Soft Matter and Complex Systems Seminar

We study the onset of 3D buckling of a slender elastic filament in a viscous shear flow at low Reynolds number and high Péclet number. Using the Euler–Bernoulli (elastica) description linearized about a straight configuration of arbitrary orientation, we show that the 3D stability problem can be reduced to a universal spectral problem governed by an orientation-dependent combination of the elastoviscous number and the shear geometry. Building on earlier in-plane eigenmodes, we solve the 3D eigenproblem and propose a simple analytic approximation of the unstable eigenfunctions as Gaussian wave packets. This yields the central scaling result: for highly flexible filaments, the characteristic wavenumber of the most unstable mode grows proportionally to the square root of this elastoviscous measure. Finally, we validate the predicted eigenshapes by numerical simulations of finite-thickness filaments using a bead model and the HYDROMULTIPOLE codes. The talk is based on our paper: P. Sznajder, P. Zdybel, L. Liu, and M. L. Ekiel-Jeżewska, Phys. Rev. E 110, 025104 (2024).