Breakup of finite-size liquid filaments: Transition from no-breakup to breakup including substrate effects⋆

Abstract

This work studies the breakup of finite-size liquid filaments, when also including substrate effects, using direct numerical simulations. The study focuses on the effects of three parameters: Ohnesorge number, the ratio of the viscous forces to inertial and surface tension forces, the liquid filament aspect ratio, and where there is a substrate, a measure of the fluid slip on the substrate, i.e. slip length. Through these parameters, it is determined whether a liquid filament breaks up during the evolution toward its final equilibrium state. Three scenarios are identified: a collapse into a single droplet, the breakup into one or multiple droplets, and recoalescence into a single droplet after the breakup (or even possibly another breakup after recoalescence). The results are compared with the ones available in the literature for free-standing liquid filaments. The findings show that the presence of the substrate promotes breakup of the filament. The effect of the degree of slip on the breakup is also discussed. The parameter domain regions are comprehensively explored when including the slip effects. An experimental case is also carried out to illustrate the collapse and breakup of a finite-size silicon oil filament supported on a substrate, showcasing a critical length of the breakup in a physical configuration. Finally, direct numerical simulations reveal striking new details into the breakup pattern for low Ohnesorge numbers, where the dynamics are fast and the experimental imaging is not available; our results therefore significantly extend the range of Ohnesorge number over which filament breakup has been considered.

The Mathematical Model for the Secondary Breakup of Dropping Liquid

“…C. Tirell, M.-C. Renoult and C. Dumouchel [48] proposed the methodology for measuring extensional properties during a jet breakup. A. Dziedzic et al [49] studied the substrate effects on the breakup of liquid filaments. J. Zhang et al [50] investigated the process of an in-fiber breakup.…”

A numerical study of the solidification process of a retracting fluid filament

“…θ 0 is the denotation of the initial normalized temperature. Because we consider small fluid filaments, the effect of gravity force plays minor role [23,24,35,36]. Therefore, in this study, we ignore the effect of gravity, i.e., Bo = 0.…”

“…The authors found that each value of the aspect ratio, Ohnesorge number and the relative perturbation amplitude leads to merge into a single droplet or breakup into the sub-droplets. Dziedzic et al [23] monitored the transition from a non-breakup to a breakup of a fluid filament with the effect of substrates and parameters such as Ohnesorge number (Oh) and aspect ratio (Ar). Recently, the retraction of a compound fluid filament leading to break up into sub-droplets and non-breakup was studied by Ho et al [24].…”

Challenges of Numerical Simulation of Dynamic Wetting Phenomena: A Review

“…While numerical investigations can enhance our understanding of the physics involved, simulating dynamic contact line flows is complicated by the mathematical paradox of a contact line moving along a no-slip solid surface, first discussed by Huh and Scriven in [30]. Here we will review major difficulties involved in continuum-level numerical simulations in the VOF numerical framework, mainly: (i) how to specify the dynamic contact angle; and (ii) how to modify the no-slip boundary condition to remove the stress singularity [6,31].…”