Equation of change for ellipsoidal drops in viscous flow

Maffettone, Pier Luca; Minale, Mario

doi:10.1016/s0377-0257(98)00065-2

Cited by 315 publications

(289 citation statements)

References 22 publications

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“…In unbounded flow and for systems with Newtonian components, the three droplet axes L, B and W and the droplet orientation with respect to the flow direction are well described by the Maffettone-Minale model (Maffettone and Minale 1998). In this model, the droplet shape is represented by a symmetric, positive-definite, second rank tensor S, with eigenvalues representing the squared dimensionless semiaxes of the ellipsoid.…”

Section: This Viscoelastic Materials Was Combined With Mixtures Of Polmentioning

confidence: 99%

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Droplet relaxation in blends with one viscoelastic component: bulk and confined conditions

Cardinaels

Moldenaers

2010

Rheol Acta

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Using a counter rotating parallel plate shear flow cell, the shape relaxation of deformed droplets in a quiescent matrix is studied microscopically. Both the effects of geometrical confinement and component viscoelasticity are systematically explored at viscosity ratios of 0.45 and 1.5. The flow conditions are varied from a rather low to a nearly critical Ca-number. Under all conditions investigated, viscoelasticity of the droplet phase has no influence on shape relaxation, whereas matrix viscoelasticity and geometrical confinement result in a slower droplet retraction. Up to high confinement ratios, the relaxation curves for ellipsoidal droplets can be superposed onto a master curve. Confined droplets with a sigmoidal shape relax in two stages; the first consists of a shape change to an ellipsoid with a limited amount of retraction, the second is the retraction of this ellipsoid. The latter can be

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Section: This Viscoelastic Materials Was Combined With Mixtures Of Polmentioning

confidence: 99%

“…and f 1 is a parameter in the bulk Maffettone-Minale (Maffettone and Minale 1998) and Minale models (Minale 2004). It can be deduced from Eq.…”

mentioning

confidence: 99%

Droplet relaxation in blends with one viscoelastic component: bulk and confined conditions

Cardinaels

Moldenaers

2010

Rheol Acta

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“…By assuming an ellipsoidal drop shape and Newtonian rheology in both components, Maffettone and Minale [31] developed a phenomenological relationship between the shape relaxation of the drop and the interfacial tension,…”

Section: Drop Retraction and Apparent Interfacial Tensionmentioning

confidence: 99%

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Yue

Feng

et al. 2005

Journal of Colloid and Interface Science

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Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.  2005 Elsevier Inc. All rights reserved.

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“…The drop evolves monotonously toward the stationary state. Behavior at sufficiently low deformation is also captured by several phenomenological models; for example, the Maffettone-Minale model [7].…”

Section: Introductionmentioning

confidence: 99%

Influence of viscoelasticity on drop deformation and orientation in shear flow. Part 2: Dynamics

Verhulst

Cardinaels

Moldenaers

et al. 2009

Journal of Non-Newtonian Fluid Mechanics

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An experimental study of drop dynamics under shear is conducted for five fluid pairs: a reference Newtonian system, two systems with a viscoelastic drop in a Newtonian matrix, one with a Newtonian drop in a viscoelastic matrix, all at drop to matrix viscosity ratio λ = 1.5, and a separate case at λ = 0.75. The viscoelastic liquids are either a Boger fluid or a shear-thinning viscoelastic fluid satisfying an Ellis model. Deborah numbers in the range 1 to 2 and a range of capillary numbers from low to above breakup conditions are addressed. The results focus on three aspects: relaxation after cessation of shear, a new viscoelastic drop breakup scenario, and the effect of shear flow history on drop breakup. Numerical simulations with the 3D volume-of-fluid PROST method complement the experimental results.

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Equation of change for ellipsoidal drops in viscous flow

Cited by 315 publications

References 22 publications

Droplet relaxation in blends with one viscoelastic component: bulk and confined conditions

Droplet relaxation in blends with one viscoelastic component: bulk and confined conditions

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Influence of viscoelasticity on drop deformation and orientation in shear flow. Part 2: Dynamics

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