Impact dynamics of a solid sphere falling into a viscoelastic micellar fluid

Akers, Benjamin F.; Belmonte, Andrew

doi:10.1016/j.jnnfm.2006.01.004

Cited by 85 publications

(74 citation statements)

References 47 publications

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“…As time evolves, the ambient liquid crystal fluid squeezes the viscous drop into an ellipsoid shape (Figure 7(b)). This is similar and consistent to the experiment reported in [1] and the numerical simulation in [50]. The final profile of the director field is shown in Figure 7(c).…”

Section: Numerical Simulationssupporting

confidence: 90%

Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids

Shen¹,

Yang²

2014

SIAM J. Sci. Comput.

108

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Abstract. We consider in this paper numerical approximations of phase-field models for twophase complex fluids. We first reformulate the phase-field models derived from an energetic variational formulation into a form which is suitable for numerical approximation and establish their energy laws. Then, we construct two classes, stabilized and convex-splitting, of decoupled time discretization schemes for the coupled nonlinear systems. These schemes are unconditionally energy stable and lead to decoupled elliptic equations to solve at each time step. Furthermore, these elliptic equations are linear for the stabilized version. Stability analysis and ample numerical simulations are presented.Key words. phase-field, liquid crystals, multiphase flows, Navier-Stokes, Allen-Cahn, CahnHilliard, stability AMS subject classifications. 65M12, 65M70, 65Z05 DOI. 10.1137/130921593 1. Introduction. Complex fluids have great practical utility since the microstructure can be manipulated to produce useful mechanical, optical, or thermal properties [4,23]. Numerical studies of multiphase complex fluids is a rich area for research with important applications that can be addressed. Some numerical difficulties are (i) the moving interfaces between various components; (ii) open issues regarding wellposedness of many multiphase models leading to confusion as to whether numerical pathologies are due to the model or the methods; and most important, (iii) nonlinear coupling (hydrodynamics, interface, and microstructure) makes it very difficult to design easy-to-implement, energy stable numerical schemes.For the first two issues above, the diffuse-interface/phase-field models, whose origin can be traced back to [38] and [46], have been proved efficient with much success. A particular advantage of the phase-field approach is that models can often be derived from an energy-based variational formalism (energetic variational approaches), leading to well-posed nonlinear coupled systems that satisfy thermodynamics-consistent energy dissipation laws. This makes it possible to carry out mathematical analysis and design numerical schemes which satisfy a corresponding discrete energy dissipation law. In recent years, the phase-field method has become one of the major tools to study a variety of interfacial phenomena (cf. [17,2,36,19,32,49] and recent review papers [44,22] and the references therein).For phase-field models which satisfy a dissipative energy law, it is especially desirable to design numerical schemes that preserve the energy dissipation law at the

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Section: Numerical Simulationssupporting

confidence: 90%

Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids

Shen¹,

Yang²

2014

SIAM J. Sci. Comput.

108

View full text Add to dashboard Cite

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“…Furthermore, only solid particles have been considered in theoretical studies so far, even though most of the experimental observations have come from emulsions with isotropic droplets suspended in nematics (Poulin & Weitz 1998). If the interfacial tension is not so strong as to overwhelm the surface anchoring, the interplay between the two is known to lead to unique drop and bubble shapes (Nastishin et al 2005;Akers & Belmonte 2006;Zhou et al 2007). These lacunae in our current understanding have motivated the present simulations based on the Leslie-Ericksen theory.…”

