Simulations and integral-equation theories for dipolar density interacting disks

Integral equation theories (IETs) based on the Ornstein-Zernike (OZ) relation can be used as an analytical tool to predict structural and thermodynamic properties and phase behavior of fluids with low numerical cost. However, there are no studies of the IETs for the dipolar density interaction potential in 2D systems, a relevant inter-domain interaction in lipid monolayers with phase coexistence. This repulsive interaction arises due to the excess dipole density of the domains, which are aligned perpendicular to the interface. This work studies the performance of three closures of the OZ equation for this novel system: Rogers-Young (RY), Modified Hypernetted Chain (MHNC), and Variational Modified Hypernetted Chain (VMHNC). For the last two closures the bridge function of a reference system is required, being the hard disk the most convenient reference system. Given that in 2D there is no analytical expressions for the hard disk correlation functions, two different approximations are proposed: one based on the Percus-Yevick approximation (PY), and the other based on an extension of the hard spheres Verlet-Weis-Henderson-Grundke parameterization (LB). The accuracy of the five approaches is evaluated by comparison of the pair correlation function and the structure factor with Monte Carlo simulation data. The results show that RY closure is only satisfactory for low-structured regimes. MHNC and VMHNC closures perform globally well and there are no significant differences between them. However, the reference system in some cases affects their performance; when the pair correlation function serves as the measure, the LB--based closures quantitatively outperform the PY ones. From the point of view of its applicability, LB--based closures do not have a solution for all studied interaction strength parameters, and, in general, PY--based closures are numerically preferable.Comment: 9 pages, 4 figure

Accelerated Stokesian dynamics: Brownian motion

A new Stokesian dynamics (SD) algorithm for Brownian suspensions is presented. The implementation is based on the recently developed accelerated Stokesian dynamics (ASD) simulation method [Sierou and Brady, J. Fluid Mech. 448, 115 (2001)] for non-Brownian particles. As in ASD, the many-body long-range hydrodynamic interactions are computed using fast Fourier transforms, and the resistance matrix is inverted iteratively, in order to keep the computational cost O(N log N). A fast method for computing the Brownian forces acting on the particles is applied by splitting them into near- and far-field contributions to avoid the O(N3) computation of the square root of the full resistance matrix. For the near-field part, representing the forces as a sum of pairwise contributions reduces the cost to O(N); and for the far-field part, a Chebyshev polynomial approximation for the inverse of the square root of the mobility matrix results in an O(N1.25 log N) computational cost. The overall scaling of the method is thus roughly of O(N1.25 log N) and makes possible the simulation of large systems, which are necessary for studying long-time dynamical properties and/or polydispersity effects in colloidal dispersions. In this work the method is applied to study the rheology of concentrated colloidal suspensions, and results are compared with conventional SD. Also, a faster approximate method is presented and its accuracy discussed

Collective diffusion in charge-stabilized suspensions: Concentration and salt effects

The authors present a joint experimental-theoretical study of collective diffusion properties in aqueous suspensions of charge-stabilized fluorinated latex spheres. Small-angle x-ray scattering and x-ray photon correlation spectroscopy have been used to explore the concentration and ionic-strength dependence of the static and short-time dynamic properties including the hydrodynamic function H (q), the wave-number-dependent collective diffusion coefficient D (q), and the intermediate scattering function over the entire accessible range. They show that all experimental data can be quantitatively described and explained by means of a recently developed accelerated Stokesian dynamics simulation method, in combination with a modified hydrodynamic many-body theory. In particular, the behavior of H (q) for de-ionized and dense suspensions can be attributed to the influence of many-body hydrodynamics, without any need for postulating hydrodynamic screening to be present, as it was done in earlier work. Upper and lower boundaries are provided for the peak height of the hydrodynamic function and for the short-time self-diffusion coefficient over the entire range of added salt concentrations.Fil: Gapinski, J.. A. Mickiewicz University; PoloniaFil: Patkowski, A.. A. Mickiewicz University; PoloniaFil: Banchio, Adolfo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Holmqvist, P.. Helmholtz Gemeinschaft. Forschungszentrum Jülich; AlemaniaFil: Meier, Guillermo Enrique. Helmholtz Gemeinschaft. Forschungszentrum Jülich; AlemaniaFil: Lettinga, M.P.. Helmholtz Gemeinschaft. Forschungszentrum Jülich; AlemaniaFil: Nägele, G.. Helmholtz Gemeinschaft. Forschungszentrum Jülich; Alemani

Short-time Rheology and Diffusion in Suspensions of Yukawa-type Colloidal Particles

A comprehensive study is presented on the short-time dynamics in suspensions of charged colloidal spheres. The explored parameter space covers the major part of the fluid-state regime, with colloid concentrations extending up to the freezing transition. The particles are assumed to interact directly by a hard-core plus screened Coulomb potential, and indirectly by solvent-mediated hydrodynamic interactions (HIs). By comparison with accurate accelerated Stokesian Dynamics (ASD) simulations of the hydrodynamic function H(q), and the high-frequency viscosity, we investigate the accuracy of two fast and easy-to-implement analytical schemes. The first scheme, referred to as the pairwise additive (PA) scheme, uses exact two-body hydrodynamic mobility tensors. It is in good agreement with the ASD simulations of H(q) and the high-frequency viscosity, for smaller volume fractions up to about 10% and 20%, respectively. The second scheme is a hybrid method combining the virtues of the \delta\gamma-scheme by Beenakker and Mazur with those of the PA scheme. It leads to predictions in good agreement with the simulation data, for all considered concentrations, combining thus precision with computational efficiency. The hybrid method is used to test the accuracy of a generalized Stokes-Einstein (GSE) relation proposed by Kholodenko and Douglas, showing its severe violation in low salinity systems. For hard spheres, however, this GSE relation applies decently well

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres

We present a detailed study of short-time dynamic properties in concentrated suspensions of charge-stabilized and of neutral colloidal spheres. The particles in many of these systems are subject to significant many-body hydrodynamic interactions. A recently developed accelerated Stokesian dynamics (ASD) simulation method is used to calculate hydrodynamic functions, wave-number-dependent collective diffusion coefficients, self-diffusion and sedimentation coefficients, and high-frequency limiting viscosities. The dynamic properties are discussed in dependence on the particle concentration and salt content. Our ASD simulation results are compared with existing theoretical predictions, notably those of the renormalized density fluctuation expansion method of Beenakker and Mazur [Physica A 126, 349 (1984)], and earlier simulation data on hard spheres. The range of applicability and the accuracy of various theoretical expressions for short-time properties are explored through comparison with the simulation data. We analyze, in particular, the validity of generalized Stokes-Einstein relations relating short-time diffusion properties to the high-frequency limiting viscosity, and we point to the distinctly different behavior of de-ionized charge-stabilized systems in comparison to hard spheres