Martinez-Calvo, A. , RIVERO RODRIGUEZ, JAVIER, Scheid, B. , Sevilla, A.
No
J. Fluid Mech.
Article
Científica
1
1
3.627
1.72
25/01/2020
000508121500035
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 epsilon, and whose wavelength is the most unstable one deduced from linear stability theory. We demonstrate that, in the limit epsilon -> 0, the problem depends on two dimensionless parameters, namely the Laplace number, La = rho sigma(0)(R) over bar/mu(2), and the elasticity parameter, beta = E/sigma(0), where rho, mu and sigma(0) are the liquid density, viscosity and initial surface tension, respectively, E is the Gibbs elasticity and (R) over bar is the unperturbed thread radius. A parametric study is presented to quantify the influence of La and beta on two key quantities: the satellite droplet volume and the mass of surfactant trapped at the satellite's surface just prior to pinch-off, V-sat and Sigma(sat), respectively. We identify a weak-elasticity regime, beta less than or similar to 0.05, in which the satellite volume and the associated mass of surfactant obey the scaling law Vsat D Sigma(sat) = 0.0042La(1.64) for La less than or similar to 2. For La greater than or similar to 10, V-sat and Sigma(sat) sat reach a plateau of about 3% and 2:9 %, respectively, V-sat 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 V-sat and Sigma(sat) at a critical elasticity, beta(c)(La), with beta(c) -> 0.98 for La less than or similar to 0.2, such that V-sat and Sigma(sat) abruptly increase at beta = beta(c) for increasing beta. The jumps experienced by both quantities reach a plateau when La less than or similar to 0.2, while they decrease monotonically as La increases up to La = 7.5, where both become zero.
capillary flows; breakup/coalescence