Bridging diverse physical scales with the discrete-particle paradigm in modeling colloidal dynamics with mesoscopic features

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).