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Oct 2005

Volume 17, Issue 10, Articles (10xxxx)

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Preface: Transport phenomena in micro- and nanodevices

Mohamed Gad-el-Hak

Phys. Fluids 17, 100501 (2005); http://dx.doi.org/10.1063/1.2047552 (1 page)

Online Publication Date: 3 October 2005

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Abstract Unavailable
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01.30.-y Physics literature and publications
85.85.+j Micro- and nano-electromechanical systems (MEMS/NEMS) and devices
47.85.Np Fluidics
73.23.-b Electronic transport in mesoscopic systems
47.10.-g General theory in fluid dynamics

An extended volume-of-fluid method for micro flows with short-range interactions between fluid interfaces

S. Hardt

Phys. Fluids 17, 100601 (2005); http://dx.doi.org/10.1063/1.1978948 (9 pages) | Cited 5 times

Online Publication Date: 3 October 2005

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A formulation is developed allowing to take into account the interaction of fluid interfaces in computational methods for free-surface flow. The necessity for such an extension of the standard computational approaches is traced back to a large number of experimental and theoretical results showing that in the presence of surfactants, fluid interfaces often interact in such a way that coalescence of bubbles or droplets is slowed down or suppressed. The strategy pursued in this paper to incorporate such effects relies on a Debye-screened scalar field which develops steep gradients in the vicinity of an interface. The force density acting in a gap between two interfaces is computed using a function of the local field values and a cut off to eliminate those regions where no interaction takes place. It is shown that in such a way a power-law behavior of the force as a function of separation between the interfaces can be reproduced. The model is implemented into a standard volume-of-fluid scheme and it is exemplified that, compared to conventional approaches, completely different scenarios for micro flows of droplets can be reproduced. The important qualitative difference is that coalescence is avoided, so that the formation and transport of multibubble∕multidroplet arrangements can be studied.
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47.55.D- Drops and bubbles
47.55.Kf Particle-laden flows
47.11.-j Computational methods in fluid dynamics
47.85.Np Fluidics

Electron vortices in semiconductors devices

Kamran Mohseni, Ali Shakouri, Rajeev J. Ram, and Mathew C. Abraham

Phys. Fluids 17, 100602 (2005); http://dx.doi.org/10.1063/1.1990215 (7 pages)

Online Publication Date: 3 October 2005

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The hydrodynamic model of electron transport in semiconductors is analyzed and, in analogy with vortices in fluid mechanics, the curl of electron velocity is defined as electron vorticity, and the transport equation for the electron vorticity is derived. Aside from the classical hydrodynamic sources of vorticity, collision terms in the continuity and momentum equations are identified as sources and sinks of electron vorticity. Similar to three-dimensional fluid flows there is a vortex stretching term in the vorticity equation. This term could be responsible for the possible cascade of electron kinetic energy to small scales and formation of chaotic turbulent electron transport regimes. A scale analysis of the electron vorticity equation is performed and the relative order of magnitude of each sources of vorticity is found. This analysis and the calculation of electron mean-free-path due to electron–electron and electron–phonon scatterings characterize a transport regime with significant electron vorticity effects. Furthermore, conditions for observation of electron vortices in semiconductor devices are predicted.
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72.20.Dp General theory, scattering mechanisms
72.20.Jv Charge carriers: generation, recombination, lifetime, and trapping
85.30.-z Semiconductor devices

Ultrasound-mediated destruction of contrast microbubbles used for medical imaging and drug delivery

Dhiman Chatterjee, Pankaj Jain, and Kausik Sarkar

Phys. Fluids 17, 100603 (2005); http://dx.doi.org/10.1063/1.2011468 (8 pages) | Cited 14 times

Online Publication Date: 3 October 2005

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Micron-size bubbles encapsulated by a stabilizing layer of surface-active materials are used in medical ultrasound imaging and drug delivery. Their destruction stimulated by ultrasound in vivo plays a critical role in both applications. We investigate the destruction process of microbubbles in a commercially available contrast agent by measuring the attenuation of ultrasound through it. The measurement is performed with single-cycle bursts from an unfocused transducer (with a center frequency of 5 MHz) for varying pressure amplitudes at 50-, 100-, and 200-Hz pulse repetition frequencies (PRF) with duty cycles 0.001%, 0.002%, and 0.004%, respectively. At low excitation, the attenuation is found to increase with time. With increased excitation level, the attenuation level decreases with time, indicating destruction of microbubbles. There is a critical pressure amplitude ( ∼ 1.2 MPa) for all three PRFs, below which there is no significant bubble destruction. Above the critical pressure amplitudes the rate of destruction depends on excitation levels. But at high-pressure amplitudes the destruction becomes independent of excitation pressure amplitude. The results are interpreted to identify two different mechanisms of bubble destruction by its signature in attenuation, namely, slow dissolution by diffusion and catastrophic shell rupture. The different modes are discussed in detail with their implications in medical applications.
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87.63.D- Ultrasonography
87.80.-y Biophysical techniques (research methods)
43.35.Yb
47.55.D- Drops and bubbles

