Stokesian dynamics[1] is a solution technique for the Langevin equation, which is the relevant form of Newton's 2nd law for a Brownian particle.
The method treats the suspended particles in a discrete sense while the continuum approximation remains valid for the surrounding fluid, i.e., the suspended particles are generally assumed to be significantly larger than the molecules of the solvent.
The particles then interact through hydrodynamic forces transmitted via the continuum fluid, and when the particle Reynolds number is small, these forces are determined through the linear Stokes equations (hence the name of the method).
Stokesian Dynamics can thus be applied to a variety of problems, including sedimentation, diffusion and rheology, and it aims to provide the same level of understanding for multiphase particulate systems as molecular dynamics does for statistical properties of matter.
is the stochastic Brownian force due to thermal motion of fluid 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.
Stokesian dynamics is used primarily for non-equilibrium suspensions where it has been shown to provide results which agree with experiments.
is the velocity of the bulk shear flow evaluated at the particle center,
are the configuration-dependent resistance matrices that give the hydrodynamic force/torque on the particles due to their motion relative to the fluid (
Note that the subscripts on the matrices indicate the coupling between kinematic (
One of the key features of Stokesian dynamics is its handling of the hydrodynamic interactions, which is fairly accurate without being computationally inhibitive (like boundary integral methods) for a large number of particles.
operations where N is the number of particles in the system (usually a periodic box).
Recent advances have reduced the computational cost to about
arises from the thermal fluctuations in the fluid and is characterized by: The angle brackets denote an ensemble average,
results from the fluctuation-dissipation theorem for the N-body system.