Advanced Particle-Based Techniques for Complex Fluids and Multiscale Flow Processes

Abstract

Particle-based methods represent a general multiscale framework to study complex flow problems at different space- and timescales. Whereas they rely on a general set of Newton’s equations of motion for a system of interacting elements, the very concept of ‘particle’ can assume different physical realizations depending on the targeted level of description and the physics of interest. At microscopic scales, particles can represent real molecules/atoms interacting with conservative classical potentials; at the mesoscale, a ‘particle’ represents a thermodynamic system containing potentially thousands of atoms/molecules and its dynamics is governed by a set of ordinary stochastic differential equations where the interaction forces are of conservative, dissipative and random nature. Finally, at the continuum macroscopic scales, it is possible to derive a suitable set of Newton’s equations such that the corresponding particle configurations represent an adaptive Lagrangian discretization of arbitrary sets of partial differential equations (e.g. Navier–Stokes), that is, a computational fluid dynamics technique. All the different levels can be integrated in a general thermodynamic framework for discrete systems which satisfies basic physical laws such as energy conservation, entropy increase or—in the case of Brownian systems—the fluctuation–dissipation theorem at the very discrete level. In this chapter, we review the use of mesoscopic and macroscopic particle techniques for the modelling and simulation of complex fluids such as polymer or particle suspensions. It will be shown how complex microstructural properties can be incorporated in different ways, i.e. from micro-mechanical to field-based equations, depending on the available information and computational requirements. The development of hybrid particle methods coupling simultaneously dynamics occurring at different scales will be also discussed in relation to the problem of cellular transport/adhesion in biofluidics.