Effect of the surface charge on ion transport through nanoslits

Reto B. Schoch, Harald van Lintel, and Philippe Renaud

Phys. Fluids 17, 100604 (2005); http://dx.doi.org/10.1063/1.1896936 (5 pages) | Cited 23 times

Online Publication Date: 3 October 2005

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A description of ion transport through geometrically defined nanoslits is presented. It is characterized by the effective surface charge density and was obtained by impedance spectroscopy measurements of electrolytes with different physicochemical properties. The fluid channels were fabricated in a Pyrex–Pyrex field assisted bonding process with an intermediate layer of amorphous silicon. The height of the nanoslits was defined by the 50 nm thickness of the amorphous silicon layer. Two microfluidic channels, containing electrodes for the characterization of the nanoslits, maintained fresh liquid on both sides of the nanoapertures. By changing the KCl concentration of the electrolyte, a conductance plateau (in log–log scale) was observed due to the dominance of the effective surface charge density, resulting in an excess of mobile counterions in the nanoslits at low salt concentrations. The effective surface charge density of the Pyrex nanoslits could be modified by changing the pH of the solution. It was verified that at higher pH values the nanoslit conductance increased. Field-effect experiments allowed changing the effective surface charge density as well. The polarity of the external voltage could be chosen such that the effective surface charge density was increased or decreased, resulting in a higher or lower nanoslit conductance. This regulation of ionic flow can be exploited for the fabrication of nanofluidic devices.
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47.70.Fw Chemically reactive flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
82.45.Hk Electrolysis
82.45.Gj Electrolytes
82.45.Rr Electroanalytical chemistry
82.80.Fk Electrochemical methods

Droplet formation and ejection from a micromachined ultrasonic droplet generator: Visualization and scaling

J. M. Meacham, M. J. Varady, F. L. Degertekin, and A. G. Fedorov

Phys. Fluids 17, 100605 (2005); http://dx.doi.org/10.1063/1.1921249 (8 pages) | Cited 19 times

Online Publication Date: 3 October 2005

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Visualization and scaling of drop-on-demand and continuous-jet fluid atomization of water are presented to elucidate the fluid physics of the ejection process and characterize the modes of operation of a novel micromachined ultrasonic droplet generator. The device comprises a fluid reservoir that is formed between a bulk ceramic piezoelectric transducer and an array of liquid horn structures wet etched into (100) silicon. At resonance, the transducer generates a standing ultrasonic pressure wave within the cavity and the wave is focused at the tip of the nozzle by the horn structure. Device operation has been demonstrated by water droplet ejection from 5 to 10 μm orifices at multiple resonant frequencies between 1 and 5 MHz. The intimate interactions between focused ultrasonic pressure waves and capillary waves formed at the liquid–air interface located at the nozzle tip are found to govern the ejection dynamics, leading to different ejection modalities ranging from individual droplets to continuous jet. Specifically, we report the results of high-resolution stroboscopic optical imaging of the liquid–air interface evolution during acoustic pumping to elucidate the role of capillary waves in the droplet formation and ejection process. A basic understanding of the governing physics gained through careful visualization and scaling forms the basis for development of improved theoretical models for the droplet formation and ejection processes by accounting for key fluid mechanical features of the phenomena.
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47.55.D- Drops and bubbles
47.55.Kf Particle-laden flows
47.27.wg Turbulent jets
47.60.-i Flow phenomena in quasi-one-dimensional systems
43.35.Ei
43.38.Fx
85.50.-n Dielectric, ferroelectric, and piezoelectric devices
77.65.-j Piezoelectricity and electromechanical effects
77.84.Ek Niobates and tantalates
77.84.Cg PZT ceramics and other titanates

Characterization of surface roughness effects on pressure drop in single-phase flow in minichannels

Satish G. Kandlikar, Derek Schmitt, Andres L. Carrano, and James B. Taylor

Phys. Fluids 17, 100606 (2005); http://dx.doi.org/10.1063/1.1896985 (11 pages) | Cited 51 times

