On the deformation and drag of a type-A multiple drop at low Reynolds number

Brunn, P. O.; Roden, T.

doi:10.1017/s0022112085003457

Cited by 20 publications

(18 citation statements)

References 9 publications

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“…(20)- (24). First, in the limit of a very thin shell (λ → 1) or a very viscous shell (μ 23 → ∞), the velocity field vanishes.…”

Section: B Fluid Flow Equations and Their Solutionsmentioning

confidence: 99%

“…Inertia correction to the solution of Ref. [23] was made by Brunn and Roden [24], who found that the drop will deform in creeping flow, in contrast to the solution for simple drops that asserts the drop remains spherical, regardless of the capillary number [25]. The authors showed that the fluid flow tends to elongate the inner drop in the direction of the gravity, while it elongates the outer drop in the perpendicular direction.…”

Section: Introductionmentioning

confidence: 99%

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Electrohydrodynamics of a compound drop

Behjatian

Esmaeeli

2013

Phys. Rev. E

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The behavior of a compound drop, comprising two concentric fluid spheres, in a uniform electric field is studied analytically. The governing electrohydrodynamic equations are solved for Newtonian and immiscible fluids in the framework of leaky-dielectric theory and in the limit of small electric field strength and fluid inertia. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the globule, in terms of the direction of the external flow (pole-to-equator vs equator-to-pole) and the number of vortices (single-vortex vs double vortices) in the shell, and that the senses of the net electric shear stresses at the surfaces of the inner and the outer drops and their relative importance are the key parameters in setting these patterns. A circulation map is constructed, which is used to infer about the likelihood of the flow patterns and transition from one pattern to another for representative fluid systems. For small distortion from the spherical shape, the deformations of the inner and the outer drops are found using normal stress balances at the corresponding surfaces. It is shown that there will be four possible modes for the deformation of the compound drop, which are determined by the net normal electric and hydrodynamic stresses at the pertinent surfaces. The dynamic responses of the inner and the outer drops for representative fluid systems are studied using a deformation map, which characterizes the possibilities of the deformation modes and transition from one mode to another as a function of the fluid properties.

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“…(20)- (24). First, in the limit of a very thin shell (λ → 1) or a very viscous shell (μ 23 → ∞), the velocity field vanishes.…”

Section: B Fluid Flow Equations and Their Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electrohydrodynamics of a compound drop

Behjatian

Esmaeeli

2013

Phys. Rev. E

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“…Returning to Brunn and Roden (1985), these authors also obtained a linearized result (small Re) for shell deformation-again under the same, rather stringent assumption that the core remains at the center of the shell. They then, in a sense, generalized the Taylor-Acrivos results for a simple droplet to a (concentric) compound droplet.…”

Section: Compound Drop In Free-fallmentioning

confidence: 94%

“…On the assumption that the core is concentric and thus motionless (no translation) relative to the shell, Brunn and Roden (1985) obtained the potentially important result that both core and shell are still perfect spheres (for droplets at their terminal velocity and Re = 0)-a result that, like the simple drop, even holds true for yC and yS + 0.…”

Section: Dropmentioning

confidence: 99%

Some Aspects of the Hydrodynamics of the Microencapsulation Route to NIF Mandrels

Gresho

1999

Fusion Technology

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Spherical plastic shells for use as mandrels for the fabrication of ICF (Inertial Confinement Fusion) target capsules can be produced by solution-based microencapsulation techniques. The specifications for these mandrels in terms of sphericity are extremely rigorous, and it is clear that various aspects of the solution hydrodynamics associated with their production are important in controlling the quality of the final product. This paper explores what we know (and need to know) about the hydrodynamics of the microencapsulation process in order to lay the foundation for process improvements as well as identify inherent limits.

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“…Fluid mechanics of such multiple emulsion drops or bubbles has been discussed extensively by Johnson and Sadhal 7 and Sadhal et al 8 Although a number of works deserve to be referred to as a basis of the present study, we restrict our attention here to the related problem of a concentric double emulsion droplet. Rushton and Davies 9 studied the translation of a concentric spherical double emulsion drop in an infinite fluid and Brunn and Roden 10 extended their work to consider the inertia correction to the translating drop. The most interesting result of these analyses is that the drop deforms at zero Reynolds numbers, unlike a single translating drop, which remains spherical at zero Reynolds number independently of the magnitude of capillary number.…”

Section: Introductionmentioning

confidence: 99%

Fluid dynamics of a double emulsion droplet in an electric field

Yang

1999

Physics of Fluids

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One of general free boundary problems concerning the electrohydrodynamic effects on a concentric double emulsion drop is studied theoretically for the three constituent phases of leaky dielectric fluids. In order to proceed the problem analytically, the domain perturbation procedure is utilized in the small deformation limit. The patterns of electric-field-driven flow are successfully characterized by examining the distribution of induced surface charges at the inner and outer drop interfaces. The second recirculating flow is generated in the annular phase when the inner and outer interfaces are charged with the same sense. The deformation type of inner and outer interfaces can be roughly interpreted by the flow patterns, although the exact description on the deformation requires consideration of the combined contributions from both electric and flow fields. In addition, the presence of double emulsion droplets alters the stress field of the continuous phase. The electric-field-induced ''particle stress'' not only changes the effective viscosity of dispersion of the double emulsion droplets but yields the normal stress difference, which is typical of a viscoelastic fluid. Finally, the heat transfer rate enhanced by the electric-field-driven flow is also considered.

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On the deformation and drag of a type-A multiple drop at low Reynolds number

Cited by 20 publications

References 9 publications

Electrohydrodynamics of a compound drop

Electrohydrodynamics of a compound drop

Some Aspects of the Hydrodynamics of the Microencapsulation Route to NIF Mandrels

Fluid dynamics of a double emulsion droplet in an electric field

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