Deformation of a flexible fiber in a viscous flow past an obstacle

International audienceWe study the deformation and transport of elastic fibers in a viscous Hele-Shaw flow with curved streamlines. The variations of the global velocity and orientation of the fiberfollow closely those of the local flow velocity. The ratios of the curvatures of the fibersby the corresponding curvatures of the streamlines reflect a balance between elastic and viscous forces: this ratio is shown experimentally to be determined by a dimensionless {\it Sperm number} $Sp$ combining the characteristic parameters of the flow (transverse velocity gradient, viscosity, fiber diameter/cell gap ratio) and those of the fiber (diameter, effective length, Young's modulus). For short fibers, the effective length is that of the fiber; for long ones, it is equal to the transverse characteristiclength of the flow. For $S_p \lesssim 250$, the ratio of the curvatures increases linearly with $Sp$; For $S_p \gtrsim 250$, the fiber reaches the same curvature as the streamlines