Universal Stokesian Dynamics based procedure for determining the relationship between the effective and geometric aspect ratio of a particle

Jeffery's theory[1] of the orbital motion of a spheroid in unbounded shear flow, as extended by Bretherton[2] to any axisymmetric particle with fore-aft symmetry (APFAS), permits straightforward rapid dynamical calculation for either one such particle or a dilute suspension thereof. Although this approach eliminates the need for costly numerical methods, it requires substituting the effective aspect ratio (EAR) of the APFAS for the geometric aspect ratio (GAR) of the spheroid in the Jeffery formalism. The EAR of any APFAS is a function of its GAR determined by the APFAS shape but unknown in advance. To overcome this obstacle, we exploit our rigid body Stokesian Dynamics approach[3], as recently extended to allow for the presence of a linear flow[4], to provide a universal computational procedure for obtaining empirically the functional dependence of the EAR on the GAR for an APFAS of any shape. We illustrate this procedure for a rod and note its usefulness for other interesting shapes.

[1] G. B. Jeffery, Proc. R. Soc. Lond. A 102, 161 (1922).
[2] F. P. Bretherton, J. Fluid Mech. 14, 284 (1962).
[3] R. Kutteh, J. Chem. Phys. 132, 174107 (2010).
[4] See other talk "Stokesian Dynamics of Arbitrary-Shape Passive and Active Particles in Linear Flow: Constraint and Rigid Body Approaches"