The matching of a “one-dimensional” numerical simulation and experiment results for low viscosity Newtonian and non-Newtonian fluids during fast filament stretching and subsequent break-up

Tembely, Moussa; Vadillo, Damien; Mackley, M. R.; Soucémarianadin, Arthur

doi:10.1122/1.3669647

Cited by 31 publications

(35 citation statements)

References 45 publications

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“…Throughout we focus on the case of a highly viscoelastic filament of sufficiently large initial cross sectional area that surface tension can be safely ignored in comparison with the bulk viscoelastic stresses, at least in considering the initial stages of neck formation. In this way, we ignore any filament breakup and beading instabilities driven by surface tension [61][62][63][64][65].…”

Section: Introductionmentioning

confidence: 99%

Necking after extensional filament stretching of complex fluids and soft solids

Hoyle

Fielding

2017

Journal of Non-Newtonian Fluid Mechanics

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We perform linear stability analysis and nonlinear slender filament simulations of extensional necking in complex fluids and soft solids, during the stress relaxation process following an interrupted strain ramp. We start by deriving analytical criteria for necking within a highly simplified and generalised scalar constitutive model. Within this, we find two different possible modes of necking: one associated with an upward curvature in the stress relaxation function on a log-linear plot, and another related to a carefully defined 'elastic' derivative of the tensile force with respect to an imagined sudden strain increment. We showed these two criteria to agree fully with simulations of the Oldroyd B and Giesekus models of polymeric solutions, and with the Rolie-Poly model of more concentrated polymeric solutions and melts, without polymer chain stretch. With chain stretch included, we find a slightly more complicated analytical criterion for necking during the stress relaxation, although with key ingredients that closely mirror counterpart ingredients of the simpler criteria obtained within the scalar model. We show this criterion to agree fully with slender filament simulations of the Rolie-Poly model with chain stretch, and with the scenario discussed by the Copenhagen group in Refs. [1,2]. In particular, we see delayed necking after strain ramps with an accumulated strain exceeding¯ ≈ 0.7, for ramp rates exceeding the inverse chain stretch relaxation timescale. We discuss finally an analogy between this delayed necking following an interrupted extensional strain ramp and delayed shear banding following an interrupted shear strain ramp [3]. This work provides the counterpart, for interrupted extensional strain ramps, to earlier papers giving criteria for necking in the protocols of constant imposed Hencky strain rate [4] and of constant imposed tensile stress or constant imposed tensile force [5].

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Section: Introductionmentioning

confidence: 99%

Necking after extensional filament stretching of complex fluids and soft solids

Hoyle

Fielding

2017

Journal of Non-Newtonian Fluid Mechanics

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“…Accordingly, we set the surface tension to zero in our calculations. We therefore do not address capillary breakup as studied in CaBeR rheometers [13,[37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Criteria for extensional necking instability in complex fluids and soft solids. Part II: Imposed tensile stress and force protocols

Hoyle¹,

Fielding²

2016

Journal of Rheology

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We study the necking of a filament of complex fluid or soft solid subject to uniaxial tensile stretching, separately under conditions of constant imposed tensile stress and constant imposed tensile force, by means of linear stability analysis and nonlinear simulations at the level of a slender filament approximation. We demonstrate necking to be a flow instability that arises as an unavoidable consequence of the viscoelastic constitutive behaviour of essentially any material (with a possible rare exception). We derive criteria for the onset of necking that can be reported in terms of characteristic signatures in the shapes of the experimentally measured material functions, and that should therefore apply universally to all viscoelastic materials. To confirm their generality, we show them to hold numerically in six constitutive models: the Oldroyd B, Giesekus, non-stretch Rolie-Poly, finite-stretch Rolie-Poly and Pom-pom models, and a simplified toy model of coil-stretch hysteresis, which has a non-monotonic underlying extensional constitutive curve. Under conditions of constant imposed tensile stress, we find two distinct dynamical regimes as a function of the time since the inception of the flow. In the first regime the strain rate quickly attains a value prescribed by the fluid's underlying stationary homogeneous extensional constitutive curve, at the given imposed stress. During this first regime, no appreciable (or only minimal) necking arises. A second regime then ensues in which the initially homogeneous flow destabilises to form a neck. This necking instability can occur via two distinct possible modes. The first mode is relatively gentle and arises in any regime where the slope of the extensional constitutive curve is positive. It has a rate of necking per accumulated strain unit set by the inverse of the slope of the constitutive curve on a log-log plot. The second mode sets in when a carefully defined 'elastic derivative' of the tensile force first slopes down as a function of the time since the inception of the flow. We discuss the way in which these modes of instability manifest themselves in entangled polymeric fluids, demonstrating four distinct regimes of necking behaviour as a function of imposed stress. Under conditions of constant imposed tensile force, typically the flow sweeps up the underlying constitutive curve of the fluid in question, again with instability to necking in any regime where that curve is positively sloping. arXiv:1606.07705v2 [cond-mat.soft]

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“…Study [16] demonstrated that a onedimensional long-wave model, as used in several of the above cited studies, exhibits good agreement with 2D axisymmetric computations. Therefore such computations have become a common approach when studying liquid jets and bridges [17].…”

Section: Introductionmentioning

confidence: 99%

Pinch-off of a stretching viscous filament and drop transport

2015

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This study is focused on the stretching and breakup of a Newtonian liquid bridge between two parallel plates, one of which moves with a constant acceleration. The experimental device is designed to achieve high acceleration (up to 200 m s −2 ) with high precision. The shape evolution of the liquid bridge and its pinch-off are captured using a high-speed video system. At high enough acceleration the evolution of the midpoint diameter of the bridge is universal; it depends neither on the acceleration nor on the liquid viscosity. Moreover, at high acceleration rates even the breakup time does not depend on the acceleration, but is determined solely by the liquid viscosity. A model is proposed which predicts the instant of the liquid bridge pinch-off. Finally, the volumes of the residual liquid on both fixed and moving plates (which do not include the total volume of the residual secondary drops) is measured. It is shown that the volume on the fixed plate remains almost constant, the volume on the accelerating plate reduces as the acceleration increases.

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The matching of a “one-dimensional” numerical simulation and experiment results for low viscosity Newtonian and non-Newtonian fluids during fast filament stretching and subsequent break-up

Cited by 31 publications

References 45 publications

Necking after extensional filament stretching of complex fluids and soft solids

Necking after extensional filament stretching of complex fluids and soft solids

Criteria for extensional necking instability in complex fluids and soft solids. Part II: Imposed tensile stress and force protocols

Pinch-off of a stretching viscous filament and drop transport

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