Stokesian dynamics

Stokesian Dynamics [cite journal
last =Brady
first =John
coauthors = Bossis G.
title = Stokesian Dynamics
journal = Ann. Rev. Fluid Mech.
volume = 20
pages = 111–157
date = 1988
doi = 10.1146/annurev.fl.20.010188.000551] is a solution technique for the Langevin equation, which is the relevant form of Newton's 2nd law for a Brownian particle:$mfrac\{du\}\{dt\}\; =\; F^\{H\}\; +\; F^\{B\}\; +\; F^\{P\}$In the above equation $F^\{H\}$ is the hydrodynamic force, i.e., force exerted by the fluid on the particle due to relative motion between them. $F^\{B\}$ is the stochastic Brownian force due to thermal motion of fluid particles. $F^\{P\}$ is the inter particle force,e.g. electrostatic repulsion between like charged particles. Brownian dynamics is one of the popular techniques of solving the Langevin equation, but the hydrodynamic interaction in Brownian dynamics is highly simplified and normally includes only the isolated body resistance. On the other hand, Stokesian dynamics includes the many body hydrodynamic interactions. Hydrodynamic interaction is very important for non-equilibrium suspensions, like a sheared suspension, where it plays a vital role in its microstructure and hence its properties. So, Stokesian dynamics is used primarily for non-equilibrium suspensions and gives excellent agreement with experiments.

Hydrodynamic Interaction

One of the key features of Stokesian Dynamics is its handing of the hydrodynamic interaction, which is fairly accurate without being computationally inhibitive (like Boundary Integral Methods) for a large number of particles. Classical Stokesian dynamics requires $O(N^\{3\})$ operation where N is the number of particles in the system (usually a periodic box). Recent advances has brought down the computational cost to $O(N\; ln\; N)$ [cite journal
last =Brady
first =John
coauthors = Sierou A.
title = Accelerated Stokesian Dynamics simulations
journal = Journal of Fluid Mechanics
volume = 448
pages = 115–146
date = 2001
doi = ]

See also

* Immersed Boundary Method

References