available compute resources most effectively with resolving the system as well as needed. Various techniques for the simulation of particle suspensions have been implemented at the Institute for Computational Physics allowing us to study the properties of clay-like systems, where Brownian motion is important, more macroscopic particles like glass spheres or fibers solved in liquids, or even the pneumatic transport of powders in pipes. In this paper we will present the various methods we applied and developed and discuss their individual advantages.Comment: 31 pages, 11 figures, to appear in Lecture Notes in Applied and Computational Mechanics, Springer (2006

Equilibrium and nonequilibrium thermodynamics of particle-stabilized thin liquid films

Our recent quasi-two-dimensional thermodynamic description of thin-liquid films stabilized by colloidal particles is generalized to describe nonuniform equilibrium states of films in external potentials and nonequilibrium transport processes produced in the film by gradients of thermodynamic forces. Using a Monte--Carlo simulation method, we have determined equilibrium equations of state for a film stabilized by a suspension of hard spheres. Employing a multipolar-expansion method combined with a flow-reflection technique, we have also evaluated the short-time film-viscosity coefficients and collective particle mobility.Comment: 16 pages, 10 figure

Shear Viscosity of Clay-like Colloids in Computer Simulations and Experiments

Dense suspensions of small strongly interacting particles are complex systems, which are rarely understood on the microscopic level. We investigate properties of dense suspensions and sediments of small spherical Al_2O_3 particles in a shear cell by means of a combined Molecular Dynamics (MD) and Stochastic Rotation Dynamics (SRD) simulation. We study structuring effects and the dependence of the suspension's viscosity on the shear rate and shear thinning for systems of varying salt concentration and pH value. To show the agreement of our results to experimental data, the relation between bulk pH value and surface charge of spherical colloidal particles is modeled by Debye-Hueckel theory in conjunction with a 2pK charge regulation model.Comment: 15 pages, 8 figure

Direct numerical simulations for non-Newtonian rheology of concentrated particle dispersions

The non-Newtonian behavior of a monodisperse concentrated dispersion of spherical particles was investigated using a direct numerical simulation method, that takes into account hydrodynamic interactions and thermal fluctuations accurately. Simulations were performed under steady shear flow with periodic boundary conditions in the three directions. The apparent shear viscosity of the dispersions was calculated at volume fractions ranging from 0.31 to 0.56. Shear-thinning behavior was clearly observed at high volume fractions. The low- and high-limiting viscosities were then estimated from the apparent viscosity by fitting these data into a semi-empirical formula. Furthermore, the short-time motions were examined for Brownian particles fluctuating in concentrated dispersions, for which the fluid inertia plays an important role. The mean square displacement was monitored in the vorticity direction at several different Peclet numbers and volume fractions so that the particle diffusion coefficient is determined from the long-time behavior of the mean square displacement. Finally, the relationship between the non-Newtonian viscosity of the dispersions and the structural relaxation of the dispersed Brownian particles is examined

Hi-Fidelity Simulation of the Self-Assembly and Dynamics of Colloids and Polymeric Solutions with Long Range Interactions

Modeling the equilibrium properties and dynamic response of the colloidal and polymeric solutions provides valuable insight into numerous biological and industrial processes and facilitates development of novel technologies. To this end, the centerpiece of this research is to incorporate the long range electrostatic or hydrodynamic interactions via computationally efficient algorithms and to investigate the effect of these interactions on the self-assembly of colloidal particles and dynamic properties of polymeric solutions. Specifically, self-assembly of a new class of materials, namely bipolar Janus nano-particles, is investigated via molecular dynamic simulation in order to establish the relationship between individual particle characteristics, such as surface charge density, particle size, etc., and the final structure formation. Furthermore, the importance of incorporating the long range electrostatic interaction in achieving the corresponding final morphology is discussed. The dynamic properties of polymeric solutions are investigated via two parallel pathways. In the first approach, force-extension behavior of the flexible polyelectrolytes is probed via fine-grained Brownian dynamics simulation of the bead-rod model. The presented model accurately incorporates the excluded volume interaction in order to capture the effect of salt concentration on the force-extension response of polyelectrolyte chain as observed in the single chain experiments. It is shown that accurate incorporation of the excluded volume effect on a long chain of more than 500 Kuhn segments is necessary to reach the universal scaling both for equilibrium properties and force-extension response. Next, a new force law is extracted using a novel discrete Pade approximant from the constant-force ensemble result of the bead-rod model. The new force law is implemented in the coarse-grained meso-scale bead-spring model with hydrodynamic interactions in order to investigate the dynamics of flexible macromolecules in the athermal solvent. In the second approach the computational cost of the long range hydrodynamic interaction in dilute solution of polymeric chains with constrains is reduced via development of a new computational technique based on the conjugate gradient and Krylov subspace methods. Moreover, an algorithm for estimating the contribution of various forces to the transient polymeric stress tensor is introduced and employed in order to investigate transient dynamics of the solution of the flexible polymeric chains

