Influence of the surface viscous stress on the pinch-off of free surfaces loaded with nearly-inviscid surfactants

A Ponce-Torres,M A Herrada,J Eggers,J M Montanero,M Rubio

doi:10.1038/s41598-020-73007-1

A Ponce-Torres, M A Herrada + Show 3 more

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https://doi.org/10.1038/s41598-020-73007-1

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Abstract

We analyze the breakup of a pendant water droplet loaded with SDS. The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the Navier–Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear and dilatational viscosities. We study numerically the distribution of Marangoni and viscous stresses over the free surface as a function of the time to the pinching, and describe how surface viscous stresses grow in the pinching region as the free surface approaches its breakup. When Marangoni and surface viscous stresses are taken into account, the surfactant is not swept away from the thread neck in the time interval analyzed. Surface viscous stresses eventually balance the driving capillary pressure in in the pinching region for small enough values of the time to pinching. Based on this result, we propose a scaling law to account for the effect of the surface viscosities on the last stage of temporal evolution of the neck radius.

Highlights

We analyze the breakup of a pendant water droplet loaded with Sodium Dodecyl Sulfate (SDS)
Zell et al.[6] reported that the surface shear viscosity of Sodium Dodecyl Sulfate (SDS) was below the sensitivity limit of their experimental technique (∼ 10−8 Pa s m). This raises doubts about the role played by surface shear rheology in the stability of foams and emulsions treated with soluble surfactants
One can reasonably expect surface viscosity to considerably affect the dynamics of interfaces for sufficiently small spatiotemporal scales even for nearly-inviscid s urfactants[7]

Summary

Introduction

We analyze the breakup of a pendant water droplet loaded with SDS. The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the Navier–Stokes equations for different values of the shear and dilatational surface viscosities. Zell et al.[6] reported that the surface shear viscosity of Sodium Dodecyl Sulfate (SDS) was below the sensitivity limit of their experimental technique (∼ 10−8 Pa s m) This raises doubts about the role played by surface shear rheology in the stability of foams and emulsions treated with soluble surfactants. In the pinching of a Newtonian liquid free surface, the system spontaneously approaches a finite-time singularity, which offers a unique opportunity to observe the behavior of fluids with arbitrarily small length and time scales This property and its universal character (insensitivity to both initial and boundary conditions) turn this problem into an ideal candidate to question our knowledge of fundamental aspects of fluid dynamics. The thinning of the liquid thread passes through an inertio-capillary regime characterized by the power law

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