Droplet Detachment and Satellite Bead Formation in Viscoelastic Fluids

Wagner, Christian; Amarouchène, Yacine; Bonn, Daniel; Eggers, Jens

doi:10.1103/physrevlett.95.164504

Cited by 140 publications

(138 citation statements)

References 17 publications

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“…The front factor obtained from full numerical simulations is approximately 0.7 (cf. Figure 3 in Chen et al 21 ), and this value is also found to agree well with an experimental value of 0.8 obtained from our present experiments, as well as other recent experiments with aqueous polymer solutions 35,48 . When elastic stresses are absent, equation (7) is therefore expected to have a solution of the functional form (in dimensional variables)…”

Section: A Model For Inertio-elastic Pinchingsupporting

confidence: 93%

“…Such a description cannot be expected to provide quantitative agreement with experiments or full numerical simulations because it neglects axial variations in the structure of the thread. In particular, for inviscid irrotational flows it has been shown that the simplified one-dimensional Euler equations exhibit a singularity before the point of breakup is reached 48 . Numerical simulations 49,50 show that in fact the free-surface of the droplet close to the singularity overturns.…”

Section: A Model For Inertio-elastic Pinchingmentioning

confidence: 99%

“…Wagner et al 48 have also recently presented experiments and numerical simulations for pinching viscoelastic threads using a full 1 dimensional model that establishes the conditions under which a bead does, or does not, form by comparing the growth rate of the most unstable Rayleigh mode on the cylinder with the necking rate of the filament.…”

Section: (3 )mentioning

confidence: 99%

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Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

2006

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The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical “pinch time” tp, an inertial-capillary balance leads to the expected 2∕3-power scaling of the minimum radius with time: Rmin∼(tp−t)2∕3. However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>tp. In this region, the filament radius decreases exponentially with time Rmin∼exp[(tp−t)∕λ1], where λ1 is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions.

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Section: A Model For Inertio-elastic Pinchingsupporting

confidence: 93%

Section: A Model For Inertio-elastic Pinchingmentioning

confidence: 99%

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Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

2006

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“…In the linear regime (at short times) polymer effects are negligible. Of course this situation changes dramatically in the nonlinear regime (Amarouchene et al (2001); Wagner et al (2005)). The volume V µ of a single bead represents the lower limit for the terminal gobbling drop when reaching the transition to pure jetting and is also compared in figure 13 to the critical gobbling conditions.…”

Section: )mentioning

confidence: 99%

‘Gobbling drops’: the jetting–dripping transition in flows of polymer solutions

et al. 2009

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This paper discusses the breakup of capillary jets of dilute polymer solutions and the dynamics associated with the transition from dripping to jetting. High speed digital video imaging reveals a new scenario of transition and breakup via periodic growth and detachment of large terminal drops. The underlying mechanism is discussed and a basic theory for the mechanism of breakup is also presented. The dynamics of the terminal drop growth and trajectory prove to be governed primarily by mass and momentum balances involving capillary, gravity and inertial forces, whilst the drop detachment event is controlled by the kinetics of the thinning process in the viscoelastic ligaments that connect the drops. This thinning process of the ligaments that are subjected to a constant axial force is driven by surface tension and resisted by the viscoelasticity of the dissolved polymeric molecules. Analysis of this transition provides a new experimental method to probe the rheological properties of solutions when minute concentrations of macromolecules have been added.

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“…[45] These thin filaments are then largely absorbed into the main drops, minimising the formation of satellite droplets and increasing the average droplet size (Figure 3). [46,47] Agricultural spraying is however often carried out at a higher issuing velocity than the Rayleigh regime where the aerodynamic forces dominate (the atomization regime, Figure 4). Here there is complete jet disruption at the nozzle exit, producing droplets with a diameter significantly less than the jet.…”

Section: Agricultural Spraying Overviewmentioning

confidence: 99%

Polymeric Drift Control Adjuvants for Agricultural Spraying

Lewis

Evans

Malic

et al. 2016

Macro Chemistry & Physics

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---------The movement of a pesticide or herbicide to an off-target site during agricultural spraying can cause injury to wildlife, plants and contamination of surface water. This phenomenon is known as spray drift and can be controlled by spraying during favorable environmental conditions, and by using low drift nozzles and drift control adjuvants (DCAs). Polymeric DCAs are the most common type of DCA and function by increasing the droplet size produced during spraying. There are, however, two main drawbacks of polymeric DCAs; they are prone to mechanical degradation during spraying which reduces their performance and they can produce oversized drops which reduces the efficacy of the spray. In this review, existing DCA technology is reviewed including the mechanism through which they function.This then provides a platform for the discussion of novel polymeric architectures which have currently not been applied in DCA formulations.-2 -

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Droplet Detachment and Satellite Bead Formation in Viscoelastic Fluids

Cited by 140 publications

References 17 publications

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

‘Gobbling drops’: the jetting–dripping transition in flows of polymer solutions

Polymeric Drift Control Adjuvants for Agricultural Spraying

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