3.4 Particle-based mesoscopic models
Earlier, we outlined the connection between the Boltzmann equation (a particular case of the master equation) and the continuum transport equations. However, at the nano to mesoscopic lengthscales, neither the molecular description using molecular dynamics nor a continuum description based on the Navier-Stokes equation are optimal to study nanofluid flows. The number of atoms is too large for MD to be computationally tractable. The microscopic-level details, including thermal fluctuations, play an essential role in demonstrating the dynamic behavior, an effect which is not readily captured in continuum transport equations. Development of particle-based mesoscale simulation methods overcomes these difficulties, and the most common coarse-grained models used to simulate the nanofluid flows are Brownian dynamics (BD) and multi-particle collision dynamics (MPCD) methods. The general approach used in all these methods is to average out relatively insignificant microscopic details in order to obtain reasonable computational efficiency while preserving the essential microscopic-level details.
3.4.1 Brownian dynamics (BD) simulations: The physical system of nanofluids contains relatively small solvent molecules and relatively larger nanoparticles, which move much more slowly due to their larger size. A broad range of time scales, from short time steps for the fast motion to very long runs for the evolution of the slower mode, needs to be accommodated by any simulation method as applied to nanofluids, making the process time-consuming. However, in the BD simulation technique, explicit solvent molecules are replaced by a stochastic force, and the hydrodynamic forces mediated by them are accounted for through a hydrodynamic interaction (HI) kernel. The BD equation thus replaces Newton’s equations of motion in the absence of inertia: