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Aug 2012

Volume 24, Issue 8, Articles (08xxxx)

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Phys. Fluids 24, 085102 (2012); http://dx.doi.org/10.1063/1.4737892 (21 pages)

Ankit Bhagatwala and Sanjiva K. Lele
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Announcement: Free access to Letters published in Physics of Fluids

Mark M. Cassar

Phys. Fluids 24, 080201 (2012); http://dx.doi.org/10.1063/1.4746090 (1 page)

Online Publication Date: 16 August 2012

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01.10.Cr Announcements, news, and awards
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Pulsatility role in cylinder flow dynamics at low Reynolds number

Adnan Qamar, Ravi Samtaney, and Joseph L. Bull

Phys. Fluids 24, 081701 (2012); http://dx.doi.org/10.1063/1.4740504 (7 pages)

Online Publication Date: 16 August 2012

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We present dynamics of pulsatile flow past a stationary cylinder characterized by three non-dimensional parameters: the Reynolds number (Re), non-dimensional amplitude (A) of the pulsatile flow velocity, and Keulegan-Carpenter number (KC = Uo/Dωc). This work is motivated by the development of total artificial lungs (TAL) device, which is envisioned to provide ambulatory support to patients. Results are presented for 0.2 ≤ A ≤ 0.6 and 0.57 ≤ KC ≤ 2 at Re = 5 and 10, which correspond to the operating range of TAL. Two distinct fluid regimes are identified. In both regimes, the size of the separated zone is much greater than the uniform flow case, the onset of separation is function of KC, and the separation vortex collapses rapidly during the last fraction of the pulsatile cycle. The vortex size is independent of KC, but with an exponential dependency on A. In regime I, the separation point remains attached to the cylinder surface. In regime II, the separation point migrates upstream of the cylinder. Two distinct vortex collapse mechanisms are observed. For A < 0.4 and all KC and Re values, collapse occurs on the cylinder surface, whereas for A > 0.4 the separation vortex detaches from the cylinder surface and collapses at a certain distance downstream of the cylinder. The average drag coefficient is found to be independent of A and KC, and depends only on Re. However, for A > 0.4, for a fraction of the pulsatile cycle, the instantaneous drag coefficient is negative indicating a thrust production.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.32.Ff Separated flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
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Ideal stochastic forcing for the motion of particles in large-eddy simulation extracted from direct numerical simulation of turbulent channel flow

B. J. Geurts and J. G. M. Kuerten

Phys. Fluids 24, 081702 (2012); http://dx.doi.org/10.1063/1.4745857 (7 pages) | Cited 1 time

Online Publication Date: 16 August 2012

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The motion of small particles in turbulent conditions is influenced by the entire range of length- and time-scales of the flow. At high Reynolds numbers this range of scales is too broad for direct numerical simulation (DNS). Such flows can only be approached using large-eddy simulation (LES), which requires the introduction of a sub-filter model for the momentum dynamics. Likewise, for the particle motion the effect of sub-filter scales needs to be reconstructed approximately, as there is no explicit access to turbulent sub-filter scales. To recover the dynamic consequences of the unresolved scales, partial reconstruction through approximate deconvolution of the LES-filter is combined with explicit stochastic forcing in the equations of motion of the particles. We analyze DNS of high-Reynolds turbulent channel flow to a priori extract the ideal forcing that should be added to retain correct statistical properties of the dispersed particle phase in LES. The probability density function of the velocity differences that need to be included in the particle equations and their temporal correlation display a striking and simple structure with little dependence on Reynolds number and particle inertia, provided the differences are normalized by their RMS, and the correlations expressed in wall units. This is key to the development of a general “stand-alone” stochastic forcing for inertial particles in LES.
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47.55.Kf Particle-laden flows
47.60.Dx Flows in ducts and channels
47.27.ek Direct numerical simulations
47.27.ep Large-eddy simulations
47.27.nb Boundary layer turbulence
47.27.nd Channel flow
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Fluid elasticity can enable propulsion at low Reynolds number

Nathan C. Keim, Mike Garcia, and Paulo E. Arratia

Phys. Fluids 24, 081703 (2012); http://dx.doi.org/10.1063/1.4746792 (7 pages)

Online Publication Date: 17 August 2012

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Conventionally, a microscopic particle that performs a reciprocal stroke cannot move through its environment. This is because at small scales, the response of simple Newtonian fluids is purely viscous and flows are time-reversible. We show that by contrast, fluid elasticity enables propulsion by reciprocal forcing that is otherwise impossible. We present experiments on rigid objects actuated reciprocally in viscous fluids, demonstrating for the first time a purely elastic propulsion set by the object's shape and boundary conditions. We describe two different artificial “swimmers” that experimentally realize this principle.
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62.10.+s Mechanical properties of liquids
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Characterization of the transport topology in patient-specific abdominal aortic aneurysm models

