Surfactants role on the deformation of colliding small bubbles

Valkovska, Dimitrina S.; Danov, Krassimir D.; Ivanov, Ivan B.

doi:10.1016/s0927-7757(99)00120-x

Cited by 41 publications

(28 citation statements)

References 23 publications

(60 reference statements)

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“…The reality could be more complex-for example, the surfaces could be partially mobile and, in this case, more complex boundary conditions at the bubble surface are required. [11][12][13]63 To find a general solution for this theoretical problem is an extremely difficult task which has not been solved so far. However, theoretical models for some specific cases (diffusion or barrier control of surfactant adsorption), [82][83][84] as well as some preliminary estimates accounting for the effects of surface elasticity 85 have shown that the power-law index m could vary in wide range, including values which are significantly lower than 1/2.…”

Section: 2346mentioning

confidence: 99%

“…), because the foam behaviour is governed by relatively well understood interplay of capillary effects and viscous friction in the foam films, formed between neighbouring bubbles. 1,[6][7][8][9][10][11][12][13][14][15][16][17][18] In addition, the relatively large bubble size allows direct optical observation of the dynamics of individual bubbles in flowing foams. [18][19][20][21] All these circumstances provide unique possibility for detailed theoretical modelling and experimental studies of foams at a microstructural level, which is impossible for the other systems of interest.…”

Section: Introductionmentioning

confidence: 99%

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The role of surfactant type and bubble surface mobility in foam rheology

et al. 2009

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This paper is an overview of our recent understanding of the effects of surfactant type and bubble surface mobility on foam rheological properties. The focus is on the viscous friction between bubbles in steadily sheared foams, as well as between bubbles and confining solid wall. Large set of experimental results is reviewed to demonstrate that two qualitatively different classes of surfactants can be clearly distinguished. The first class is represented by the typical synthetic surfactants (such as sodium dodecylsulfate) which are characterised with low surface modulus and fast relaxation of the surface tension after a rapid change of surface area. In contrast, the second class of surfactants exhibits high surface modulus and relatively slow relaxation of the surface tension. Typical examples for this class are the sodium and potassium salts of fatty acids (alkylcarboxylic acids), such as lauric and myristic acids. With respect to foam rheology, the second class of surfactants leads to significantly higher viscous stress and to different scaling laws of the shear stress vs. shear rate in flowing foams. The reasons for these differences are discussed from the viewpoint of the mechanisms of viscous dissipation of energy in sheared foams and the respective theoretical models. The process of bubble breakup in sheared foams (determining the final bubble-size distribution after foam shearing) is also discussed, because the experimental results and their analysis show that this phenomenon is controlled by foam rheological properties.

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Section: 2346mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The role of surfactant type and bubble surface mobility in foam rheology

et al. 2009

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“…From this pressure balance one can derive the following expression for the initial film thickness, , where μ is dynamic viscosity of continuous phase, σ is interfacial tension, and R N is radius of curvature of the bubble surface in the contact zone, just before the foam film formation [12,15]. As in Ref.…”

Section: Figmentioning

confidence: 99%

Jamming in Sheared Foams and Emulsions, Explained by Critical Instability of the Films between Neighboring Bubbles and Drops

et al. 2009

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Phenomenon of foam and emulsion jamming at low shear rates is explained by considering the dynamics of thinning of the transient films, formed between neighboring bubbles and drops. After gradually thinning down to a critical thickness, these films undergo instability transition and thin stepwise, forming the so-called "black films", which are only several nanometers thick and, thereby, lead to strong adhesion between the dispersed particles. Theoretical analysis shows that such film thickness instability occurs only if the contact time between the bubbles/drops in sheared foam/emulsion is sufficiently long, which corresponds to sufficiently low (critical) rate of shear. Explicit expression for this critical rate is proposed and compared to experimental data. 83.80.Iz, 83.60.Wc, 47.57.Bc, 82.70.Rr, 82.70.Kj. PACS:Non-homogeneous flow, often discussed in terms of "shear banding" or "jammingunjamming transitions", attracted researchers' attention in several areas, because it appears as a generic phenomenon in various systems, such as glassy and granular materials, concentrated suspensions, foams, emulsions, and micellar solutions [1][2][3][4][5][6][7][8][9][10]. This phenomenon is still poorly understood and appropriate theoretical modeling, beyond the phenomenological description, is missing. Foams and emulsions seem particularly suitable for studying and modeling such nonhomogenous flow and related phenomena, because the behavior of these systems is governed by a relatively well understood interplay of capillary effects and viscous friction in the films, formed between neighboring bubbles and drops [11][12][13][14][15]. This understanding provides the unique possibility for detailed theoretical modeling and experimental studies of these systems at the microstructural level (viz. at the level of single drops, bubbles, and films), which is impossible for the other systems of interest.Recently, several systematic studies were performed [1-10] to clarify the main factors controlling jamming/unjamming transitions in foams and emulsions. Some of the conclusions, relevant to the current study are: (i) Jamming is observed at a certain "critical" shear rate. When this critical rate is reached from above, the bubbles/drops in the dispersion "stick" to each other, thus creating jammed zones. (ii) Critical shear rate depends on several factors, such as the drop and bubble size, volume fraction, and most importantly, on the interaction between dispersed particles. The effect of interparticle forces was convincingly demonstrated with moderately concentrated emulsions (drop volume fraction Φ = 0.73), for which jamming transition was observed in the systems with attractive interdroplet forces only [10]. Until now these observations lack clear explanations and quantitative description.The main purpose of the current letter is to demonstrate that jamming transitions in flowing foams and emulsions could be explained by considering the dynamics of thinning of the films formed 1

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“…Manor, Lavrenteva & Nir (2008) extended LeVan's results to account for variable surface viscosities. Valkovska, Danov & Ivanov (1999) studied how the deformation of bubbles, a related physical model, is affected by surface viscosity and Marangoni stress during collisions. More recently, the effect of surface viscosity on the dynamics of a spherical droplet in Poiseuille flow has been studied.…”

Section: Introductionmentioning

confidence: 99%

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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Surfactants role on the deformation of colliding small bubbles

Cited by 41 publications

References 23 publications

The role of surfactant type and bubble surface mobility in foam rheology

The role of surfactant type and bubble surface mobility in foam rheology

Jamming in Sheared Foams and Emulsions, Explained by Critical Instability of the Films between Neighboring Bubbles and Drops

Influence of surface viscosity on droplets in shear flow

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