An Improved Self-Consistent One-Dimensional Slender Jet Model

TL;DR

This paper presents a new self-consistent one-dimensional slender jet model that accurately incorporates viscosity and surface tension, leading to different instability predictions especially at low Reynolds numbers.

Contribution

We derive a fully self-consistent momentum equation for the slender jet model, improving the accuracy of viscosity and surface tension representation.

Findings

Different Plateau-Rayleigh instability dynamics predicted

Significant differences at small Reynolds numbers

Enhanced modeling accuracy for viscous effects

Abstract

In 1994, Eggers and Dupont suggested the slender jet model, a one-dimensional model that describes the motion of a thin axisymmetric column of viscous, incompressible fluid with a free surface. In their model, the momentum equation was derived in a manner that was not completely self-consistent. Consequently, the viscosity term was described with less accuracy than the surface tension term. In this paper, we derive a novel slender jet momentum equation in completely self-consistent manner that allows us to describe both the viscosity and the surface tension forces with the same accuracy as the surface tension term in the Eggers-Dupont model. Our derivation does not affect the volume conservation equation, which remains identical to the one in the Eggers-Dupont model. We show that our model predicts different Plateau-Rayleigh instability dynamics as compared to the Eggers-Dupont's model. The differences between the models are particularly large at small Reynolds numbers, where the viscosity plays a prominent role in development the Plateau-Rayleigh instability.