Amirhossein Arzani and Shawn C. Shadden

Phys. Fluids 24, 081901 (2012); http://dx.doi.org/10.1063/1.4744984 (16 pages) | Cited 2 times

Online Publication Date: 10 August 2012

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Abdominal aortic aneurysm (AAA) is characterized by disturbed blood flow patterns that are hypothesized to contribute to disease progression. The transport topology in six patient-specific abdominal aortic aneurysms was studied. Velocity data were obtained by image-based computational fluid dynamics modeling, with magnetic resonance imaging providing the necessary simulation parameters. Finite-time Lyapunov exponent (FTLE) fields were computed from the velocity data, and used to identify Lagrangian coherent structures (LCS). The combination of FTLE fields and LCS was used to characterize topological flow features such as separation zones, vortex transport, mixing regions, and flow impingement. These measures offer a novel perspective into AAA flow. It was observed that all aneurysms exhibited coherent vortex formation at the proximal segment of the aneurysm. The evolution of the systolic vortex strongly influences the flow topology in the aneurysm. It was difficult to predict the vortex dynamics from the aneurysm morphology, motivating the application of image-based flow modeling.
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87.19.rh Fluid transport and rheology
87.61.Np Flow imaging
87.85.gf Fluid mechanics and rheology
47.63.Cb Blood flow in cardiovascular system
47.63.Jd Microcirculation and flow through tissues

Liquid injection in confined co-flow: Application to portal vein embolization by glue injection

M.-C. Sandulache, P. Paullier, R. Bouzerar, T. Yzet, O. Balédent, and A.-V. Salsac

Phys. Fluids 24, 081902 (2012); http://dx.doi.org/10.1063/1.4740059 (19 pages)

Online Publication Date: 16 August 2012

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Drop formation in liquid-liquid systems has received considerable attention over the last century owing to its many industrial applications. More recent applications may be found in the field of endovascular/percutaneous treatments. The present study focuses on portal vein embolization (PVE), which consists in the blockage of part of the portal trunk though the injection of surgical glue. The short-time injection is dominated by fluid dynamic effects: the influence of polymerization is secondary owing to the presence of ethiodized oil in the injected mixture. If the mechanism of liquid injection is well understood for injections in unconfined fluids at rest, fewer studies have so far considered the case of outer liquids flowing in confined environments. The objective is therefore to conduct a large range parametric study of liquid injections in confined co-flows. An experimental setup has been designed to simulate in vitro the injection in an immiscible liquid flowing in a cylindrical tube. The transition from the dripping to the jetting regimes is found to be independent of confinement, but to depend on the ratio of the inertial forces of the injected liquid to the surface tension, i.e., the Weber number of the inner flow Wei. The confinement, however, has an influence on the drop size in the dripping regime. Its influence diminishes in the first phase of the jetting regime, as the drop size largely decreases. In the fully established jetting regime, the drop size is finally only a function of the ejection tube diameter. To predict the size of the drops in the dripping regime, we have developed a semiempirical model that takes into account the effects of both the tube confinement and outer flow. It will help the interventional radiologists predict the drop size depending on the geometrical and velocimetric conditions at the site of embolization. All these results can then serve as a base to optimize the PVE technique during clinical practice.
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47.63.Cb Blood flow in cardiovascular system
47.85.md Polymer processing flows
87.19.U- Hemodynamics
87.85.gf Fluid mechanics and rheology
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.55.D- Drops and bubbles
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A low-dimensional deformation model for cancer cells in flow

A. M. Lee, M. A. Berny-Lang, S. Liao, E. Kanso, P. Kuhn, O. J. T. McCarty, and P. K. Newton

Phys. Fluids 24, 081903 (2012); http://dx.doi.org/10.1063/1.4748811 (14 pages)

Online Publication Date: 30 August 2012

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A low-dimensional parametric deformation model of a cancer cell under shear flow is developed. The model is built around an experiment in which MDA-MB-231 adherent cells are subjected to flow with increasing shear. The cell surface deformation is imaged using differential interference contrast microscopy imaging techniques until the cell releases into the flow. We post-process the time sequence of images using an active shape model from which we obtain the principal components of deformation. These principal components are then used to obtain the parameters in an empirical constitutive equation determining the cell deformations as a function of the fluid normal and shear forces imparted. The cell surface is modeled as a 2D Gaussian interface which can be deformed with three active parameters: H (height), σx (x-width), and σy (y-width). Fluid forces are calculated on the cell surface by discretizing the surface with regularized Stokeslets, and the flow is driven by a stochastically fluctuating pressure gradient. The Stokeslet strengths are obtained so that viscous boundary conditions are enforced on the surface of the cell and the surrounding plate. We show that the low-dimensional model is able to capture the principal deformations of the cell reasonably well and argue that active shape models can be exploited further as a useful tool to bridge the gap between experiments, models, and numerical simulations in this biological setting.
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87.85.Pq Biomedical imaging
87.85.G- Biomechanics
87.17.Rt Cell adhesion and cell mechanics
47.80.Jk Flow visualization and imaging
02.50.Ey Stochastic processes
47.11.-j Computational methods in fluid dynamics
back to top Micro- and Nanofluid Mechanics