Online Publication Date: 3 October 2005

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Roughness features on the walls of a channel wall affect the pressure drop of a fluid flowing through that channel. This roughness effect can be described by (i) flow area constriction and (ii) increase in the wall shear stress. Replotting the Moody’s friction factor chart with the constricted flow diameter results in a simplified plot and yields a single asymptotic value of friction factor for relative roughness values of ε/D>0.03 in the fully developed turbulent region. After reviewing the literature, three new roughness parameters are proposed (maximum profile peak height Rp, mean spacing of profile irregularities RSm, and floor distance to mean line Fp). Three additional parameters are presented to consider the localized hydraulic diameter variation (maximum, minimum, and average) in future work. The roughness ε is then defined as Rp+Fp. This definition yields the same value of roughness as obtained from the sand-grain roughness [ H. Darcy, Recherches Experimentales Relatives au Mouvement de L’Eau dans les Tuyaux (Mallet-Bachelier, Paris, France, 1857) ; J. T. Fanning, A Practical Treatise on Hydraulic and Water Supply Engineering (Van Nostrand, New York, 1877, revised ed. 1886) ; J. Nikuradse, “Laws of flow in rough pipes” [“Stromungsgesetze in Rauen Rohren,” VDI-Forschungsheft 361 (1933)]; Beilage zu “Forschung auf dem Gebiete des Ingenieurwesens,” Ausgabe B Band 4, English translation NACA Tech. Mem. 1292 (1937) ]. Specific experiments are conducted using parallel sawtooth ridge elements, placed normal to the flow direction, in aligned and offset configurations in a 10.03 mm wide rectangular channel with variable gap (resulting hydraulic diameters of 325 μm–1819 μm with Reynolds numbers ranging from 200 to 7200 for air and 200 to 5700 for water). The use of constricted flow diameter extends the applicability of the laminar friction factor equations to relative roughness values (sawtooth height) up to 14%. In the turbulent region, the aligned and offset roughness arrangements yield different results indicating a need to further characterize the surface features. The laminar to turbulent transition is also seen to occur at lower Reynolds numbers with an increase in the relative roughness.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.nb Boundary layer turbulence
47.27.N- Wall-bounded shear flow turbulence
68.35.B- Structure of clean surfaces (and surface reconstruction)
47.27.Cn Transition to turbulence
47.27.Jv High-Reynolds-number turbulence
47.15.G- Low-Reynolds-number (creeping) flows

Flow of gaseous mixtures through rectangular microchannels driven by pressure, temperature, and concentration gradients

S. Naris, D. Valougeorgis, D. Kalempa, and F. Sharipov

Phys. Fluids 17, 100607 (2005); http://dx.doi.org/10.1063/1.1896986 (12 pages) | Cited 8 times

Online Publication Date: 3 October 2005

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The flow of binary gaseous mixtures through rectangular microchannels due to small pressure, temperature, and molar concentration gradients over the whole range of the Knudsen number is studied. The solution is based on a mesoscale approach, formally described by two coupled kinetic equations, subject to diffuse scattering boundary conditions. The model proposed by McCormack substitutes the complicated collision term and the resulting kinetic equations are solved by an accelerated version of the discrete velocity method. Typical results are presented for the flow rates and the heat fluxes of two different binary mixtures (Ne–Ar and He–Xe) with various molar concentrations, in two-dimensional microchannels of different aspect (height to width) ratios. The formulation is very efficient and can be used instead of the classical method of solving the Navier–Stokes equations with slip boundary conditions, which is restricted by the hydrodynamic regime. Moreover, the present formulation is a good alternative to the direct simulation Monte Carlo method, which often becomes computationally inefficient.
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47.11.-j Computational methods in fluid dynamics
47.45.-n Rarefied gas dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems

Spreading behavior of an impacting drop on a structured rough surface

D. Sivakumar, K. Katagiri, T. Sato, and H. Nishiyama

Phys. Fluids 17, 100608 (2005); http://dx.doi.org/10.1063/1.2033627 (10 pages) | Cited 15 times

Online Publication Date: 3 October 2005

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The spreading of water drops impinging on structured rough surfaces is studied experimentally. The rough surfaces are specially prepared with a regular pattern of surface asperities. The arrangement of the square-shaped surface asperities creates channel-like grooves on the surface. A video microscope along with a controlled light exposure system is used to construct the image sequences of the spreading process. The images are digitally analyzed to measure the temporal variation of the spreading drop diameter 2R. Results are obtained for three rough surfaces with varying asperity heights in the range of 100–500 μm and for different impact drop conditions with Weber number We in the range of 35–225. The results on the temporal variation of 2R show that, on the structured rough surfaces, the spreading occurs simultaneously both inside and above the texture pattern of the surfaces. For a given surface geometry, the volume of liquid flowing inside the grooves of the surface increases with increasing We. Consequently, the values of 2R measured inside the texture pattern are larger than those measured above the texture pattern, and their difference increases with increasing We. The arrangement of the surface asperities influences the spreading pattern of an impacting drop spreading axisymmetrically. For the texture geometry used in the present study, the spreading pattern resembles a regular rhombus shape for the impact of low We drops and becomes complex at high We. The spreading distances, measured both inside and above the texture pattern of the structured rough surfaces, are nearer to the measurements recorded on the smooth surface if the asperity height of the rough surface is smaller than the thickness of the spreading liquid lamella; however, the surface asperities influence the spreading pattern drastically and create a liquid splash.
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47.55.D- Drops and bubbles
47.55.Kf Particle-laden flows
68.08.Bc Wetting
47.54.-r Pattern selection; pattern formation

