Chemical Engineering Science 61 (2006) 2169 – 2185 www.elsevier.com/locate/ces Bridging diverse physical scales with the discrete-particle paradigm in modeling colloidal dynamics with mesoscopic features Witold Dzwinel a , ∗ , David A. Yuen b , Krzysztof Boryczko a a Institute of Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland b Minnesota Supercomputing Institute, University of Minnesota, MN 55455, Minneapolis, USA Received 1 March 2003; accepted 6 January 2004 Available online 5 July 2005 Abstract Microstructural dynamics and boundary singularities generate complex multiresolution patterns, which are difficult to model with the continuum approaches using partial differential equations. To provide an effective solver across the diverse scales with different physics the continuum dynamics must be augmented with atomistic models, such as non-equilibrium molecular dynamics (NEMD). The spatio- temporal disparities between continuum and atomistic approaches make this coupling a computationally demanding task. We present a multiresolution homogeneous particle paradigm, as a cross-scale model, which allows producing the microscopic and macroscopic modes in the mesoscopic scale. We describe a discrete-particle model in which the following spatio-temporal scales are obtained by subsequent coarse-graining of hierarchical systems consisting of atoms, molecules, fluid particles and moving grid nodes. We then show some examples of 2-D and 3-D modeling of the Rayleigh–Taylor fluid instability, phase separation, colloidal arrays and colloidal dynamics in the mesoscale by using fluid particles as the exemplary discretized model. The modeled multiresolution patterns are similar to those observed in laboratory experiments. We show that they can mimic scales ranging from single micelle, colloidal crystals, colloidal aggregates up to the macroscopic phenomena involving the clustering of red blood cells in the vascular system. We can summarize the computationally homogeneous discrete-particle model in the following hierarchical scheme: non-equilibrium molecular dynamics (NEMD), fluid particle model (FPM), thermodynamically consistent DPD and smoothed particle hydrodynamics (SPH).  2005 Elsevier Ltd. All rights reserved. Keywords: Discrete-particle methods; Non-equilibrium molecular dynamics; Dissipative particle dynamics; Fluid particle model; Smoothed particle hydrodynamics; Colloidal dynamics; Blood flow 1. Introduction Progress in nanosciences has resulted in a desire for ad- equate theory and large-scale numerical simulations to un- derstand the various roles that are played by surface effects, edge effects or bulk effects in nanomaterials. Moreover, the dynamics of colloidal particle transport call for not only pas- sive transport, but additional processes such as agglomer- ation/dispersion, driven interfaces, adsorption to pore wall ∗ Corresponding author. Tel.: +48 12 6173520. E-mail addresses: dzwinel@agh.edu.pl (W. Dzwinel), davey@msi.umn.edu (D.A. Yuen), boryczko@uci.agh.edu.pl (K. Boryczko). 0009-2509/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.01.075 grains, and biofilm interactions ( Albert et al., 1998; Benson, 1998; Kechagia et al., 2001; Knutson and Travis, 2002; Davis, 2002). In many cases, there is a critical need to inves- tigate these multiscale structures, ranging from nanometers to micrometers in complex geometries, such as in vascu- lar and porous systems (Davis and Lobo, 1992; Li et al., 1999; Davis, 2002). Currently, the most cost-effective nu- merical approach, which is able to couple some of these processes and capture their feedback effects on the macro- scropic flow field is the continuum multiscale multi-grid approaches (Hou and Wu, 1997; Moulton et al., 1998), the lattice-Boltzmann gas (LBG) (see e.g., Travis et al., 1993; Ladd and Verberg, 2001) and atomistic/continuum hybrid algorithms (Hadjiconstantinou and Patera, 1997; Nakano et al., 1998).