Deformation and burst of a liquid droplet freely suspended in a linear shear field

Barthès-Biesel, Dominique; Acrivos, Andreas

doi:10.1017/s0022112073000534

Cited by 262 publications

(149 citation statements)

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“…This equation has been recovered by several authors (Barthès-Biesel & Acrivos 1973;Rallison 1980;Vlahovska et al 2005Vlahovska et al , 2009a who calculate the power expansion in a small parameter, mainly the capillary number Ca, of all the physical quantities: shape deformation, curvature, pressure, velocities and stress tensor. It means in particular that the viscous stress must be small, λCa 1 contrary to the model of Cox (1969).…”

Section: Clean Droplet In Shear Flowmentioning

confidence: 99%

“…Such computational work has been shown to be consistent with experimental results (Rumscheidt & Mason 1961;Kwak & Pozrikidis 1998). Many authors have also determined well known analytical results based on the main assumption of small deformation theory: (Taylor 1934;Chaffey & Brenner 1967;Cox 1969;Barthès-Biesel & Acrivos 1973;Rallison 1980;Vlahovska, Blawzdziewicz & Loewenberg 2005, 2009a. These approaches have their own domain of validity (Acrivos 1983;Rallison 1984).…”

Section: Clean Droplet In Shear Flowmentioning

confidence: 99%

“…Cox (1969) used small deformation analysis to describe the time evolution of droplets in linear flows and accounted for the viscosity contrast between droplet and the external flow. The small deformation theory of Barthès-Biesel & Acrivos (1973) explored the conditions for droplet breakup in shear flow. These conditions are quantified by the critical capillary number Ca c , beyond which a droplet does not have a stable steady state.…”

Section: Introductionmentioning

confidence: 99%

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Influence of surface viscosity on droplets in shear flow

et al. 2016

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The behaviour of a single droplet in an immiscible external fluid, submitted to shear flow is investigated using numerical simulations. The surface of the droplet is modelled by a Boussinesq-Scriven constitutive law involving the interfacial viscosities and a constant surface tension. A numerical method using Loop subdivision surfaces to represent droplet interface is introduced. This method couples boundary element method for fluid flows and finite element method to take into account the stresses due to the surface dilational and shear viscosities and surface tension. Validation of the numerical scheme with respect to previous analytic and computational work is provided, with particular attention to the viscosity contrast and the shear and dilational viscosities characterized both by a Boussinesq number B q . Then, influence of equal surface viscosities on steady-state characteristics of a droplet in shear flow are studied, considering both small and large deformations and for a large range of bulk viscosity contrast. We find that small deformation analysis is surprisingly predictive at moderate and high surface viscosities. Equal surface viscosities decrease the Taylor deformation parameter and tank-treading angle and also strongly modify the dynamics of the droplet: when the Boussinesq number (surface viscosity) is large relative to the capillary number (surface tension), the droplet displays damped oscillations prior to steady-state tank-treading, reminiscent from the behaviour at large viscosity contrast. In the limit of infinite capillary number Ca, such oscillations are permanent. The influence of surface viscosities on breakup is also investigated, and results show that the critical capillary number is increased. A diagram (B q ; Ca) of breakup is established with the same inner and outer bulk viscosities. Additionally, the separate roles of shear and dilational surface viscosity are also elucidated, extending results from small deformation analysis. Indeed, shear (dilational) surface viscosity increases (decreases) the stability of drops to breakup under shear flow. The steady-state deformation (Taylor parameter) varies nonlinearly with each Boussinesq number or a linear combination of both Boussinesq numbers. Finally, the study shows that for certain combinations of shear and dilational viscosities, drop deformation for a given capillary number is the same as in the case of a clean surface while the inclination angle varies.

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Section: Clean Droplet In Shear Flowmentioning

confidence: 99%

Section: Clean Droplet In Shear Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Influence of surface viscosity on droplets in shear flow

et al. 2016

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“…On the theoretical side, the onset of bursting has been investigated by Barthès-Biesel and Acrivos [31] using a perturbation method up to the second power (Ca d ) 2 , followed by a linear stability analysis to determine the onset of bursting. This analysis is in good agreement with experiments [30,32].…”

Section: Dynamics Of Newtonian Droplets In a Shear Flowmentioning

confidence: 99%

Rheology and dynamics of vesicle suspension in comparison with droplet emulsion

Danker¹,

Verdier²,

Misbah³

2008

Journal of Non-Newtonian Fluid Mechanics

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This paper deals with the study of dynamics and rheology of a dilute suspension of vesicles. The study is analytical and is based on the small deformation theory. Vesicles in the small deformation limit exhibit, under shear flow, rich dynamics in comparison to droplets (in the regime where the droplet maintains its integrity). For example, droplets only assume a fixed orientation with respect to the flow, while vesicles undergo three types of motions: (i) tank-treading (tt, where the vesicle assumes a fixed orientation with respect to the flow, while the membrane makes a tanktreading motion, (ii) tumbling (tb), which occurs as a saddle-node bifurcation from the tank-treading motion for a certain critical viscosity ratio, (iii) vacillating-breathing (vb), where the vesicle long axis undergoes oscillations around the shear direction whereas its shape executes a breathing-like motion. This mode is found to coexist with tumbling in the high shear rate limit (or high capillary number C a ≡γτ , whereγ is the shear rate and τ is the relaxation time towards equilibrium shape of the vesicle). After analyzing these modes and comparing dynamics to droplets, we study rheology. It is found that the constitutive law, written in the co-moving frame, is nonlinear even to leading order. This markedly contrasts with droplet emulsion where the equation is linear to leading order. We make a link between rheology and the above three dynamical states. It is found that the effective viscosity undergoes a cusp singularity at the tumbling bifurcation (which happens at small enough C a ), while the normal stress differences collapse in the tumbling and VB regimes.At high enough C a the tb transition is preceded by the vb mode. We also report on shear thinning and the behavior of the normal stress difference as a function ofγ.

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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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Deformation and burst of a liquid droplet freely suspended in a linear shear field

Cited by 262 publications

References 11 publications

Influence of surface viscosity on droplets in shear flow

Influence of surface viscosity on droplets in shear flow

Rheology and dynamics of vesicle suspension in comparison with droplet emulsion

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

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