The usefulness of higher-order constitutive relations for describing the Knudsen layer

Duncan A. Lockerby, Jason M. Reese, and Michael A. Gallis

Phys. Fluids 17, 100609 (2005); http://dx.doi.org/10.1063/1.1897005 (6 pages) | Cited 13 times

Online Publication Date: 3 October 2005

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Show Abstract
The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad’s 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight.
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47.11.-j Computational methods in fluid dynamics
47.45.Dt Free molecular flows
47.45.Gx Slip flows and accommodation

Molecular number flux detection using oxygen sensitive luminophore

Hideo Mori, Tomohide Niimi, Madoka Hirako, and Hiroyuki Uenishi

Phys. Fluids 17, 100610 (2005); http://dx.doi.org/10.1063/1.1921927 (6 pages) | Cited 7 times

Online Publication Date: 3 October 2005

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Experimental analyses of thermofluid phenomena with a high Knudsen number, related to low-density gas flows or nanotechnologies, need the measurement techniques based on atoms or molecules, such as emission and absorption of photons. Because the principle of the pressure sensitive paint (PSP) technique is based on oxygen quenching of luminescence, the technique has the capability to be applied to high Knudsen number flows such as microflows and low-density gas flows. In this study, to inspect the feasibility of PSP for measurement of pressure on a solid surface in high Knudsen number flows, fundamental properties of three types of PSP [palladium tetrakis (pentafluorophenyl) porphyrin, palladium octaethylporphyrin (PdOEP), and platinum tetrakis (pentafluorophenyl) porphyrin bound by poly[1–(trimethylsilyl)-1–propyne] (poly(TMSP))] are examined especially in the range of pressure below 130 Pa (about 1 Torr). As an application of PSP to high Knudsen number flows, we measure the pressure distribution on a jet-impinging solid surface using PdOEP/poly(TMSP) with very high sensitivity. Moreover, the “pressure” distribution obtained by the PSP is compared with the distribution of the molecular number flux onto the solid surface to investigate the feasibility of number flux measurement by PSP.
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47.80.-v Instrumentation and measurement methods in fluid dynamics
47.45.Dt Free molecular flows
47.27.wg Turbulent jets
78.55.Kz Solid organic materials

Oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes

Nicolas G. Hadjiconstantinou

Phys. Fluids 17, 100611 (2005); http://dx.doi.org/10.1063/1.1874193 (9 pages) | Cited 20 times

Online Publication Date: 3 October 2005

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We investigate oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes. Analytical results valid through slip flow and the early transition regime are obtained using a recently proposed, rigorous second-order slip model with no adjustable coefficients. Analytical solution of the collisionless Boltzmann equation provides a description of the high Knudsen number limit (Kn⪢1) including the bounded shear layers present in the limit of high oscillation frequency. These layers are analogous to the Stokes layers observed in the Kn⪡1 limit, but contrary to the latter, they exhibit a nonconstant wave speed as demonstrated by Park, Bahukudumbi, and Beskok in Phys. Fluids. 16, 317 (2004) . All theoretical results are validated by direct Monte Carlo simulations. We find that the second-order slip results are in good agreement with direct simulation Monte Carlo (DSMC) solutions up to Kn ≈ 0.4; in some cases these results continue to provide useful approximations to quantities of engineering interest, such as the shear stress, well beyond Kn ≈ 0.5. The collisionless theory provides, in general, a good description of DSMC results for Kn≳10, while in the high frequency limit the agreement is very good for Knundsen numbers as low as Kn ≈ 5.
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47.45.Dt Free molecular flows
47.45.Gx Slip flows and accommodation
47.35.-i Hydrodynamic waves
47.27.N- Wall-bounded shear flow turbulence
47.11.-j Computational methods in fluid dynamics

Liquids: The holy grail of microfluidic modeling

Mohamed Gad-el-Hak

Phys. Fluids 17, 100612 (2005); http://dx.doi.org/10.1063/1.1897009 (13 pages) | Cited 12 times

Online Publication Date: 3 October 2005

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Traditional fluid mechanics edifies the indifference between liquid and gas flows as long as certain similarity parameters—most prominently the Reynolds number—are matched. This may or may not be the case for flows in nanodevices or microdevices. The customary continuum, Navier–Stokes modeling is ordinarily applicable for both air and water flowing in macrodevices. Even for common fluids such as air or water, such modeling is bound to fail at sufficiently small scales, but the onset for such failure is different for the two forms of matter. Moreover, when the no-slip, quasiequilibrium Navier–Stokes system is no longer applicable, the alternative modeling schemes are different for gases and liquids. For dilute gases, statistical methods are applied and the Boltzmann equation is the cornerstone of such approaches. For liquid flows, the dense nature of the matter precludes the use of the kinetic theory of gases, and numerically intensive molecular dynamics simulations are the only alternative rooted in first principles. The present paper discusses the above issues as well as outlines physical phenomena unique to liquid flows in minute devices.
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47.85.Np Fluidics
47.85.Gj Aerodynamics
47.40.-x Compressible flows; shock waves
47.10.-g General theory in fluid dynamics

