Motion of a nonrectilinear fiber in a viscous fluid flow

The plane problem of dynamic interaction of a laminar viscous fluid flow and an inextensible pliable fiber of finite length is solved using the perturbation method. Two types of rheological two-dimensional flows – pure shear and simple shear – are considered. Formulas are obtained for the evolution of the tensile force and the shape of the fiber. Results of asymptotic and numerical calculations are compared.