Evolution and breaking of liquid film flowing on a vertical cylinder

Abstract

An amplitude equation is derived, which describes the evolution of a disturbed film interface H(τ,Z,Y) flowing down an infinite vertical cylindrical column. Using a new approach, which accounts for fast spatial changes, the nonlinear evolution of the interface is shown to be governed by H τ+βH H Z +αH Z Z +γ∇2{N[(1/ω2)H+∇2 H]}=0, where ω is the normalized cylinder radius and α, β, and γ are constants, ∇≡(∂ Z , ∂ Y ), and N=[1+ε4(∇H)2]− 3 / 2. It is shown numerically that for some linearly unstable equilibria the evolving waves break in a finite time.