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Showing papers by "Yuriko Renardy published in 2008"


Journal ArticleDOI
TL;DR: In this paper, the motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry.
Abstract: The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry. Initially, the drop is spherical and placed at a distance away from the magnet. The governing equations are the Maxwell equations for a non-conducting flow, momentum equation and incompressibility. A numerical algorithm is derived to model the interface between a magnetized fluid and a non-magnetic fluid via a volume-of-fluid framework. A continuum-surface-force formulation is used to model the interfacial tension force as a body force, and the placement of the liquids is tracked by a volume fraction function. Three cases are studied. First, where inertia is dominant, the magnetic Laplace number is varied while the Laplace number is fixed. Secondly, where inertial effects are negligible, the Laplace number is varied while the magnetic Laplace number is fixed. In the third case, the magnetic Bond number and inertial effects are both small, and the magnetic force is of the order of the viscous drag force. The time taken by the droplet to travel through the medium and the deformations in the drop are investigated and compared with a previous experimental study and accompanying simpler model. The transit times are found to compare more favourably than with the simpler model.

76 citations


Journal ArticleDOI
Yuriko Renardy1
TL;DR: In this article, a volume-of-fluid algorithm with a paraboloid reconstruction of the interface for the calculation of the surface tension force for three-dimensional direct numerical simulations for a Newtonian drop in an Oldroyd-B liquid near criticalities was implemented.
Abstract: Recent two-dimensional numerical simulations and experiments have shown that, when a drop undergoes shear in a viscoelastic matrix liquid, the deformation can undergo an overshoot. I implement a volume-of-fluid algorithm with a paraboloid reconstruction of the interface for the calculation of the surface tension force for three-dimensional direct numerical simulations for a Newtonian drop in an Oldroyd-B liquid near criticalities. Weissenberg numbers up to 1 at viscosity ratio 1 and retardation parameter 0.5 are examined. Critical capillary numbers rise with the Weissenberg number. Just below criticality, drop deformation begins to undergo an overshoot when the Weissenberg number is sufficiently high. The overshoot becomes more pronounced, and at higher matrix Weissenberg numbers, such as 0.8, drop deformation undergoes novel oscillations before settling to a stationary shape. Breakup simulations are also described.

15 citations


Journal ArticleDOI
Yuriko Renardy1
TL;DR: In this paper, a spherical drop is suspended in another liquid and sheared between parallel walls, and an oscillator model is developed for the manner in which momentum is transferred to the drop and how it is distributed into surface deformation and dissipation as a function of the Reynolds number and capillary number.

15 citations


Proceedings ArticleDOI
14 Jul 2008
TL;DR: In this paper, the motion and shape of a ferrofluid droplet placed in a non-magnetic viscous fluid and driven by a magnetic field are modeled numerically.
Abstract: The motion and shape of a ferrofluid droplet placed in a non‐magnetic viscous fluid and driven by a magnetic field are modeled numerically. The governing equations are the Maxwell equations, momentum equation and incompressibility. The numerical simulation uses a volume‐of‐fluid algorithm with a continuum‐surface‐force formulation for an axisymmetric geometry. The deformations in the drop under non‐uniform magnetic fields are simulated. Droplets exhibit shape changes along the applied magnetic field. We have found that the ferrofluid droplet forms a prolate ellipsoid in the presence of a non‐uniform magnetic field. For higher magnetic field strengths, the droplet undergoes dramatic deformation. This in turn influences the motion of the droplet through the viscous medium.

6 citations


Proceedings ArticleDOI
14 Jul 2008
TL;DR: In this paper, the steady deformation and orientation of droplets in shear flow, both under bulk and confined conditions, were investigated for blends with one viscoelastic phase and a viscosity ratio of 1.5.
Abstract: The steady deformation and orientation of droplets in shear flow, both under bulk and confined conditions, is microscopically studied for blends with one viscoelastic phase and a viscosity ratio of 1.5. The experiments are performed with a Linkam shearing cell and a counter rotating setup, based on a Paar Physica MCR300. For bulk shear flow, it is shown that matrix viscoelasticity suppresses droplet deformation and promotes droplet orientation towards the flow direction. Interestingly, these effects saturate at Deborah numbers above 2. For ellipsoidal droplets, viscoelasticity of the droplet fluid hardly affects the droplet deformation and droplet orientation, even up to Deborah numbers as high as 16. When the droplet is confined between two plates, the droplet deformation and the orientation towards the flow direction increase with confinement ratio, as in fully Newtonian systems. At a Deborah number of 1, the effect of component viscoelasticity under confined conditions remains qualitatively the same as under bulk conditions, at least up to a confinement ratio 2R/H of 0.6. The experiments under bulk conditions are compared with the predictions of phenomenological models, such as the Maffettone‐Minale model, for droplet deformation. The Shapira‐Haber model, which analytically describes the effects of the walls on the droplet deformation for fully Newtonian systems, is used to describe the experimental results under confinement. Here, this model is combined with the bulk phenomenological models to include bulk viscoelasticity effects. Under the present conditions, the adapted Shapira‐Haber model describes the steady droplet deformation under confinement rather well. Finally, the experimentally obtained droplet shapes are compared with the results of 3D simulations, performed with a volume‐of‐fluid algorithm.

