High Precision Transport Properties of Cylinders by the Boundary Element Method
In this work we apply the boundary element method to obtain very precise computations of the hydrodynamic transport properties for rectangular, sphero, and open cylinders. This work numerically solves the exact integral equations for Stokes flow with stick boundary conditions and includes the tensor values for the translational and rotational diffusion coefficients, and the intrinsic viscosity for three types of cylinders with axial ratios between 1 and 100. We describe the properties of the triangular tessellations that yield essentially numerically exact properties, with estimated uncertainties of 0.07% or better. The data are summarized by fairly simple mathematical expressions as a function of the axial ratio of the cylinders which are constructed to satisfy the correct asymptotic expressions, yielding formulas that are valid for 1 ≤ p < ∞. The end effects for the three different types of caps are discussed?such end effects are noticeable for small axial ratios and become unimportant for large axial ratios. The open cylinders behave in a similar fashion to the closed end cylinders, despite the absence of caps. For the intrinsic viscosity, we introduce a new formula with correct asymptotic limits and high accuracy at unit axial ratio which greatly improves the description over traditional expressions derived from slender body theory. We compare our results with previous formulas available in the literature for different types of cylinders and conclude that, except for the path integral method results, most previous work has significant inaccuracies. The expressions obtained in this work, will be useful in the description of the transport properties of interesting macromolecular structures such as carbon nanotubes, microtubules, and viruses.