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 twodimensional 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.