Section: Introductionmentioning

confidence: 99%

The rise of Newtonian drops in a nematic liquid crystal

2007

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We simulate the rise of Newtonian drops in a nematic liquid crystal parallel to the far-field molecular orientation. The moving interface is computed in a diffuseinterface framework, and the anisotropic rheology of the liquid crystal is represented by the Leslie-Ericksen theory, regularized to permit topological defects. Results reveal interesting coupling between the flow field and the orientational field surrounding the drop, especially the defect configuration. The flow generally sweeps the point and ring defects downstream, and may transform a ring defect into a point defect. The stability of these defects and their transformation are depicted in a phase diagram in terms of the Ericksen number and the ratio between surface anchoring and bulk elastic energies. The nematic orientation affects the flow field in return. Drops with planar anchoring on the surface rise faster than those with homeotropic anchoring, and the former features a vortex ring in the wake. These are attributed to the viscous anisotropy of the nematic. With homeotropic anchoring, the drop rising velocity experiences an overshoot, owing to the transformation of the initial surface ring defect to a satellite point defect. With both types of anchoring, the drag coefficient of the drop decreases with increasing Ericksen number as the flow-alignment of the nematic orientation reduces the effective viscosity of the liquid crystal.

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“…The behavior in the bulk is reminiscent of that of an object sinking in viscoelastic or stratified liquids for which oscillations are known to occur [15][16][17], albeit with two major experimental differences: First, for viscoelastic fluids there is an elastic rebound (oscillations in the position), whereas for our suspension the object continues to sink, with oscillations in the velocity. Second, in viscoelastic fluids the oscillation is observed to be strongly damped.…”

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confidence: 99%

Nonmonotonic settling of a sphere in a cornstarch suspension

et al. 2011

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Cornstarch suspensions exhibit remarkable behavior. Here, we present two unexpected observations for a sphere settling in such a suspension: In the bulk of the liquid the velocity of the sphere oscillates around a terminal value, without damping. Near the bottom the sphere comes to a full stop, but then accelerates again toward a second stop. This stop-go cycle is repeated several times before the object reaches the bottom. We show that common shear thickening or linear viscoelastic models cannot account for the observed phenomena, and propose a minimal jamming model to describe the behavior at the bottom. Concentrated particulate suspensions consist of a homogeneous fluid containing particles, larger than 1 μm. They can be found everywhere, and their flow is important in nature, industry, and even health care [1]. In spite of their significance, many aspects of the flow of these dense suspensions remain poorly understood. In order to study these materials, people have used methods inspired by classical rheology, and typically characterized them in terms of a constitutive relation of stress versus shear rate [2][3][4][5][6]. A general result is that, when increasing the shear rate, dense suspensions first tend to become less viscous (shear thinning) and subsequently shear thicken.Probably the most conspicuous example of a dense suspension is formed by a high concentration of cornstarch in water. Recent rheological experiments in cornstarch have revealed the existence of a mesoscopic length scale [6,7], a shear thinning regime that terminates in a sudden shear thickening [8], a dynamic jamming point [4], and fracturing [9]. Merkt et al. [10] observed in a vertically shaken, thin layer of cornstarch suspension that, among other exotic phenomena, stable oscillating holes can be formed at certain frequencies and amplitudes [10,11], which were subsequently described using a phenomenological model based on a hysteretic constitutive equation [12]. At present, however, we are still far from a detailed understanding of dense suspensions.In this Rapid Communication we subject a cornstarch suspension to a basic experiment, in which we observe and describe the settling of a spherical object in a deep bath of suspension. This yields two interesting observations. In the bulk, we find that the object velocity is oscillating in addition to going toward a terminal value. Near the bottom we observe a second phenomenon: The object comes to a full stop before the bottom, but then accelerates again, and this stop-go cycle can repeat up to seven times. We will show that both bulk and bottom behavior are conceptually different from that observed in a wide range of other fluids. We propose a jamming model for the stop-go cycles near the bottom that specifically includes the liquid-grain interactions.Experiment. Our experimental setup is shown in Fig. 1(a). It consists of a 12 × 12 × 30 cm 3 glass container containing a mixture of cornstarch and liquid. For the liquid we use either demineralized water or an aqueous solution of CsCl with...

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Impact dynamics of a solid sphere falling into a viscoelastic micellar fluid

Cited by 85 publications

References 47 publications

Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids

Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids

The rise of Newtonian drops in a nematic liquid crystal

Nonmonotonic settling of a sphere in a cornstarch suspension

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