The deformation of a drop in a general time-dependent fluid flow

Cox, R. G.

doi:10.1017/s0022112069000759

Cited by 500 publications

(315 citation statements)

References 6 publications

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“…was also shown that the existence of a waist in the initial shape always led to breakup. Nearly spherical drops of arbitrary viscosity ratio were studied via domain perturbation techniques by Cox (1969} andRallison (1980}, and shown to attain steady shapes in an oscillatory manner in flows with vorticity. Finally, Rallison & Acrivos (1978) and Rallison (1981) have used the boundary-integral method to investigate some aspects of the time evolution of the drop shape and observed that the critical shear rate and mode of drop burst depended on the history of the flow.…”

Section: Introductionmentioning

confidence: 99%

An experimental study of transient effects in the breakup of viscous drops

1986

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A computer-controlled four-roll mill is used to examine two transient modes of deformation of a liquid drop: elongation in a steady flow and interfacial-tensiondriven motion which occurs after the flow is stopped abruptly. For modest extensions, drop breakup does not occur with the flow on, but may occur following cessation of the flow as a result of deterministic motions associated with internal pressure gradients established by capillary forces. These relaxation and breakup phenomena depend on the initial drop shape and the relative viscosities of the two fluids. Capillary-wave instabilities at the fluid-fluid interface are observed only for highly elongated drops. This study is a natural extension of G. I. Taylor's original studies of the deformation and burst of droplets in well-defined flow fields.

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Section: Introductionmentioning

confidence: 99%

An experimental study of transient effects in the breakup of viscous drops

1986

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“…The droplet does not deform easily for K > 4. Cox 21) predicted the steady-state shape of the droplet and derived the following expression for the predicted ellipsoid. The time change in droplet shape under shear flow was observed for the PDMS82/PIB95 system at 23°C.…”

Section: Steady Shear Flow Methodsmentioning

confidence: 99%

Measurement of Interfacial Tension between Polymer Liquids : Pendant Drop, Improved Imbedded Fiber Retraction and Steady Shear Flow Methods

Hayashi

Takahashi

Yamane

2000

J. Soc. Rheol., Jpn

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The interfacial tension between a poly (isobutylene) (PIB) and a poly (dimethylsiloxane) (PDMS) was obtained by an improved imbedded fiber retraction method from the observation of the PDMS (or PIB) droplet shape in the PIB (or PDMS) matrix after application of the step shear strain. The interfacial tension was also obtained from the observation of the PDMS (or PIB) droplet shape during the steady shear flow. We compared the values of interfacial tension obtained by these methods with the value determined by the pendant drop method. It was found that these values agree fairly well when the viscosity ratio of the droplet to the matrix is around unity.

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“…The forces and deformation of dispersed droplets in flow fields have been studied for a long time, especially for the Newtonian droplets in Newtonian continuous phase, various models have been developed to predict the complex break-up behavior of droplets as well as coalescence [29][30][31][32][33]. The better understanding of dispersion mechanism has an important role in petroleum production and operation.…”

Section: Mechanistic Modelmentioning

confidence: 99%

The Role of Shearing Energy and Interfacial Gibbs Free Energy in the Emulsification Mechanism of Waxy Crude Oil

Wang

Lin

Rui³

et al. 2017

Energies

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Abstract:Crude oil is generally produced with water, and the water cut produced by oil wells is increasingly common over their lifetime, so it is inevitable to create emulsions during oil production. However, the formation of emulsions presents a costly problem in surface process particularly, both in terms of transportation energy consumption and separation efficiency. To deal with the production and operational problems which are related to crude oil emulsions, especially to ensure the separation and transportation of crude oil-water systems, it is necessary to better understand the emulsification mechanism of crude oil under different conditions from the aspects of bulk and interfacial properties. The concept of shearing energy was introduced in this study to reveal the driving force for emulsification. The relationship between shearing stress in the flow field and interfacial tension (IFT) was established, and the correlation between shearing energy and interfacial Gibbs free energy was developed. The potential of the developed correlation model was validated using the experimental and field data on emulsification behavior. It was also shown how droplet deformation could be predicted from a random deformation degree and orientation angle. The results indicated that shearing energy as the energy produced by shearing stress working in the flow field is the driving force activating the emulsification behavior. The deformation degree and orientation angle of dispersed phase droplet are associated with the interfacial properties, rheological properties and the experienced turbulence degree. The correlation between shearing stress and IFT can be quantified if droplet deformation degree vs. droplet orientation angle data is available. When the water cut is close to the inversion point of waxy crude oil emulsion, the interfacial Gibbs free energy change decreased and the shearing energy increased. This feature is also presented in the special regions where the suddenly changed flow field can be formed. Hence, the shearing energy is an effective form that can show the contribution of kinetic energy for the oil-water mixtures to interfacial Gibbs free energy in emulsification process, and the emulsification mechanism of waxy crude oil-water emulsions was further explained from the theoretical level.

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The deformation of a drop in a general time-dependent fluid flow

Cited by 500 publications

References 6 publications

An experimental study of transient effects in the breakup of viscous drops

An experimental study of transient effects in the breakup of viscous drops

Measurement of Interfacial Tension between Polymer Liquids : Pendant Drop, Improved Imbedded Fiber Retraction and Steady Shear Flow Methods

The Role of Shearing Energy and Interfacial Gibbs Free Energy in the Emulsification Mechanism of Waxy Crude Oil

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