Modeling mesoscopic fluids with discrete-particles -methods, algorithms, and results

Mesoscopic features embedded within macroscopic phenomena in colloids and suspensions, when coupled together with micro-structural dynamics and boundary singularities, produce complex multi-resolution patterns, which are difficult to capture with the continuum model using partial differential equations, i.e., the Navier-Stokes equation and the Cahn-Hillard equation. The continuum model must be augmented with discretized microscopic models, such as molecular dynamics (MD), in order to provide an effective solver across the diverse scales with different physics. The high degree of spatial and temporal disparities of this approach makes it a computationally demanding task. In this survey we present the off-grid discrete-particles methods, which can be applied in modeling cross-scale properties of complex fluids. We can view the cross-scale endeavor characteristic of a multi-resolution homogeneous particle model, as a manifestation of the interactions present in the discrete particle model, which allow them to produce the microscopic and macroscopic modes in the mesoscopic scale. First, we describe a discrete-particle models in which the following spatio-temporal scales are obtained by subsequent coarse-graining of hierarchical systems consisting of atoms, molecules, fluid particles and moving mesh nodes. We then show some examples of 2D and 3D modeling of the RayleighTaylor mixing, phase separation, colloidal arrays, colloidal dynamics in the mesoscale and blood flow in microscopic vessels. The modeled multi-resolution patterns look amazingly similar to those found in laboratory experiments and can mimic a single micelle, colloidal crystals, largescale colloidal aggregates up to scales of hydrodynamic instabilities and the macroscopic phenomenon involving the clustering of red blood cells in capillaries. We can summarize the computationally homogeneous discrete particle model in the following hierarchical scheme: nonequilibrium molecular dynamics (NEMD), dissipative particle dynamics (DPD), fluid particle model (FPM), smoothed particle hydrodynamics (SPH) and thermodynamically consistent DPD. An idea of powerful toolkit over the GRID can be formed from these discrete particle schemes to model successfully multiple-scale phenomena such as biological vascular and mesoscopic porous-media systems.