Theoretical modeling of the Casimir force-induced instability in freestanding nanowires with circular cross-section

The Casimir force can induce instability and adhesion in freestanding nanostructures. Previous research efforts in this area have exclusively focused on modeling the instability in structures with planar or rectangular cross-section, while, to the best knowledge of the authors, no attention has been paid to investigate this phenomenon for nanowires with circular cross-section. In this study, effects of the Casimir force on the instability and adhesion of freestanding Cylinder–Plate and Cylinder–Cylinder geometries are investigated, which are commonly encountered in real nanodevices. To compute the Casimir force, two approaches, i.e. the proximity force approximation (PFA) for small separations and Dirichlet asymptotic approximation (scattering theory) for large separations, are considered. A continuum mechanics theory is employed, in conjunction with the Euler-beam model, to obtain constitutive equations of the systems. The governing nonlinear constitutive equations of the nanostructures are solved using two different approaches, i.e. the analytical modified Adomian decomposition (MAD) and the numerical finite difference method (FDM). The detachment length and minimum gap, both of which prevent the Casimir force-induced adhesion, are computed for both configurations.