Extensional flow ?a mathematical perspective

Petrie, C. J. S.

doi:10.1007/bf00396051

Cited by 29 publications

(17 citation statements)

References 60 publications

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“…Here we omit most of the detail and catalogue them in a similar way to James & Walters [15] and this author's earlier paper [6]:…”

Section: Experimental Methods and Resultsmentioning

confidence: 99%

“…Different values of the applied force and different positions along the spinline give results throughout the shaded region shown in Fig. 4 [6]. The initial extra- stress values are not varied so this demonstration does not even include the possible effects of different deformation histories prior to the spinline.…”

Section: "Transient Extensional Viscosity"mentioning

confidence: 99%

“…The normal stress difference σ 11 − σ 22 is used in order to avoid any dependence on hydrostatic pressure. This matter is discussed further elsewhere [5,6]. For simplicity, our discussion of other extensional flows and of the various extensional viscosities that are defined in Eqns.…”

Section: Uniaxial Extensionmentioning

confidence: 99%

“…For simplicity, our discussion of other extensional flows and of the various extensional viscosities that are defined in Eqns. (6), (8), (9), (12) and (13) below (Section 3), refers to incompressible fluids in the absence of surface tension.…”

Section: Uniaxial Extensionmentioning

confidence: 99%

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Extensional viscosity: A critical discussion

Petrie

2006

Journal of Non-Newtonian Fluid Mechanics

141

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The issue of whether extensional viscosity is a concept that causes more confusion than enlightenment is addressed. This author's view is that misuse of the concept certainly has caused much confusion and, although it is in principle a simple and straightforward idea, it continues to be misused. What is straightforward is the formal definition of extensional viscosity, for steady uniform extensional flow. What gives rise to confusion is the careless use of measurements in flows which are not both steady and spatially uniform.

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“…Here we omit most of the detail and catalogue them in a similar way to James & Walters [15] and this author's earlier paper [6]:…”

Section: Experimental Methods and Resultsmentioning

confidence: 99%

Section: "Transient Extensional Viscosity"mentioning

confidence: 99%

Section: Uniaxial Extensionmentioning

confidence: 99%

Section: Uniaxial Extensionmentioning

confidence: 99%

See 2 more Smart Citations

Extensional viscosity: A critical discussion

Petrie

2006

Journal of Non-Newtonian Fluid Mechanics

141

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“…This resistance is characterized by the extensional viscosity, and the value of g E for viscoelastic solutions can be several orders of magnitude higher than the corresponding shear viscosities. [10][11][12][13] In many biological and industrial applications such as flow of biological fluids through contractions and valves, the flow of liquid foodstuffs through orifices, 14 or atomization of paints in an air-spray nozzle, the kinematics of the flow is dominated by elongational deformation, leading to dramatic effects of the extensional rheological properties on the flow.…”

Section: Introductionmentioning

confidence: 99%

Micro-scale extensional rheometry using hyperbolic converging/diverging channels and jet breakup

Keshavarz

McKinley

2016

Biomicrofluidics

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Understanding the elongational rheology of dilute polymer solutions plays an important role in many biological and industrial applications ranging from microfluidic lab-on-a-chip diagnostics to phenomena such as fuel atomization and combustion. Making quantitative measurements of the extensional viscosity for dilute viscoelastic fluids is a long-standing challenge and it motivates developments in microfluidic fabrication techniques and high speed/strobe imaging of millifluidic capillary phenomena in order to develop new classes of instruments. In this paper, we study the elongational rheology of a family of dilute polymeric solutions in two devices: first, steady pressure-driven flow through a hyperbolic microfluidic contraction/expansion and, second, the capillary driven breakup of a thin filament formed from a small diameter jet (D j $ Oð100 lmÞ). The small length scale of the device allows very large deformation rates to be achieved. Our results show that in certain limits of low viscosity and elasticity, jet breakup studies offer significant advantages over the hyperbolic channel measurements despite the more complex implementation. Using our results, together with scaling estimates of the competing viscous, elastic, inertial and capillary timescales that control the dynamics, we construct a dimensionless map or nomogram summarizing the operating space for each instrument. Published by AIP Publishing. [http://dx

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Determination of steady-state elongational viscosity for rubber compounds using bell-mouthed dies

Clarke

Petera

1997

J. Appl. Polym. Sci.

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A bell-mouthed die geometry was designed to cause convergent flow at a constant, uniform, elongational strain rate. An equation was derived, which showed that steady-state elongational viscosity could be calculated from a plot of pressure drop due to elongation against a simple function of die length. To obtain values of pressure drop due to elongation, it was necessary to correct the total pressure drop measured across the bell-mouthed dies for the contribution from shear occurring near the die wall. For this purpose, a simplified shape for the bell-mouthed dies was assumed, comprising several parallel sided segments. Applying a formula to pressure drop data measured across straight dies corresponding to these segments gave an estimate of the pressure drop due to shear across the bell-mouthed dies. Pressure drops due to elongation were determined by subtracting the pressure drop due to shear from the total pressure drop measured across the bell-mouthed dies. Measurements were also carried out with lubrication to validate the shear correction method. The results indicate that for the compound used in this study, a combination of bell-mouthed and straightsided dies can be used in a conventional capillary rheometer to determine steady-state elongational viscosity. An elongational viscosity of 190 kPa s at 90ЊC and at a strain rate of 10 s 01 was determined for a simple styrene -butadiene rubber compound.

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Extensional flow ?a mathematical perspective

Cited by 29 publications

References 60 publications

Extensional viscosity: A critical discussion

Extensional viscosity: A critical discussion

Micro-scale extensional rheometry using hyperbolic converging/diverging channels and jet breakup

Determination of steady-state elongational viscosity for rubber compounds using bell-mouthed dies

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