  The analysis of complex fibrous systems or materials on the micro- and
nanoscale, which have a high practical relevance for many technical or
biological systems, requires accurate analytical descriptions of the adhesive
and repulsive forces acting on the fiber surfaces. While such analytical
expressions are generally needed both for theoretical studies and for
computer-based simulations, the latter motivates us here to derive
disk-cylinder interaction potential laws that are valid for arbitrary mutual
orientations in the decisive regime of small surface separations. The chosen
type of fundamental point-pair interaction follows the simple Lennard-Jones
model with inverse power laws for both the adhesive van der Waals part and the
steric, repulsive part. We present three different solutions, ranging from
highest accuracy to the best trade-off between simplicity of the expression and
sufficient accuracy for our intended use. The validity of simplifying
approximations and the accuracy of the derived potential laws is thoroughly
analyzed, using both numerical and analytical reference solutions for specific
interaction cases. Most importantly, the correct asymptotic scaling behavior in
the decisive regime of small separations is achieved, and also the
theoretically predicted $(1\!/\!\sin\!\alpha)$-angle dependence (for
non-parallel cylinders) is obtained by the proposed analytical solutions. As we
show in the outlook to our current research, the derived analytical
disk-cylinder interaction potential laws may be used to formulate highly
efficient computational models for the interaction of arbitrarily curved
fibers, such that the disk represents the cross-section of the first and the
cylinder a local approximation to the shape of the second fiber.

Computational Engineering, Finance, and Science