The dynamics of liquid drops and their interaction with solids of varying wettabilities

J. E. Sprittles and Y. D. Shikhmurzaev

Phys. Fluids 24, 082001 (2012); http://dx.doi.org/10.1063/1.4739933 (17 pages) | Cited 2 times

Online Publication Date: 1 August 2012

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Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation free-surface flows is confirmed by a comparison with previous numerical studies for the large amplitude oscillations of free liquid drops. Our code's ability to produce high resolution benchmark calculations for dynamic wetting flows is then demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the process which go beyond the resolution available to experimental analysis. Strong interfacial effects which are observed at the microfluidic scale are then harnessed by designing surfaces of varying wettability that allow new methods of flow control to be developed.
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47.55.dr Interactions with surfaces
47.85.L- Flow control
68.08.Bc Wetting
47.11.-j Computational methods in fluid dynamics

Ferrofluid flow in a spherical cavity under an imposed uniform rotating magnetic field: Spherical spin-up flow

I. Torres-Diaz and C. Rinaldi

Phys. Fluids 24, 082002 (2012); http://dx.doi.org/10.1063/1.4734345 (18 pages)

Online Publication Date: 1 August 2012

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An analytical solution is obtained for the ferrohydrodynamic problem of flow of a ferrofluid in a spherical cavity under the influence of a uniform rotating magnetic field produced by a fluxball winding. The ferrohydrodynamics equations are decoupled for low values of the applied magnetic field amplitude to allow analytical solution. A governing equation for the divergence of spin velocity is obtained and used to demonstrate that the divergence of the spin velocity is zero under conditions of small uniform magnetic field. The condition of zero spin viscosity results in no flow being predicted in the cavity. For the case of non-zero spin viscosity the condition of zero divergence of spin results in the inability of the ferrohydrodynamics equations to satisfy boundary conditions for both the normal and tangential components of the spin velocity at the sphere wall. Solutions are obtained for cases where boundary conditions are imposed on either the normal or tangential component of the spin velocity. In both cases, the solutions predict that the ferrofluid rotates rigid-body-like about the axis of field rotation in the core and there is a region near the outer wall where flow reduces to satisfy the no slip boundary condition on the translational velocity. However, the two solutions differ in their asymptotic behavior when the spin viscosity vanishes. It is found that when the boundary condition is applied to the tangential component of the spin velocity, the zero spin viscosity solution is recovered as η′ → 0, whereas when the boundary condition is applied to the normal component of the spin velocity the solution diverges as η′ → 0. The results indicate that studying the flow of ferrofluids in a spherical cavity could yield important tests of long-held, arguably ad hoc assumptions surrounding the governing equations and boundary conditions of ferrofluid flow.
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47.65.Cb Magnetic fluids and ferrofluids
75.50.Mm Magnetic liquids
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.10.Fg Dynamical systems methods
47.32.Ef Rotating and swirling flows

Alternating current induced-charge electrophoresis of leaky dielectric Janus particles

Alicia M. Boymelgreen and Touvia Miloh

Phys. Fluids 24, 082003 (2012); http://dx.doi.org/10.1063/1.4739932 (16 pages)

Online Publication Date: 16 August 2012

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We hereby provide a semi-analytic and numerical solution for the nonlinear, induced-charge electrophoretic motion of an electrically inhomogeneous Janus sphere—comprising two hemispheres with differing dielectric permittivities—under the application of a uniform, time-dependent (ac) electric field. No assumptions are made regarding the size of the electric double layer (EDL) and thus the analysis remains valid even in the case of nanoparticles where the particle radius can be of the same order as the EDL thickness. We consider a number of practical and realistic configurations of metallic and dielectric hemispheres and predict the variations in particle mobility as a function of the conductivity of the two hemispheres and the electrolyte, the frequency of the applied electric field and the EDL length. It is determined that there exist critical values for the conductivity of each hemisphere and the frequency of the applied field, which when exceeded, can cause the mobility to decay rapidly to zero.
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82.45.Gj Electrolytes
02.60.-x Numerical approximation and analysis
47.65.-d Magnetohydrodynamics and electrohydrodynamics
77.22.Ch Permittivity (dielectric function)

The contribution of diffusion to gas microflow: An experimental study

Thomas Veltzke, Michael Baune, and Jorg Thöming

Phys. Fluids 24, 082004 (2012); http://dx.doi.org/10.1063/1.4745004 (13 pages)

