A nonlinear theory for describing the propagation of disturbances on a capillary jet

Abstract

The problem of the growth of disturbances on a capillary jet has received much attention in the past. However, previous theories have produced only limited correlation with experimental evidence. Traditional perturbation approaches to the problem are not well suited to describing the highly nonlinear behavior of disturbances on a capillary jet, especially near the tip of the jet where it breaks up into isolated drops. On the other hand, numerical solutions necessitate the use of an extremely fine spatial resolution over a large extent to follow disturbances as they progress along the jet and grow in amplitude over several orders of magnitude. In this paper, a new approach to this well-studied problem is described. The new approach is based on a weighted residual technique and takes advantage of the particular strengths of both analytical and numerical methods. The method is shown to correctly predict many of the nonlinear phenomena observed on actual jets and offers some fresh insight into the dynamical processes taking place within the jet.