The non-Newtonian rheology of dilute colloidal suspensions

The non-Newtonian rheology is calculated numerically to second order in the volume fraction in steady simple shear flows for Brownian hard spheres in the presence of hydrodynamic and excluded volume interactions. Previous analytical and numerical results for the low-shear structure and rheology are confirmed, demonstrating that the viscosity shear thins proportional to Pe2, where Pe is the dimensionless shear rate or Péclet number, owing to the decreasing contribution of Brownian forces to the viscosity. In the large Pe limit, remnants of Brownian diffusion balance convection in a boundary-layer in the compressive region of the flow. In consequence, the viscosity shear thickens when this boundary-layer coincides with the near-contact lubrication regime of the hydrodynamic interaction. Wakes are formed at large Pe in the extensional zone downstream from the reference particle, leading to broken symmetry in the pair correlation function. As a result of this asymmetry and that in the boundary-layer, finite normal stress differences are obtained as well as positive departures in the generalized osmotic pressure from its equilibrium value. The first normal stress difference changes from positive to negative values as Pe is increased when the hard-sphere limit is approached. This unusual effect is caused by the hydrodynamic lubrication forces that maintain particles in close proximity well into the extensional quadrant of the flow. The study demonstrates that many of the non-Newtonian effects observed in concentrated suspensions by experiments and by Stokesian dynamics simulations are present also in dilute suspensions

Large-Graph Layout with the Fast Multipole Multilevel Method

The visualization of of large and complex networks or graphs is an indispensable instrument for getting deeper insight into their structure. Force-directed graph-drawing algorithms are widely used to draw such graphs. However, these methods do not guarantee a sub-quadratic running time in general. We present a new force-directed method that is based on a combination of an efficient multilevel scheme and a strategy for approximating the repulsive forces in the system by rapidly evaluating potential fields. Given a graph G=(V,E), the asymptotic worst-case running time of this method is O(|V|log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs with 100000 nodes in less than 5 minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other methods

Modelling uncertainty of the radiation energy emitted by extensive air showers

Recently, the energy determination of extensive air showers using radio emission has been shown to be both precise and accurate. In particular, radio detection offers the opportunity for an independent measurement of the absolute energy of cosmic rays, since the radiation energy (the energy radiated in the form of radio signals) can be predicted using first-principle calculations involving no free parameters, and the measurement of radio waves is not subject to any significant absorption or scattering in the atmosphere. Here, we verify the implementation of radiation-energy calculations from microscopic simulation codes by comparing Monte Carlo simulations made with the two codes CoREAS and ZHAireS. To isolate potential differences in the radio-emission calculation from differences in the air-shower simulation, the simulations are performed with equivalent settings, especially the same model for the hadronic interactions and the description of the atmosphere. Comparing a large set of simulations with different primary energies and shower directions we observe differences amounting to a total of only 3.3 %. This corresponds to an uncertainty of only 1.6 % in the determination of the absolute energy scale and thus opens the potential of using the radiation energy as an accurate calibration method for cosmic ray experiments.Comment: 8 pages, 2 figures, ICRC2017 contributio