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The analysis of complex fibrous systems or materials on the micro- andnanoscale, which have a high practical relevance for many technical orbiological systems, requires accurate analytical descriptions of the adhesiveand repulsive forces acting on the fiber surfaces. While such analyticalexpressions are generally needed both for theoretical studies and forcomputer-based simulations, the latter motivates us here to derivedisk-cylinder interaction potential laws that are valid for arbitrary mutualorientations in the decisive regime of small surface separations. The chosentype of fundamental point-pair interaction follows the simple Lennard-Jonesmodel with inverse power laws for both the adhesive van der Waals part and thesteric, repulsive part. We present three different solutions, ranging fromhighest accuracy to the best trade-off between simplicity of the expression andsufficient accuracy for our intended use. The validity of simplifyingapproximations and the accuracy of the derived potential laws is thoroughlyanalyzed, using both numerical and analytical reference solutions for specificinteraction cases. Most importantly, the correct asymptotic scaling behavior inthe decisive regime of small separations is achieved, and also thetheoretically predicted $(1\!/\!\sin\!\alpha)$-angle dependence (fornon-parallel cylinders) is obtained by the proposed analytical solutions. As weshow in the outlook to our current research, the derived analyticaldisk-cylinder interaction potential laws may be used to formulate highlyefficient computational models for the interaction of arbitrarily curvedfibers, such that the disk represents the cross-section of the first and thecylinder a local approximation to the shape of the second fiber.

Analytical disk-cylinder interaction potential laws for the computational modeling of adhesive, deformable (nano)fibers