Stability of a viscoelastic jet

Middleman, Stanley

doi:10.1016/0009-2509(65)80105-1

Cited by 124 publications

(72 citation statements)

References 4 publications

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“…The linear stability of a viscoelastic fluid thread subject to capillary-driven perturbations has been considered in detail for a range of constitutive models [56][57][58] . In each case, the initial mode of disturbance is found to be essentially unchanged from the Newtonian analog, since the polymer chains are initially unstretched and contribute little stress at short times.…”

Section: A Model For Inertio-elastic Pinchingmentioning

confidence: 99%

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 Pinchingmentioning

confidence: 99%

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

2006

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“…The dramatic effects of dilute amounts of high molecular weight additives on the breakup of aqueous fluid filaments is well known and has been extensively studied since the pioneering work of Middleman (1965) and Goldin et al (1969). The hydrodynamic consequences of small amounts of polymeric additives can be rationalized in terms of the unraveling and extension of the initially-coiled polymeric molecules by strong extensional flows (Entov & Yarin (1984); Bazilevskii et al (1990b); Anna & McKinley (2001); Clasen et al (2006b)).…”

Section: Gobbling: Introduction and Physical Picturementioning

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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“…It has been known for at least 40 years that the dynamics of capillary thinning and breakup of polymeric jets and threads are substantially different from the equivalent processes in Newtonian fluids. 1,2 The capillary necking induced by surface tension results in a strong uniaxial stretching flow in the thread, which leads to a large molecular elongation and inhibits the finite time singularity associated with breakup in a Newtonian fluid jet. 3,4 The large viscoelastic stresses ensuing from this stretching can also result in the formation of a characteristic morphology known as a beadson-a-string structure, in which spherical fluid droplets are interconnected by long thin fluid ligaments.…”

mentioning

confidence: 99%

Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of highly extensible flexible polymers

2005

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A new instrument for dynamic helical squeeze flow which superposes oscillatory shear and oscillatory squeeze flow Rev. Sci. Instrum. 83, 085105 (2012) The effects of hydrodynamic interaction and inertia in determining the high-frequency dynamic modulus of a viscoelastic fluid with two-point passive microrheology Phys. Fluids 24, 073103 (2012) MHD free convection flow of a visco-elastic (Kuvshiniski type) dusty gas through a semi infinite plate moving with velocity decreasing exponentially with time and radiative heat transfer AIP Advances 1, 022132 (2011) Transitional flow of a non-Newtonian fluid in a pipe: Experimental evidence of weak turbulence induced by shearthinning behavior Phys. Fluids 22, 101701 (2010) Effects of viscoelasticity on the probability density functions in turbulent channel flow

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Stability of a viscoelastic jet

Cited by 124 publications

References 4 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

Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of highly extensible flexible polymers

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