Online Publication Date: 16 August 2012

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Moderately rarefied gas flows are clearly distinguished from viscous flow in the continuum regime and from molecular diffusion at high rarefaction. They are an intermediate of the two border cases referred to as slip flow and transition regime flow. Here, we present a new pencil-and-paper approach for modeling flows in these regimes by a superposition of convection and Fickian diffusion. It allows us to predict mass flows for helium, argon, nitrogen, and carbon dioxide in microducts with parallel walls and with slightly varying cross section. The model was validated by measurement series taken from literature and by own permeation experiments on tapered microchannels. Analytical investigation of the approach showed that the diffusive flow is proportional to the cross-sectional area at the channel entrance. Hence, the mass flow in a tapered channel is unequal in both directions when diffusion dominates due to increased rarefaction. In contrary to the common Maxwellian slip approach the superposition model describes the data reliably. From this we conclude that deviations from continuum behavior in the intermediate cannot be explained by slip flow at the walls and tangential momentum accommodation, but by Fickian diffusion. Now predictions are possible without any usage of fitted parameters such as the tangential momentum accommodation coefficient.
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47.45.Gx Slip flows and accommodation
47.80.-v Instrumentation and measurement methods in fluid dynamics
51.20.+d Viscosity, diffusion, and thermal conductivity
47.60.Dx Flows in ducts and channels

Dielectric-solid polarization at strong fields: Breakdown of Smoluchowski's electrophoresis formula

Ory Schnitzer and Ehud Yariv

Phys. Fluids 24, 082005 (2012); http://dx.doi.org/10.1063/1.4748967 (12 pages) | Cited 3 times

Online Publication Date: 30 August 2012

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We investigate the thin-double-layer electrophoretic drift of a uniformly charged dielectric particle, driven by an intense electric field comparable to the transverse Debye-layer field. Under these circumstances, solid polarization affects the leading-order electrokinetic transport in the fluid by inducing a nonuniform zeta-potential distribution. The resulting expression for the particle velocity is accordingly nonlinear in the applied field. The electrophoretic “mobility”—the ratio of this velocity and the applied field—depends upon two parameters, the first quantifying the surface-charge density, and the second constituting the product of the solid-to-liquid permittivity ratio and the scaled applied-field magnitude. At weak values of this product, solid polarization results in field-cubed deviations from Smoluchowski's velocity; at large values of it, the particle velocity is a slowly increasing function of the applied field, essentially varying with its logarithm. The transition between these two limits features a shift from zeta-potential proportionality to a charge-density proportionality. For all values of the two governing parameters solid polarization acts so as to reduce the electrophoretic velocity relative to the Smoluchowski limit.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
77.22.Ej Polarization and depolarization
77.22.Ch Permittivity (dielectric function)
82.45.Un Dielectric materials in electrochemistry
back to top Interfacial Flows

Coalescence of surfactant covered drops in extensional flows: Effects of the interfacial diffusivity

Carolina Vannozzi

Phys. Fluids 24, 082101 (2012); http://dx.doi.org/10.1063/1.4737659 (37 pages)

Online Publication Date: 9 August 2012

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Boundary integral simulations and scaling theory were employed to study the effects of insoluble surfactant surface diffusivity Ds and concentration Γ on the coalescence process of two equal-sized viscous drops. The drops underwent head-on collisions in a biaxial extensional flow, in the Stokes flow limit and low capillary numbers. The simulations were compared with the drainage time experiments of Yoon et al. [Phys. Fluids 19, 023102 (2007)10.1063/1.2409735] concerned with a polymeric system, polybutadiene (PBd) drops in a polydimethylsyloxane (PDMS) matrix, stabilized by block-copolymers acting as insoluble surfactants to explain the mechanism underneath their findings. An ad hoc equation of state, derived by mean field theory, specific for the block-copolymers in the experiments of Yoon et al., able to match the experimental surface tension data without fitting parameters, was used. We were able to reproduce the experimental drainage time data, although an additional attractive force, besides the usual van der Waals interactions, had to be introduced for high block-copolymer concentrations, probably as a result of the entropic attraction between the two facing dry brushes formed in the thin film between the two drops. According to simulations, the puzzling experimental drainage time transition for low surfactant concentrations, from high drainage time to low drainage time as Ca increases, was a consequence of the oscillating behavior of the minimum film thickness, which takes place for Marangoni numbers Ma < 5 and surface Peclet number Pes > 60. In this regard, a master curve was obtained for the scaled relative minimum film thickness attained during the oscillation as a function of Ma. This enabled to determine both the minimum value of the dimensionless attractive forces to avoid coalescence for each concentration studied and the range of Ma that favors early coalescence. The coalescence process was found very sensitive to Pes and for Pes O(100–1000) even trace amounts of surfactants can be as effective stabilizers as high surfactant concentrations. Moreover, for the polymeric system of interest, the range of Ds in which the drainage time changes from the saturation value to the clean interface value was computed as a function of the surfactant concentration. In the specific, for the PDMS/PBd system of interest the Ds range studied was O(10−12–10−5 cm2 s−1). Additionally, our scaling analysis further validates our simulations, also highlighting the effect on the drainage process of the different parameters, in particular, of the external pushing force, which is increased compared to a clean interface system, as Pes is increased or as the surfactant concentration is increased, because of the reduction in the interfacial mobility of the drop. Finally, our study suggests that matching simulations with four-roll mill drainage time experiments can be an effective method to determine block-copolymer surface diffusivity.
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47.55.df Breakup and coalescence
47.55.pf Marangoni convection
47.57.eb Diffusion and aggregation
68.03.Hj Liquid surface structure: measurements and simulations
02.30.Rz Integral equations
47.11.Hj Boundary element methods