Current and current fluctuations in quantum shuttles

Antti-Pekka Jauho, Christian Flindt, Tomáš Novotný, and Andrea Donarini

Phys. Fluids 17, 100613 (2005); http://dx.doi.org/10.1063/1.1949207 (8 pages) | Cited 4 times

Online Publication Date: 3 October 2005

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We review the properties of electron shuttles, i.e., nanoelectromechanical devices that transport electrons one by one by utilizing a combination of electronic and mechanical degrees of freedom. We focus on the extreme quantum limit, where the mechanical motion is quantized. We introduce the main theoretical tools needed for the analysis, e.g., generalized master equations and Wigner functions, and we outline the methods how the resulting large numerical problems can be handled. Illustrative results are given for current, noise, and full counting statistics for a number of model systems. Throughout the review we focus on the physics behind the various approximations, and some simple examples are given to illustrate the theoretical concepts. We also comment on the experimental situation.
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85.35.Ds Quantum interference devices
85.85.+j Micro- and nano-electromechanical systems (MEMS/NEMS) and devices
72.70.+m Noise processes and phenomena
73.23.-b Electronic transport in mesoscopic systems
07.10.Cm Micromechanical devices and systems
01.30.Rr Surveys and tutorial papers; resource letters

Transient micromixing: Examples of laminar and chaotic stirring

James P. Gleeson

Phys. Fluids 17, 100614 (2005); http://dx.doi.org/10.1063/1.1928627 (9 pages) | Cited 18 times

Online Publication Date: 3 October 2005

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The efficiency of a micromixing device may be quantified by the time taken for a given initial state of separated fluids to reach a desired level of homogenization. In the physically relevant case of high Peclet number the accurate prediction of the mixing time is a challenging problem, even in simple two-dimensional flows within bounded domains. In this paper a closed-form solution for the time dependence of mixing in an annular micromixer is derived and verified by numerical simulation. The mixing time is found to scale with Peclet number as a power law, but the power-law exponent depends on the level of homogeneity desired in the final state. Numerical simulation of a recent model of chaotic mixing reveals a vortexlike stirring effect in quasiperiodic islands of the Poincaré map of the flow, which strongly influences the mixing time. This stirring effect is identified with an exponential decrease in solute variance on an intermediate time scale, being subdominant to the asymptotic long-time decay, but sensitive to the initial loading of fluids in the mixer. The subdominant decay rate is calculated to scale with Peclet number as the square root of the dominant decay rate.
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47.15.Cb Laminar boundary layers
47.52.+j Chaos in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.Ff Separated flows
47.32.C- Vortex dynamics
47.11.-j Computational methods in fluid dynamics
02.30.Uu Integral transforms

The impact of subcontinuum gas conduction on topography measurement sensitivity using heated atomic force microscope cantilevers

Nathan D. Masters, Wenjing Ye, and William P. King

Phys. Fluids 17, 100615 (2005); http://dx.doi.org/10.1063/1.1932313 (8 pages) | Cited 13 times

Online Publication Date: 3 October 2005

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Nanometer-scale topographical imaging using heated atomic force microscope (AFM) cantilevers, referred to here as thermal sensing AFM (TSAFM), is a promising technology for high resolution topographical imaging of nanostructured surfaces. Heated AFM cantilevers were developed for high-density data storage, where the heated cantilever tip can form and detect 20 nm indents made in a thermoplastic polymer. The scan height of the cantilever heater platform is typically near 500 nm, but could be made much smaller to improve reading sensitivity. Under atmospheric conditions the continuum models used in previous studies to model the gas phase heat transfer are invalid for the smallest operating heights. The present study uses a molecular model of subcontinuum heat transfer coupled with a finite difference simulation to predict the behavior of a TSAFM system. A direct simulation Monte Carlo model and a kinetic theory based macromodel are separately developed and used to model subcontinuum gas conduction. For the working gas (argon) the simple macromodel is found to be accurate and is used to predict cantilever operation. This systems-level modeling approach for TSAFM operation can aid data interpretation and seeks to improve microcantilever design.
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06.30.Bp Spatial dimensions (e.g., position, lengths, volume, angles, and displacements)
07.79.Lh Atomic force microscopes
61.46.-w Structure of nanoscale materials
44.10.+i Heat conduction
51.10.+y Kinetic and transport theory of gases
02.50.Ng Distribution theory and Monte Carlo studies
02.70.Bf Finite-difference methods

Boundary-layer exchange by bubble: A novel method for generating transient nanofluidic layers

