Drop formation in a one-dimensional approximation of the Navier–Stokes equation

TLDR

The study examines viscous flow in a thin axisymmetric fluid column with a free surface. The paper investigates the detailed nature of singularities that arise during fluid neck pinch‑off. The authors derive a one‑dimensional Navier–Stokes–based equation for velocity and radius and validate it against experiments on liquid‑jet breakup and drop‑orifice bifurcation. The derived equations predict singularities occurring during fluid neck pinch‑off.

Abstract

We consider the viscous motion of a thin axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier–Strokes equation. We compare our results with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.