Free vibrations of a spherical drop constrained at an azimuth

Santhosh Ramalingam, Doraiswami Ramkrishna, and Osman A. Basaran

Phys. Fluids 24, 082102 (2012); http://dx.doi.org/10.1063/1.4742339 (20 pages) | Cited 3 times

Online Publication Date: 10 August 2012

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Two droplets coupled through a liquid filled (a) hole in a plate or (b) tube is referred to as a double droplet system (DDS) or a capillary switch. Such capillary systems are gaining increasing attention due to their utility in applications. A particularly exciting application is one where a DDS is employed as a liquid lens, one flavor of which entails using a DDS as a variable focus lens by keeping it under sustained oscillations at its natural frequencies. The natural modes of oscillation of a DDS are determined analytically here in the limit in which the plate thickness (or tube length) is vanishingly small and when the effect of gravity is negligible compared to that of surface tension. In this limit, a DDS at rest reduces to two spherical caps that are pinned to and coupled along a common circular ring of contact of negligible thickness. Here, the caps are taken to be complementary pieces of a sphere so that the equilibrium state of the system is a sphere that is constrained by a ring of negligible thickness at an azimuthal angle with respect to the center of the sphere. Both the constrained drop and the fluid exterior to it are taken to be inviscid fluids undergoing irrotational flow. Similar to the linear oscillations of a free drop first studied by Rayleigh, the analytical formulation of the linear oscillations of the constrained drop results in a linear operator eigenvalue problem but with one additional boundary condition, i.e., that which accounts for zero shape perturbation along the circle of contact. Exploiting properties of linear operators, an implicit expression is obtained for the frequency of each mode of oscillation, a feat that appears not to have been accomplished to date in any problem involving oscillations of constrained drops. An extension of a method based on Green's functions that was developed to analyze the linear oscillations of a drop in contact with a spherical bowl [M. Strani and F. Sabetta, “Free-vibrations of a drop in partial contact with a solid support,” J. Fluid Mech. 141, 233–247 (1984)]10.1017/S0022112084000811 is also employed to verify the aforementioned results. Results obtained from these two approaches are then compared to those reported by Bostwick and Steen [“Capillary oscillations of a constrained liquid drop,” Phys. Fluids 21, 032108 (2009)]10.1063/1.3103344. Careful examination of flow fields within drops reveals that by pinning a drop, it should be possible to selectively excite just a portion of a drop's surface.
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47.55.dr Interactions with surfaces
47.55.nb Capillary and thermocapillary flows
68.03.Cd Surface tension and related phenomena
47.60.Dx Flows in ducts and channels
02.30.-f Function theory, analysis

Numerical study on the effects of non-dimensional parameters on drop-on-demand droplet formation dynamics and printability range in the up-scaled model

Eunjeong Kim and Jehyun Baek

Phys. Fluids 24, 082103 (2012); http://dx.doi.org/10.1063/1.4742913 (12 pages)

Online Publication Date: 14 August 2012

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The droplet formation dynamics from a drop-on-demand printhead is numerically investigated with regard to the printability range. The numerical simulation is carried out using a volume-of-fluid model, and the qualitative effects of non-dimensional parameters on the droplet formation dynamics are evaluated. To determine the printability range, within which the droplet is ejected in a stable manner without satellite droplets, extensive numerical simulations are carried out by varying the viscosity and surface tension. Generally, the printability range is determined by a Z number, which is the inverse of the Ohnesorge number (Oh). However, it is found that the Z number alone is insufficient for describing the droplet formation dynamics. Other important non-dimensional parameters such as the Reynolds number (Re), Weber number (We), and capillary number (Ca) should also be taken into consideration. For studying the printability, the droplet formation dynamics are divided into five different regimes, and a regime map based on the Z, We, and Ca is proposed.
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47.55.db Drop and bubble formation
68.03.Cd Surface tension and related phenomena
02.60.Cb Numerical simulation; solution of equations
47.11.-j Computational methods in fluid dynamics

Forces on a boiling bubble in a developing boundary layer, in microgravity with g-jitter and in terrestrial conditions