3 citations


Proceedings ArticleDOI
14 Jul 2008
TL;DR: In this paper, the shape relaxation after cessation of shear flow and droplet breakup during shear were studied microscopically under both bulk and confined conditions, and the long tail in the droplet relaxation was qualitatively described with a phenomenological model for droplet deformation, when using a 5-mode Giesekus model for the fluid rheology.
Abstract: The transient droplet deformation and droplet orientation after inception of shear, the shape relaxation after cessation of shear and droplet breakup during shear, are microscopically studied, both under bulk and confined conditions. The studied blends contain one viscoelastic Boger fluid phase. A counter rotating setup, based on a Paar Physica MCR300, is used for the droplet visualisation. For bulk shear flow, it is shown that the droplet deformation during startup of shear flow and the shape relaxation after cessation of shear flow are hardly influenced by droplet viscoelasticity, even at moderate to high capillary and Deborah numbers. The effects of droplet viscoelasticity only become visible close to the critical conditions and a novel break‐up mechanism is observed. Matrix viscoelasticity has a more pronounced effect, causing overshoots in the deformation and significantly inhibiting relaxation. However, different applied capillary numbers prior to cessation of shear flow, with the Deborah number fixed, still result in a single master curve for shape retraction, as in fully Newtonian systems. The long tail in the droplet relaxation can be qualitatively described with a phenomenological model for droplet deformation, when using a 5‐mode Giesekus model for the fluid rheology. It is found that the shear flow history significantly affects the droplet shape evolution and the breakup process in blends with one viscoelastic component. Confining a droplet between two plates accelerates the droplet deformation kinetics, similar to fully Newtonian systems. However, the increased droplet deformation, due to wall effects, causes the steady state to be reached at a later instant in time. Droplet relaxation is less sensitive to confinement, leading to slower relaxation kinetics only for highly confined droplets. For the blend with a viscoelastic droplet, a non‐monotonous trend is found for the critical capillary number as a function of the confinement ratio. Finally, experimental data are compared with 3D simulations, performed with a volume‐of‐fluid algorithm.

3 citations


Proceedings ArticleDOI
14 Jul 2008
TL;DR: Verhulst et al. as discussed by the authors compared numerical simulations and experimental data for the investigation of the influence of viscoelasticity on drop deformation in shear, and showed that by stepping up in the capillary number gradually, a stationary states is achieved at higher capillary numbers than without the graduated steps.
Abstract: Numerical simulations and experimental data are compared for the investigation of the influence of viscoelasticity on drop deformation in shear. A viscoelastic drop suspended in a Newtonian liquid, or a Newtonian drop suspended in a viscoelastic liquid, is sheared and investigated for transients, relaxation after cessation of shear flow, and step‐up in shear rate. The numerical simulations are conducted at parameters chosen to model the experiments. We use the volume of fluid (VOF) continuum surface force (CSF) algorithm for situations dominated by shear. For drop relaxation experiments, we use the paraboloid representation of the interface in the surface tension force (PROST) algorithm. The Oldroyd‐B and Giesekus constitutive models are implemented. An interesting result is that by stepping up in the capillary number gradually, a stationary states is achieved at higher capillary numbers than without the graduated steps. The experimental work is described in Verhulst, Moldenaers and Cardinaels [l]. We present a summary of the numerical approach here. The reader is referred to [2] for details.

1 citations


Proceedings ArticleDOI
14 Jul 2008
TL;DR: In this article, a volume-of-fluid (VOF) method was used to simulate numerically the deformation and break-up of a single droplet undergoing steady or oscillatory shear.
Abstract: An investigation into the deformation and break‐up of droplets experiencing complex, time dependent strain rates such as those found in engineering flows has been carried out. A volume‐of‐fluid (VOF) method, previously used to simulate numerically the deformation and break‐up of a single droplet undergoing steady or oscillatory shear has been extended in order to study the effect of complex, time dependent shear rates on a droplet. A two‐stage approach has been used firstly to generate strain rate histories that droplets experience and secondly to simulate the effect of this strain rate history on a droplet. Simulations of sample droplets travelling along different trajectories through the same flow constriction have shown different break‐up mechanisms taking place.