Homotopy method for viscous Cosserat rod model describing electrospinning

The dynamics of viscous jets in electrospinning processes varies from drop forming, whipping to coiling depending on the parameter regime. To investigate the practically relevant whipping regime more closely we use an asymptotic Cosserat rod model that is given by a stiff boundary value problem of ordinary differential equations. For the efficient simulation of the six-parametric problem we present a numerical approach that is based on a continuation-collocation method. On top of an implicit Runge-Kutta discretization of fourth order, suitable initial guesses and global convergence of the applied Newton method are achieved by a recursive continuation strategy. The numerical results are very convincing, they show the jet characteristics observed in the experiments.