C. W. M. van der Geld, C. Colin, Q. I. E. Segers, V. H. Pereira da Rosa, and H. N. Yoshikawa

Phys. Fluids 24, 082104 (2012); http://dx.doi.org/10.1063/1.4743026 (29 pages)

Online Publication Date: 14 August 2012

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Terrestrial and microgravity flow boiling experiments were carried out with the same test rig, comprising a locally heated artificial cavity in the center of a channel near the frontal edge of an intrusive glass bubble generator. Bubble shapes were in microgravity generally not far from those of truncated spheres, which permitted the computation of inertial lift and drag from potential flow theory for truncated spheres approximating the actual shape. For these bubbles, inertial lift is counteracted by drag and both forces are of the same order of magnitude as g-jitter. A generalization of the Laplace equation is found which applies to a deforming bubble attached to a plane wall and yields the pressure difference between the hydrostatic pressures in the bubble and at the wall, Δp. A fully independent way to determine the overpressure Δp is given by a second Euler-Lagrange equation. Relative differences have been found to be about 5% for both terrestrial and microgravity bubbles. A way is found to determine the sum of the two counteracting major force contributions on a bubble in the direction normal to the wall from a single directly measurable quantity. Good agreement with expectation values for terrestrial bubbles was obtained with the difference in radii of curvature averaged over the liquid-vapor interface, ⟨(1/R2 − 1/R1)⟩, multiplied with the surface tension coefficient, σ. The new analysis methods of force components presented also permit the accounting for a surface tension gradient along the liquid-vapor interface. No such gradients were found for the present measurements.
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47.55.dp Cavitation and boiling
68.03.Cd Surface tension and related phenomena
47.60.Dx Flows in ducts and channels
64.70.fh Boiling and bubble dynamics
02.60.Gf Algorithms for functional approximation
47.11.-j Computational methods in fluid dynamics

Slip or not slip? A methodical examination of the interface formation model using two-dimensional droplet spreading on a horizontal planar substrate as a prototype system

David N. Sibley, Nikos Savva, and Serafim Kalliadasis

Phys. Fluids 24, 082105 (2012); http://dx.doi.org/10.1063/1.4742895 (36 pages) | Cited 3 times

Online Publication Date: 16 August 2012

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We consider the spreading of a thin two-dimensional droplet on a planar substrate as a prototype system to compare the contemporary model for contact line motion based on interface formation of Shikhmurzaev [Int. J. Multiphase Flow 19, 589–610 (1993)]10.1016/0301-9322(93)90090-H, to the more commonly used continuum fluid dynamical equations augmented with the Navier-slip condition. Considering quasistatic droplet evolution and using the method of matched asymptotics, we find that the evolution of the droplet radius using the interface formation model reduces to an equivalent expression for a slip model, where the prescribed microscopic dynamic contact angle has a velocity dependent correction to its static value. This result is found for both the original interface formation model formulation and for a more recent version, where mass transfer from bulk to surface layers is accounted for through the boundary conditions. Various features of the model, such as the pressure behaviour and rolling motion at the contact line, and their relevance, are also considered in the prototype system we adopt.
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47.45.Gx Slip flows and accommodation
47.55.D- Drops and bubbles
68.03.Cd Surface tension and related phenomena
47.10.ad Navier-Stokes equations

Turbulent mixing and wave radiation in non-Boussinesq internal bores

Zac Borden, Tilman Koblitz, and Eckart Meiburg

Phys. Fluids 24, 082106 (2012); http://dx.doi.org/10.1063/1.4745478 (17 pages)

Online Publication Date: 16 August 2012

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Bores, or hydraulic jumps, appear in many natural settings and are useful in many industrial applications. If the densities of the two fluids between which a bore propagates are very different (i.e., water and air), the less dense fluid can be neglected when modeling a bore analytically—a single-layer hydraulic model will accurately predict a bore's speed of propagation. A two-layer model is required, however, if the densities are more similar. Mass is conserved separately in each layer and momentum is conserved globally, but the model requires for closure an assumption about the loss of energy across a bore. In the Boussinesq limit, it is known that there is a decrease of the total energy flux across a bore, but in the expanding layer, turbulent mixing at the interface entrains high speed fluid from the contracting layer, resulting in an increase in the flux of kinetic energy across the expanding layer of a bore. But it is unclear if this finding will extend to non-Boussinesq bores. We directly examine the flux of energy within non-Boussinesq bores using two-dimensional direct numerical simulations and find that a gain of energy across the expanding layer only occurs for bores where the density ratio, defined as the ratio of the density of the lighter fluid to the heavier fluid, is greater than approximately one half. For smaller density ratios, undular waves generated at the bore's front dominate over the effects of turbulent mixing, and the expanding layer loses energy across the bore. Based on our results, we show that if one can predict the amount of energy radiated by bores through undular waves, it is possible to derive an accurate model for the propagation of non-Boussinesq bores.
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47.27.wj Turbulent mixing layers
47.35.-i Hydrodynamic waves
47.27.ek Direct numerical simulations

