On the motion of bubbles in capillary tubes

Schwartz, Leonard W.; Princen, H.M; Kiss, Andrea D.

doi:10.1017/s0022112086001738

Cited by 222 publications

(176 citation statements)

References 17 publications

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“…54,55 These theoretical results have been validated by experiments for circular capillaries 56 and by numerical simulations for both circular and rectangular microchannels. 57,58 These studies confirm that the scaling of eqn (3) holds for Ca d < 0.01.…”

Section: A Lubrication Films and Droplet Velocitymentioning

confidence: 84%

Dynamics of microfluidic droplets

2010

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This critical review discusses the current understanding of the formation, transport, and merging of drops in microfluidics. We focus on the physical ingredients which determine the flow of drops in microchannels and recall classical results of fluid dynamics which help explain the observed behaviour. We begin by introducing the main physical ingredients that differentiate droplet microfluidics from single-phase microfluidics, namely the modifications to the flow and pressure fields that are introduced by the presence of interfacial tension. Then three practical aspects are studied in detail: (i) The formation of drops and the dominant interactions depending on the geometry in which they are formed.(ii) The transport of drops, namely the evaluation of drop velocity, the pressure-velocity relationships, and the flow field induced by the presence of the drop. (iii) The fusion of two drops, including different methods of bridging the liquid film between them which enables their merging.

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Section: A Lubrication Films and Droplet Velocitymentioning

confidence: 84%

Dynamics of microfluidic droplets

2010

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“…When a plug of viscous fluid moves in the presence of a non-viscous carrier fluid, however, a thin film of carrier fluid with thickness h (m) lubricates the plug [9]. It has been shown for circular channels that h ∼ Ca 2/3 [24,25]. This relation predicts that at significantly high flow velocities, h will be large, suggesting that most of the viscous stresses in a flow will be dissipated in the lubricating film.…”

Section: Resultsmentioning

confidence: 99%

Effects of viscosity on droplet formation and mixing in microfluidic channels

Tice

Lyon

Ismagilov

2004

Analytica Chimica Acta

326

254

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This paper characterizes the conditions required to form nanoliter-sized droplets (plugs) of viscous aqueous reagents in flows of immiscible carrier fluid within microfluidic channels. For both non-viscous (viscosity of 2.0 mPa s) and viscous (viscosity of 18 mPa s) aqueous solutions, plugs formed reliably in a flow of water-immiscible carrier fluid for Capillary number less than 0.01, although plugs were able to form at higher Capillary numbers at lower ratios of the aqueous phase flow rate to the flow rate of the carrier fluid (in all the experiments performed, the Reynolds number was less than 1). The paper also shows that combining viscous and non-viscous reagents can enhance mixing in droplets moving through straight microchannels by providing a nearly ideal initial distribution of reagents within each droplet. The study should facilitate the use of this droplet-based microfluidic platform for investigation of protein crystallization, kinetics, and assays.

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“…23,46,[60][61][62][63][64][65]67. Here we outline the main assumptions in these models and their final conclusions, with the major aim to explain the origin of the different powerlaw indexes observed experimentally.…”

Section: Foam-wall Viscous Frictionmentioning

confidence: 99%

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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On the motion of bubbles in capillary tubes

Cited by 222 publications

References 17 publications

Dynamics of microfluidic droplets

Dynamics of microfluidic droplets

Effects of viscosity on droplet formation and mixing in microfluidic channels

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

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