Units

The FSD plugin uses dimensionless units so that all quantities are approximately \mathcal{O}(1). No conversion factors need to be applied to the result to get results with the expected normalization. The fundamental units are: the particle radius a, the solvent viscosity \eta, and Boltzmann’s constant k_{B}.

The fundamental units in the plugin are:
  • Distance - a
  • Translation-Force Hydrodynamic Resistance - 6\pi\eta a
  • Traslation-Torque/Rotation-Force Hydrodynamic Resistance - 6\pi\eta a^{2}
  • Rotation-Torque/Stresslet-Strain Hydrodynamic Resistance - 6\pi\eta a^{3}
  • Temperature - k_{B}T, i.e. setting T=1 in the plugin units corresponds to k_{B}T=1
With these normalizations, the dimensionless resistance tensors for isolated particles in an unbounded domain would be:
  • {\bf R}_{\rm FU} = {\bf I}
  • {\bf R}_{{\rm L}\Omega} = (4/3) \, {\bf I}
  • {\bf R}_{\rm ES} = (10/9) \, {\bf I}

Note that these exact values won’t be obtained computing the resistance for an isolated particle using the FSD plugin because the simulation is performed in periodic geometries. In particular, {\bf R}_{\rm FU} would need to be corrected for the periodic backflow described by Hasimoto (J. Fluid Mech., 1959).