5.5 Field-based coarse-graining
For specific systems such as nanoparticle and nanofluid transport, both
molecular interactions (due to biomolecular recognition) and
hydrodynamic interactions (due to fluid flow and boundary effects) are
significant. The integration of disparate length and time scales does
not fit traditional multiscale methods. The complexity lies in
integrating fluid-flow and memory for multiphase flow in complex and
arbitrary geometries, while simultaneously including thermal and
stochastic effects to simulate quasi-equilibrium distributions correctly
to enable receptor-ligand binding at the physiological temperature. This
issue is ubiquitous in multivalent binding or adhesive interactions
between nanoparticles and cells or between two cells. Bridging the
multiple length scales (from meso to molecular) and the associated time
scales relevant to the problem is essential to success herein. Multiple
macroscopic and mesoscopic time scales governing the problem include (i)
hydrodynamic time scale, (ii) viscous/Brownian relaxation time scale,
and (iii) Brownian diffusion time scale.
5.5.1 Memory function approach to coarse-graining with
hydrodynamic interactions: In the description of the dynamics of
nanosized Brownian particles in an bounded and unbounded fluid domains
the memory functions decay with algebraic correlations as enumerated by
theoretical and computational studies [46, 85, 128]. The equation of
stochastic motion for each component of the velocity of a nanoparticle
immersed in a fluid in bounded and unbounded domains takes the form of a
generalized Langevin equation (GLE) of the form of (Eq. 9); to account
for hydrodynamic interaction, a composite GLE was introduced [129,
130].