Effects of streamwise rotation on the dynamics of a droplet

Eric K. W. Poon, Jing Lou, Shaoping Quan, and Andrew S. H. Ooi

Phys. Fluids 24, 082107 (2012); http://dx.doi.org/10.1063/1.4746282 (13 pages)

Online Publication Date: 23 August 2012

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An initially streamwise rotating droplet released into a uniform cross flow is studied numerically. The computations are performed using a finite volume Navier–Stokes solver which employs a moving mesh interface tracking scheme to locate the interface. With a large initial Weber number (Wei = 40) the streamwise rotating droplet flattens along the free stream direction more quickly as rotation rate (Ω*) increases, and leads to a dramatic increase in the dynamic drag coefficient (CD/A*, where A* is the dimensionless frontal area). On the other hand, for Wei = 4 and 0.4 at Ω* ≥ 0.6, the flattening of the droplet is less pronounced and the droplet even restores to spherical shape, hence, CD/A* decreases sharply. The dynamic drag coefficient even becomes negative for Wei = 4 and 0.4 at Ω* = 1. At the largest deformation, the droplet can be classified into three major shapes: biconvex, convex-concave, and biconcave. One dominant feature of the wake downstream of the droplet is the formation and convection of vortex rings. The shape and deformation of the droplet is dependent not only on the size of the vortex ring, but also upon the free stream dynamic pressure and droplet pressure. The detachment of vortex ring in the wake leads to a substantial drag reduction, and this detachment occurs at Re ≈ 28.
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47.32.Ef Rotating and swirling flows
47.55.db Drop and bubble formation
02.70.-c Computational techniques; simulations
47.10.ad Navier-Stokes equations
47.11.Df Finite volume methods
47.32.cf Vortex reconnection and rings

Bubble pinch-off and scaling during liquid drop impact on liquid pool

Bahni Ray, Gautam Biswas, and Ashutosh Sharma

Phys. Fluids 24, 082108 (2012); http://dx.doi.org/10.1063/1.4746793 (11 pages)

Online Publication Date: 23 August 2012

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Simulations are performed to show entrapment of air bubble accompanied by high speed upward and downward water jets when a water drop impacts a pool of water surface. A new bubble entrapment zone characterised by small bubble pinch-off and long thick jet is found. Depending on the bubble and jet behaviour, the bubble entrapment zone is subdivided into three sub-regimes. The entrapped bubble size and jet height depends on the crater shape and its maximum depth. During the bubble formation, bubble neck develops an almost singular shape as it pinches off. The final pinch-off shape and the power law governing the pinching, rneck ∝ A(t0 − t)αvaries with the Weber number. Weber dependence of the function describing the radius of the bubble during the pinch-off only affects the coefficient A and not the power exponent α.
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47.55.db Drop and bubble formation
47.11.-j Computational methods in fluid dynamics
47.55.Ca Gas/liquid flows

A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow

J. M. Sullivan, C. Paterson, S. K. Wilson, and B. R. Duffy

Phys. Fluids 24, 082109 (2012); http://dx.doi.org/10.1063/1.4744980 (19 pages)

Online Publication Date: 24 August 2012

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We use the lubrication approximation to analyze three closely related problems involving a thin rivulet or ridge (i.e., a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In the Appendix, we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations.
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47.40.-x Compressible flows; shock waves
47.55.db Drop and bubble formation
47.85.Gj Aerodynamics
47.11.-j Computational methods in fluid dynamics

Predicting conditions for microscale surfactant mediated tipstreaming

Todd M. Moyle, Lynn M. Walker, and Shelley L. Anna

Phys. Fluids 24, 082110 (2012); http://dx.doi.org/10.1063/1.4746253 (21 pages)

Online Publication Date: 29 August 2012

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Microscale tipstreaming is a unique method to overcome the limiting length scale in microfluidics allowing for production of submicron-sized droplets. Tipstreaming is the ejection of small drops from a liquid thread formed by interfacial tension gradients and convective transport of surfactant. Controlling and understanding this process is essential for successful application in areas such as synthesis of nano-scale particles, manipulation of biomolecules, enzyme activity studies, and others. However, models that predict operating conditions for microscale tipstreaming do not currently exist. In this work, we develop a semi-analytical model aimed at capturing the essential physics of the tipstreaming mechanism. The model relies on interfacial shape observations indicative of microscale tipstreaming to simplify the fluid flow and surfactant transport equations. The result is an interfacial mass balance of surfactant. Conditions where the mass balance can be satisfied define the operating conditions for microscale tipstreaming. Results from the model are compared with our own experimental results. Good agreement is found between model predictions and experiments. Scaling of each boundary that controls the feasible tipstreaming region is given. Finally, the model is able to guide selection of device geometry and surfactant properties to shift or expand the feasible region where microscale tipstreaming is expected.
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47.55.dk Surfactant effects
47.11.-j Computational methods in fluid dynamics

