Title: Whipping of electrified visco-capillary jets in airflows,
Abstract: An electrified visco-capillary jet shows different dynamic behavior, such as
cone forming, breakage into droplets, whipping and coiling, depending on the
considered parameter regime. The whipping instability that is of fundamental
importance for electrospinning has been approached by means of stability
analysis in previous papers. In this work we alternatively propose a model
framework in which the instability can be computed straightforwardly as the
stable stationary solution of an asymptotic Cosserat rod description. For this
purpose, we adopt a procedure by Ribe (Proc. Roy. Soc. Lond. A, 2004)
describing the jet dynamics with respect to a frame rotating with the a priori
unknown whipping frequency that itself becomes part of the solution. The rod
model allows for stretching, bending and torsion, taking into account inertia,
viscosity, surface tension, electric field and air drag. For the resulting
parametric boundary value problem of ordinary differential equations we present
a continuation-collocation method. On top of an implicit Runge-Kutta scheme of
fifth order, our developed continuation procedure makes the efficient and
robust simulation and navigation through a high-dimensional parameter space
possible. Despite the simplicity of the employed electric force model the
numerical results are convincing, the whipping effect is qualitatively well
characterized.