Herbert P. Jennissen

Phys. Fluids 17, 100616 (2005); http://dx.doi.org/10.1063/1.1990207 (9 pages) | Cited 2 times

Online Publication Date: 26 October 2005

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Unstirred layers (i.e., Nernst boundary layers) occur on every dynamic solid-liquid interface, constituting a diffusion barrier, since the velocity of a moving liquid approaches zero at the surface (no slip). If a macromolecule-surface reaction rate is higher than the diffusion rate, the Nernst layer is solute depleted and the reaction rate becomes mass-transport limited. The thickness of a Nernst boundary layer (δN) generally lies between 5 and 50 μm. In an evanescent wave rheometer, measuring fibrinogen adsorption to fused silica, we made the fundamental observation that an air bubble preceding the sample through the flow cell abolishes the mass-transport limitation of the Nernst diffusion layer. Instead exponential kinetics are found. Experimental and simulation studies strongly indicate that these results are due to the elimination of the Nernst diffusion layer and its replacement by a dynamic nanofluidic layer (δν) maximally 200–300 nm thick. It is suggested that the air bubble leads to a transient boundary-layer separation into a novel nanoboundary layer on the surface and the bulk fluid velocity profile separated by a vortex sheet with an estimated lifetime of 30–60 s. A bubble-induced boundary-layer exchange from the Nernst to the nanoboundary layer and back is obtained, giving sufficient time for the measurement of unbiased exponential surface kinetics. Noteworthy is that the nanolayer can exist at all and displays properties such as (i) a long persistence and resistance to dissipation by the bulk liquid (boundary-layer-exchange-hysteresis) and (ii) a lack of solute depletion in spite of boundary-layer separation. The boundary-layer-exchange by bubble (BLEB) method therefore appears ideal for enhancing the rates of all types of diffusion-limited macromolecular reactions on surfaces with contact angles between 0° and 90° and only appears limited by slippage due to nanobubbles or an air gap beneath the nanofluidic layer on very hydrophobic surfaces. The possibility of producing nanoboundary layers without any nanostructuring or nanomachining should also be useful for fundamental physical studies in nanofluidics.
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47.55.Kf Particle-laden flows
47.55.D- Drops and bubbles
47.32.C- Vortex dynamics
47.32.Ff Separated flows
68.43.Mn Adsorption kinetics
82.65.+r Surface and interface chemistry; heterogeneous catalysis at surfaces
87.15.R- Reactions and kinetics
87.15.K- Molecular interactions; membrane-protein interactions
87.14.E- Proteins
68.03.Cd Surface tension and related phenomena
68.35.Fx Diffusion; interface formation
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Nonlinear oscillations and collapse of elongated bubbles subject to weak viscous effects

Kostas Tsiglifis and Nikos A. Pelekasis

Phys. Fluids 17, 102101 (2005); http://dx.doi.org/10.1063/1.2083947 (18 pages) | Cited 7 times

Online Publication Date: 4 October 2005

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The weak viscous oscillations of a bubble are examined, in response to an elongation that perturbs the initial spherical shape at equilibrium. The flow field in the surrounding liquid is split in a rotational and an irrotational part. The latter satisfies the Laplacian and can be obtained via an integral equation. A hybrid boundary-finite element method is used in order to solve for the velocity potential and shape deformation of axisymmetric bubbles. Weak viscous effects are included in the computations by retaining first-order viscous terms in the normal stress boundary condition and satisfying the tangential stress balance. An extensive set of simulations was carried out until the bubble either returned to its initial spherical shape, or broke up. For a relatively small initial elongation the bubble returned to its initial spherical state regardless of the size of the Ohnesorge number; Oh = μ/(ρRσ)1/2. For larger initial elongations there is a threshold value in Oh−1 above which the bubble eventually breaks up giving rise to a “donut” shaped larger bubble and a tiny satellite bubble occupying the region near the center of the original bubble. The latter is formed as the round ends of the liquid jets that approach each other from opposite sides along the axis of symmetry, coalesce. The size of the satellite bubble decreased as the initial elongation or Oh−1 increased. This pattern persisted for a range of large initial deformations with a decreasing threshold value of the Oh−1 as the initial deformation increased. As its equilibrium radius increases the bubble becomes more susceptible to the above collapse mode. The effect of initial bubble overpressure was also examined and it was seen that small initial overpressures, for the range of initial bubble deformations that was investigated, translate the threshold of Oh−1 to larger values while at the same time increasing the size of the satellite bubble.
Show PACS
47.35.-i Hydrodynamic waves
47.55.D- Drops and bubbles
47.55.Kf Particle-laden flows
47.32.-y Vortex dynamics; rotating fluids
47.11.-j Computational methods in fluid dynamics
47.27.wg Turbulent jets
47.54.-r Pattern selection; pattern formation
62.10.+s Mechanical properties of liquids
02.60.Nm Integral and integrodifferential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
02.70.Dh Finite-element and Galerkin methods