A mean curvature model for capillary flows in asymmetric containers and conduits

Yongkang Chen, Noël Tavan, and Mark M. Weislogel

Phys. Fluids 24, 082111 (2012); http://dx.doi.org/10.1063/1.4749816 (16 pages)

Online Publication Date: 31 August 2012

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Capillarity-driven flows resulting from critical geometric wetting criterion are observed to yield significant shifts of the bulk fluid from one side of the container to the other during “zero gravity” experiments. For wetting fluids, such bulk shift flows consist of advancing and receding menisci sometimes separated by secondary capillary flows such as rivulet-like flows along gaps. Here we study the mean curvature of an advancing meniscus in hopes of approximating a critical boundary condition for fluid dynamics solutions. It is found that the bulk shift flows behave as if the bulk menisci are either “connected” or “disconnected.” For the connected case, an analytic method is developed to calculate the mean curvature of the advancing meniscus in an asymptotic sense. In contrast, for the disconnected case the method to calculate the mean curvature of the advancing and receding menisci uses a well-established procedure. Both disconnected and connected bulk shifts can occur as the first tier flow of more complex compound capillary flows. Preliminary comparisons between the analytic method and the results of drop tower experiments are encouraging.
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68.08.Bc Wetting
47.55.nb Capillary and thermocapillary flows
68.03.Cd Surface tension and related phenomena
47.80.Jk Flow visualization and imaging
back to top Viscous and Non-Newtonian Flows

On self-similarity in the drop-filament corner region formed during pinch-off of viscoelastic fluid threads

Pradeep P. Bhat, Santosh Appathurai, Michael T. Harris, and Osman A. Basaran

Phys. Fluids 24, 083101 (2012); http://dx.doi.org/10.1063/1.4745179 (12 pages) | Cited 1 time

Online Publication Date: 16 August 2012

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A characteristic feature of pinch-off of fluid threads is the formation of drops connected to thinning filaments. This phenomenon is encountered in a number of widely used applications requiring the production of drops such as electronics microfabrication via inkjet printing, spray coating/drying, and microarraying. In pinch-off of viscoelastic fluid threads, the region that connects the drops to the filaments develops into a sharp corner. Recently, Clasen et al. [J. Fluid Mech. 556, 283–308 (2006)]10.1017/S0022112006009633 showed that such a corner evolves self-similarly. They, however, neglected the capillary pressure in the drop. A modified similarity solution is presented here that incorporates the drop capillary-pressure term, and transient simulations of corner region profiles are shown to converge onto the new similarity solution better than that of Clasen et al. Indeed, the new similarity solution is valid in all the three regions: the drop, the corner, and the filament regions. Similarity solutions, so obtained, are particularly useful in capillary-breakup rheometry where they are employed to estimate a fluid's extensional viscosity—a material property of viscoelastic fluids that influences greatly the drop formation process.
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47.55.db Drop and bubble formation
47.55.nb Capillary and thermocapillary flows
47.57.Qk Rheological aspects
47.11.-j Computational methods in fluid dynamics
47.50.Cd Modeling
47.53.+n Fractals in fluid dynamics
back to top Particulate, Multiphase, and Granular Flows

Transport of airborne particles in straight and curved microchannels

Allison Schaap, Winnie C. Chu, and Boris Stoeber

Phys. Fluids 24, 083301 (2012); http://dx.doi.org/10.1063/1.4742900 (14 pages)

Online Publication Date: 14 August 2012

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The measurement of airborne particles is important for environmental and exposure monitoring. Microfluidic technologies present potential advantages for aerosol monitoring but have been applied very little to the handling of airborne particles. In this paper, we examine the flow focusing and cross-streamline diffusion of aerosols in straight microchannels, and the size-based lateral displacement of aerosols caused by centrifugal forces in a curved channel. We present calculations, simulations, and experimental results verifying the models: measurements of the focusing and diffusion of 0.2 μm and 0.75 μm particles in straight channels and of the size-dependent lateral displacement of particles between 0.2 μm and 2 μm in curved channels are demonstrated and shown to match well with the simulations. We observe lateral dispersion of the particles: particles closer to the top and bottom wall of the channel experience less lateral displacement than particles near the center due to the flow velocity distribution across the channel cross section. These results confirm that the microchannel techniques presented are a viable method for the size-based manipulation of airborne particles.
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47.60.Dx Flows in ducts and channels
47.55.Kf Particle-laden flows
47.61.Jd Multiphase flows
47.80.Jk Flow visualization and imaging
82.70.Rr Aerosols and foams
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