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Feb 2013

Volume 25, Issue 2, Articles (02xxxx)

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Phys. Fluids 25, 025102 (2013); http://dx.doi.org/10.1063/1.4790640 (31 pages)

T. A. Casey, J. Sakakibara, and S. T. Thoroddsen
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back to top Interfacial Flows

Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis

Anjalaiah, R. Usha, and S. Millet

Phys. Fluids 25, 022101 (2013); http://dx.doi.org/10.1063/1.4789459 (26 pages)

Online Publication Date: 1 February 2013

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The stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis. The classical long-wave asymptotic expansion for small wave numbers reveals the occurrence of two modes, the Yih mode and the Marangoni mode for a clean/a contaminated film over a porous substrate and this is confirmed by the numerical solution of the Orr-Sommerfeld system using the spectral-Tau collocation method. The results show that the Marangoni mode is always stable and dominates the Yih mode for small Reynolds numbers; as the Reynolds number increases, the growth rate of the Yih mode increases, until, an exchange of stability occurs, and after that the Yih mode dominates. The role of the surfactant is to increase the critical Reynolds number, indicating its stabilizing effect. The growth rate increases with an increase in permeability, in the region where the Yih mode dominates the Marangoni mode. Also, the growth rate is more for a film (both clean and contaminated) over a thicker porous layer than over a thinner one. From the neutral stability maps, it is observed that the critical Reynolds number decreases with an increase in permeability in the case of a thicker porous layer, both for a clean and a contaminated film over it. Further, the range of unstable wave number increases with an increase in the thickness of the porous layer. The film flow system is more unstable for a film over a thicker porous layer than over a thinner one. However, for small wave numbers, it is possible to find the range of values of the parameters characterizing the porous medium for which the film flow can be stabilized for both a clean film/a contaminated film as compared to such a film over an impermeable substrate; further, it is possible to enhance the instability of such a film flow system outside of this stability window, for appropriate choices of the porous substrate characteristics.
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47.20.Dr Surface-tension-driven instability
47.35.-i Hydrodynamic waves
47.56.+r Flows through porous media
68.03.Cd Surface tension and related phenomena
68.15.+e Liquid thin films

Shape of a large drop on a rough hydrophobic surface

Joonsik Park, Jaebum Park, Hyuneui Lim, and Ho-Young Kim

Phys. Fluids 25, 022102 (2013); http://dx.doi.org/10.1063/1.4789494 (13 pages)

Online Publication Date: 1 February 2013

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Large drops on solid surfaces tend to flatten due to gravitational effect. Their shapes can be predicted by solving the Young-Laplace equation when their apparent contact angles are precisely given. However, for large drops sitting on rough surfaces, the apparent contact angles are often unavailable a priori and hard to define. Here we develop a model to predict the shape of a given volume of large drop placed on a rough hydrophobic surface using an overlapping geometry of double spheroids and the free energy minimization principle. The drop shape depends on the wetting state, thus our model can be used not only to predict the shape of a drop but also to infer the wetting state of a large drop through the comparison of theory and experiment. The experimental measurements of the shape of large water drops on various micropillar arrays agree well with the model predictions. Our theoretical model is particularly useful in predicting and controlling shapes of large drops on surfaces artificially patterned in microscopic scales, which are frequently used in microfluidics and lab-on-a-chip technology.
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47.55.dr Interactions with surfaces
47.85.L- Flow control
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
47.54.Bd Theoretical aspects

Longitudinal instability of a liquid rim

Gilou Agbaglah, Christophe Josserand, and Stéphane Zaleski

Phys. Fluids 25, 022103 (2013); http://dx.doi.org/10.1063/1.4789971 (15 pages)

Online Publication Date: 4 February 2013

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We study the transverse instability of a retracting liquid rim using a long wavelength approximation model and full numerical simulations. We observe that the instability of the rim is driven both by the Rayleigh-Taylor mechanism because of the initial rim acceleration, and by the Rayleigh-Plateau one. The coupling between the rim and the sheet stabilizes the rim at long wavelength. Full numerical simulations are in good agreement with the model and the subsequent break-up of droplets is observed in the numerical simulations when the instability is strong enough.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.df Breakup and coalescence
02.60.Cb Numerical simulation; solution of equations
02.60.Gf Algorithms for functional approximation
47.11.-j Computational methods in fluid dynamics

The effect of viscoelasticity on the dynamics of gas bubbles near free surfaces

S. J. Lind and T. N. Phillips

Phys. Fluids 25, 022104 (2013); http://dx.doi.org/10.1063/1.4790512 (32 pages)

Online Publication Date: 15 February 2013

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The dynamics of bubbles immersed in a viscoelastic fluid directly beneath an initially plane free surface is modelled using the boundary integral method. The model predicts a range of dynamics that is dependent on the Deborah number, the Reynolds number and the proximity of the bubble to the free surface. The motion of the free surface jet caused by the collapse of a bubble in a viscoelastic fluid can be significantly retarded compared with the Newtonian case. The axial jet predicted in many instances in the Newtonian case is not observed when the inertial forces are sufficiently small. In this case an annular jet forms that can penetrate the bubble. At high Deborah numbers, there is a return to Newtonian-like dynamics since the effects of viscosity are abated by elasticity to such an extent that inertia is the prevailing influence on bubble dynamics.
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47.50.Cd Modeling
47.55.dd Bubble dynamics
51.20.+d Viscosity, diffusion, and thermal conductivity
02.60.Nm Integral and integrodifferential equations

Film drainage of viscous liquid on top of bare bubble: Influence of the Bond number

Helena Kočárková, Florence Rouyer, and Franck Pigeonneau

Phys. Fluids 25, 022105 (2013); http://dx.doi.org/10.1063/1.4792310 (14 pages)

Online Publication Date: 25 February 2013

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We present experimental results of film drainage on top of gas bubbles pushed by gravity towards the free surface of highly viscous Newtonian liquid with a uniform interface tension. The temporal evolution of the thickness of the film between a single bubble and the air/liquid interface is investigated via interference method. Experiments under various physical conditions (range of viscosities and surface tension of the liquid, and bubble sizes) evidence the influence of the deformation of the thin film on the thinning rate and confirm the slow down of film drainage with Bond number as previously reported by numerical work of Pigeonneau and Sellier [Phys. Fluids 23, 092102 (2011)]10.1063/1.3629815. Considering the liquid flow in the cap squeezed by buoyancy force of the bubble, we provide an approximation of thinning rate as a function of Bond number that agrees with experimental and numerical data. Qualitatively, the smaller the area of the thin film compare to the surface of the bubble, the faster the drainage.
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47.55.dd Bubble dynamics
68.03.Cd Surface tension and related phenomena
68.15.+e Liquid thin films
66.20.-d Viscosity of liquids; diffusive momentum transport
47.55.Ca Gas/liquid flows
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