Thermocapillary instability of core-annular flows

Hsien-Hung Wei

Phys. Fluids 17, 102102 (2005); http://dx.doi.org/10.1063/1.2085190 (13 pages)

Online Publication Date: 13 October 2005

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Thermocapillary instability of a core-annular flow is asymptotically examined in the thin annulus limit. Two sets of scalings are established to study the interplays between base flows, interfacial tension, and thermocapillary effects. For each scaling case, an interfacial evolution equation is derived for describing the leading order stability of the system. Both linear and weakly nonlinear stabilities are examined. When the core fluid is warmer (cooler) than the wall, thermocapillarity linearly stabilizes (destabilizes) the system, and hence suppresses (promotes) the capillary instability. For a moderate thermocapillary force and a strong capillary force, the linear instability can be arrested within the weakly nonlinear regime. For a weak thermocapillary force and a moderately strong interfacial tension, the weakly nonlinear evolution is governed by a modified Kuramoto-Sivashinsky equation. The influence of thermocapillarity on the route to chaos is discussed.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.52.+j Chaos in fluid dynamics
68.03.Cd Surface tension and related phenomena
68.03.Kn Dynamics (capillary waves)

Dynamics and stability of a thin liquid film on a heated rotating disk film with variable viscosity

R. Usha, R. Ravindran, and B. Uma

Phys. Fluids 17, 102103 (2005); http://dx.doi.org/10.1063/1.2099007 (10 pages) | Cited 5 times

Online Publication Date: 17 October 2005

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A theoretical analysis of the thermal effects on the dynamics of a thin nonuniform film of a nonvolatile incompressible viscous fluid on a heated rotating disk has been considered and the effects of temperature-dependent viscosity and surface tension have been analyzed. A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and its stability characteristics have been examined using linear theory. It has been observed that the infinitesimal disturbances decay for small wave numbers and are transiently stable for large wave numbers, for both zero and nonzero values of Biot number.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.32.-y Vortex dynamics; rotating fluids
68.15.+e Liquid thin films
66.20.-d Viscosity of liquids; diffusive momentum transport
68.03.Cd Surface tension and related phenomena

Steady and transient thin-jet flow

Radoslav German and Roger E. Khayat

Phys. Fluids 17, 102104 (2005); http://dx.doi.org/10.1063/1.2103147 (21 pages) | Cited 2 times

Online Publication Date: 17 October 2005

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The interplay between inertia and gravity is examined in this theoretical study for the steady and transient two-dimensional thin jet flow free of surface tension. The fluid emerges from a channel and is driven by both a pressure gradient maintained inside the channel and/or gravity. The flow is dictated by the thin-film equations of the boundary layer type, which are solved by expanding the flow field in terms of orthonormal modes depthwise, and using the Galerkin projection. The strength of inertia relative to gravity is found to be of crucial significance on the film flow. Transient behavior of the film is closely examined for various flow parameters, initial and exit conditions. It is shown that under a wide range of flow parameters, the steady state cannot be achieved.
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47.27.wg Turbulent jets
47.20.-k Flow instabilities
47.35.-i Hydrodynamic waves
47.60.-i Flow phenomena in quasi-one-dimensional systems
02.70.Dh Finite-element and Galerkin methods

Dip coating in the presence of a substrate-liquid interaction potential

R. Krechetnikov and G. M. Homsy

Phys. Fluids 17, 102105 (2005); http://dx.doi.org/10.1063/1.2107927 (7 pages) | Cited 6 times

Online Publication Date: 19 October 2005

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In this work we investigate theoretically the Landau-Levich problem of dip coating in the presence of a strong interaction potential normal to the substrate. This study is motivated by dip coating at very low capillary numbers when the deposited film thickness is less than 1 μm and such interaction forces become important. The objective of this work is to demonstrate that in the presence of an extra body force the solution procedure differs significantly from the classical one and leads to substantial deviations from the Landau-Levich law for the entrained film thickness. In particular, attractive potentials produce film thickening and the resulting film thickness is independent of speed to lowest order. Repulsive potentials bring about more complicated behavior and lead either to films whose thickness is also independent of speed, or to a modification of the leading order constant in the classical Ca2/3 law. Demonstration of these effects is given for a model potential. The analysis is generally applicable to many physical situations when there is an interaction between a coating liquid and a substrate, e.g., dip coating of ferromagnetic liquids on magnetic substrates, or dip coating of liquids carrying charges.
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81.15.Lm Liquid phase epitaxy; deposition from liquid phases (melts, solutions, and surface layers on liquids)
68.55.A- Nucleation and growth

Laser-induced motion in nanoparticle suspension droplets on a surface

Mathias Dietzel and Dimos Poulikakos

Phys. Fluids 17, 102106 (2005); http://dx.doi.org/10.1063/1.2098587 (12 pages) | Cited 10 times

