Similarity solutions for breakup of jets of power law fluids

Renardy, Michael; Renardy, Yuriko

doi:10.1016/j.jnnfm.2004.01.026

Cited by 35 publications

(40 citation statements)

References 13 publications

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“…For Newtonian fluids, is either 2 3 or 1, depending on which forces are balanced. If the elongational viscosity is rate dependent, the expectation is that equals the power-law exponent of the thinning: ¼ n [5,7,8,12]. However, in our filament thinning experiments (cf.…”

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confidence: 77%

“…However, since many fluids encountered in practice do not have a simple flow behavior, recently the case of non-Newtonian fluids has attracted much attention [2][3][4][5][6][7][8][9][9][10][11][12][13][14]. The main feature that has been considered so far is the case of solutions of flexible polymers, which are stretched in the elongational flow near the pinch point, leading to a spectacular rise of the elongational viscosity.…”

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confidence: 99%

“…How does the thinning in shear flow affect the breakup dynamics, keeping in mind that the shear rate encountered during breakup is small in comparison to the rate of elongation [19]? In recent years, it has become standard practice in the literature on drop breakup to postulate the same rheological response for the extensional flow near breakup [5,6,12] as for the thinning behavior in shear flow. Other studies have included both a yield stress and shear thinning, based on the same idea [7,8].…”

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confidence: 99%

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Drop Formation in Non-Newtonian Fluids

Aytouna¹,

Paredes²,

Shahidzadeh-Bonn³

et al. 2013

Phys. Rev. Lett.

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We study the pinch off dynamics of droplets of yield stress and shear thinning fluids. To separate the two non Newtonian effects, we use a yield stress material for which the yield stress can be tuned without changing the shear thinning behavior, and a shear thinning system (without a yield stress) for which the shear thinning can be controlled over a large range, without introducing too much elasticity into the system. We find that the pinch off remains very similar to that of constant viscosity Newtonian liquids, and consequently thinning in shear flow does not imply a thinning in elongational flow.

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confidence: 77%

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confidence: 99%

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confidence: 99%

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Drop Formation in Non-Newtonian Fluids

Aytouna¹,

Paredes²,

Shahidzadeh-Bonn³

et al. 2013

Phys. Rev. Lett.

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“…Such a description has not been presented to date. It is also worth noting that there now exists substantial evidence for both viscous Newtonian fluids 26 The general form of the force balance for slender viscoelastic threads has been discussed and derived elsewhere 52 . An axial force balance coupled with a radial force balance to eliminate the unknown pressure in the thread results in an equation of the general form…”

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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“…The work of Eggers [2] has been extended to non-Newtonian fluid, such as power law fluids by Renardy &Renardy [6], and to various viscoelastic fluids, i.e. the fluids that exhibit elastic behaviour such as the memory effect as well as the fluid properties, such as a generalized PTT model by Renardy [7], generalized Newtonian fluid, K-BKZ model, and Dumbbell model by Renardy [8], and a Giesikus model by Renardy & Losh [9].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the String Structure Near Break-up of A Slender Jet of An Upper Convected Maxwell Liquid

Gunawan¹,

Budhi²

2009

itbj.sci.

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Abstract. In this paper, we analytically study the string structure near the breakup of a slender jet of a viscoelastic liquid surrounded by air. The governing equations are derived from the conservation laws of mass and momentum, and the rheological equation of the jet. The rheological equation of the jet is assumed to satisfy an Upper Convected Maxwell (UCM) model. Introducing a stretch variable and then applying a transformation, we obtain a coupled system of nonlinear differential equations. Via these equations, we then show that the UCM jet does not break up in finite time, which physically means that it has sufficient time to exhibit the string structure before it breaks up due to the dominant surface force.

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Similarity solutions for breakup of jets of power law fluids

Cited by 35 publications

References 13 publications

Drop Formation in Non-Newtonian Fluids

Drop Formation in Non-Newtonian Fluids

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

Analysis of the String Structure Near Break-up of A Slender Jet of An Upper Convected Maxwell Liquid

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