Natural break-up and satellite formation regimes of surfactant-laden liquid threads Articles uri icon

publication date

  • February 2020

start page

  • A35-1

end page

  • A35-30


  • 883

International Standard Serial Number (ISSN)

  • 0022-1120

Electronic International Standard Serial Number (EISSN)

  • 1469-7645


  • We report a numerical analysis of the unforced break-up of free cylindrical threads of viscous Newtonian liquid whose interface is coated with insoluble surfactants, focusing on the formation of satellite droplets. The initial conditions are harmonic disturbances of the cylindrical shape with a small amplitude , and whose wavelength is the most unstable one deduced from linear stability theory. We demonstrate that, in the limit e → 0, the problem depends on two dimensionless parameters, namely the Laplace number, La = ρσ0R¯ /µ2, and the elasticity parameter, β = E/σ0, where ρ, µ and σ0 are the liquid density, viscosity and initial surface tension, respectively, E is the Gibbs elasticity and R¯ is the unperturbed thread radius. A parametric study is presented to quantify the influence of La and β on two key quantities: the satellite droplet volume and the mass of surfactant trapped at the satellite"s surface just prior to pinch-off, Vsat and Σsat, respectively. We identify a weak-elasticity regime, β . 0.05, in which the satellite volume and the associated mass of surfactant obey the scaling law Vsat = Σsat = 0.0042La1.64 for La . 2. For La &# 10, Vsat and &amp;;931#sat reach a plateau of about 3 % and 2.9 %, respectively, Vsat being in close agreement with previous experiments of low-viscosity threads with clean interfaces. For La < 7.5, we reveal the existence of a discontinuous transition in Vsat and Σsat at a critical elasticity, βc(La), with βc →0.98 for La . 0.2, such that Vsat and Σsat abruptly increase at β = βc for increasing β. The jumps experienced by both quantities reach a plateau when La . 0.2, while they decrease monotonically as La increases up to La = 7.5, where both become zero.


  • Industrial Engineering


  • capillary flows; breakup/coalescence