Online Publication Date: 21 October 2005

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The fluid and particle motion in a volatile colloidal nanoparticle suspension droplet (“nano-ink”) spreading on a flat surface upon local heating through a laser beam is investigated numerically. The laser diameter, laser intensity, and the absorption coefficient of the nano-ink as well as the substrate thermal diffusivity were varied. The simulations are conducted with a finite-element method discretization of the extended axisymmetric Navier-Stokes equations in Lagrangian coordinates, accounting for evaporation, thermocapillarity, and Young-force-driven wetting for the fluid phase as well as for inertia-controlled particle motion for the solid phase. An additional continuous particle coagulation model with a locally monodispersed particle distribution is solved on the locations of the discrete computational particles for example cases. The localized heating leads, through the action of thermocapillarity, to a displacement of the liquid in the radial (outward) direction. A dimple in the droplet center region is formed as a consequence, which becomes flattened for larger laser beam diameters due to a significant enlargement in spreading. Substrates with high thermal diffusivity or large thermal contact resistance to the liquid can inhibit the Marangoni-induced enlargement of the droplet footprint. The coagulation model predicts for large absorption coefficients particle clustering primarily at the free surface, which prevents the formation of structures (built by the coagulated nanoparticles) with a uniform thickness.
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47.55.D- Drops and bubbles
47.55.Kf Particle-laden flows
47.27.tb Turbulent diffusion
47.27.T- Turbulent transport processes
47.11.-j Computational methods in fluid dynamics
47.10.-g General theory in fluid dynamics
68.08.Bc Wetting
68.03.Cd Surface tension and related phenomena
68.03.Fg Evaporation and condensation of liquids
02.70.Dh Finite-element and Galerkin methods

Interfacial waves due to a singularity in a system of two semi-infinite fluids

D. Q. Lu and Allen T. Chwang

Phys. Fluids 17, 102107 (2005); http://dx.doi.org/10.1063/1.2120447 (9 pages) | Cited 4 times

Online Publication Date: 28 October 2005

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The three-dimensional interfacial waves due to a fundamental singularity steadily moving in a system of two semi-infinite immiscible fluids of different densities are investigated analytically. The two fluids are assumed to be incompressible and homogenous. There are three systems to be considered: one with two inviscid fluids, one with an upper viscous and a lower inviscid fluid, and one with an upper inviscid and a lower viscous fluid. The Laplace equation is taken as the governing equation for inviscid flows while the steady Oseen equations are taken for viscous flows. The kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity immersed above or beneath the interface is modeled as a simple source in the inviscid fluid while as an Oseenlet in the viscous fluid. Based on the integral solutions for the interfacial waves, the asymptotic representations of wave profiles in the far field are explicitly derived by means of Lighthill’s two-stage scheme. An analytical solution is presented for the density ratio at which the maximum wave amplitude occurs. The effects of density ratio, immersion depth, and viscosity on wave patterns are analytically expressed. It is found that the wavelength of interfacial waves is elongated in comparison with that of free-surface waves in a single fluid.
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47.35.-i Hydrodynamic waves
47.54.-r Pattern selection; pattern formation
02.30.Jr Partial differential equations
02.30.Rz Integral equations

Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

R. Krechetnikov and G. M. Homsy

Phys. Fluids 17, 102108 (2005); http://dx.doi.org/10.1063/1.2112647 (16 pages) | Cited 14 times

Online Publication Date: 31 October 2005

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In this work we present an experimental study of deviations from the classical Landau-Levich law in the problem of dip coating. Among the examined causes leading to deviations are the nature of the liquid-gas and liquid-solid interfaces. The thickness of the coating film created by withdrawal of a plate from a bath was measured gravimetrically over a wide range of capillary numbers for both smooth and well-characterized rough substrates, and for clean and surfactant interface cases. In view of the dependence of the lifetime of a film on the type of liquid and substrate, and liquid-gas and liquid-solid interfaces, we characterized the range of measurability of the film thickness in the parameter space defined by the withdrawal capillary number, the surfactant concentration, and substrate roughness size. We then study experimentally the effect of a film thickening due to the presence of surfactants. Our recent theory based on a purely hydrodynamic role of the surface active substance suggests that there is a sorption-controlled coating regime in which Marangoni effects should lead to film thinning. However, our experiments conducted in this regime demonstrate film thickening, calling into question the conventional wisdom, which is that Marangoni stresses (as accounted by the conventional interfacial boundary conditions) lead to film thickening. Next we examine the effect of well-characterized substrate roughness on the coated film thickness, which also reveals its influence on wetting-related processes and an effective boundary condition at the wall. In particular, it is found that roughness results in a significant thickening of the film relative to that on a smooth substrate and a different power of capillary number than the classical Landau-Levich law.
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68.15.+e Liquid thin films
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
68.43.Mn Adsorption kinetics
68.35.B- Structure of clean surfaces (and surface reconstruction)
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