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License: MIT License
Simulation and visualization of Stokesian dynamics for N interacting particles
License: MIT License
For anisotropic particles (ellipsoids), we know the drag tensor of individual particles. In the grand mobility matrix, these can be inserted as the block diagonal elements of self-mobility. The off-block-diagonal elements are based on sphere-sphere coupling, and the best we can do for the coupling is to assume the ellipsoids are sphere-like. Some research has been done on collections of spheroids (see [ref]), but it appears quite complicated.
Claeys and Brady - 1993 - Suspensions of prolate spheroids in Stokes flow. P.pdf
The grand mobility matrix should also include pairwise interactions through the interface
In the attached paper,
Eqs. B1-B3 (self interaction)
Eqs. C1-C4 (pair interaction)
Swan and Brady - 2007 - Simulation of hydrodynamically interacting particl.pdf
In the current implementation, the hydrodynamics are pair-wise interactions. The mobility matrix M is constructed pair-wise, and the velocity in over-damped systems is V = M * F. To include many-body hydrodynamics, the mobility matrix must be extended to include higher stress-lets in the fluid field expansion. Then the larger mobility matrix is inverted to obtain the grand resistance matrix, R, which is then truncated to only translational and rotational stress-lets. The truncated R is then inverted to obtain the final mobility M, which now includes many-body terms.
Brady and Bossis - Stokesian Dynamics.pdf
pages 123-128
When two particle have a center-to-center distance within 4*radius, there are lubrication hydrodynamic forces. Lubrication forces are expected to be very important in bound nano-dimers. A rough outline for how to implement them:
Brady and Bossis - Stokesian Dynamics.pdf
Eq.(18) and the surrounding discussion for background theory
Jeffrey and Onishi - 1984 - Calculation of the resistance and mobility functio.pdf
Explicit equations for the lubrication terms in the resistance matrix
1802.08226.pdf
This is supposedly the corrected form of the equations from Jeffrey & Onishi.
2013-W(1).pdf
May have additional useful information
https://github.com/Pecnut/stokesian-dynamics
This appears to be a project that has fully implemented hydrodynamic interactions including lubrication forces. The lubrication forces are discussed explicitly here.
https://github.com/rajeshrin
Another related project
Should have a similar call to trajectory_animation and create static pictures
Is it a good idea to use a dynamic time-step for an over-damped system? The ideal time-step can be chosen at each time-step by calculating the magnitude of the maximum force vector. The time-step would need an upper limit so that the Brownian motion is not abnormally large.
Correlations with hydrodynamic interactions are correct according to the fluctuation-dissipation theorem. Also verify that they are uncorrelated without interactions. And there are single-particle correlations for anisotropic drag particles.
If a single particle is a composition of spheres (like a dimer), then only the net force and net torque effect its dynamics. Stoked would treat this as a single particle. But for certain interactions (sphere electrostatic, collisions, van-der-walls, etc.), the interactions can still be treated more precisely at the sphere-sphere level.
Add a way to tell stoked that a particle is a composite of spheres, and then use that info to obtain the correct forces from sphere-sphere interactions.
Trajectory animation does not work on macOS using the macOS backend (works with PyQT backends)
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