Fiber buckling in confined viscous flows: an absolute instability described by the Ginzburg-Landau equation

We explore the dynamics of a flexible fiber transported by a viscous flow in a Hele-Shaw cell of height comparable to the fiber height. We show that long fibers aligned with the flow experience a buckling instability. Competition between viscous and elastic forces leads to the deformation of the fiber into a wavy shape convolved by a Bell-shaped envelope. We characterize the wavelength and phase velocity of the deformation as well as the growth and spreading of the envelope. Our study of the spatio-temporal evolution of the deformation reveals a linear and absolute instability arising from a local mechanism well described by the Ginzburg-Landau equation.