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AuthorIto, Nobuyasu (10)Qian, Tiezheng (5)Watanabe, Hiroshi (5)Bressloff, Paul C. (4)Nogawa, Tomoaki (4)View MoreJournal

Physical Review E (51)

KAUST Grant NumberKUK-C1-013-04 (18)KUK-I1-005-04 (10)KUK-C1-013-4 (5)KUS-C1-018-02 (3)KUK-C1-017-12 (1)View MorePublisherAmerican Physical Society (APS) (51)TypeArticle (51)Year (Issue Date)2015 (1)2014 (3)2013 (13)2012 (12)2011 (9)View MoreItem AvailabilityMetadata Only (43)Open Access (8)

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Saffman-Taylor fingers with kinetic undercooling

Gardiner, Bennett P. J.; McCue, Scott W.; Dallaston, Michael C.; Moroney, Timothy J. (Physical Review E, American Physical Society (APS), 2015-02-23) [Article]

© 2015 American Physical Society. The mathematical model of a steadily propagating Saffman-Taylor finger in a Hele-Shaw channel has applications to two-dimensional interacting streamer discharges which are aligned in a periodic array. In the streamer context, the relevant regularization on the interface is not provided by surface tension but instead has been postulated to involve a mechanism equivalent to kinetic undercooling, which acts to penalize high velocities and prevent blow-up of the unregularized solution. Previous asymptotic results for the Hele-Shaw finger problem with kinetic undercooling suggest that for a given value of the kinetic undercooling parameter, there is a discrete set of possible finger shapes, each analytic at the nose and occupying a different fraction of the channel width. In the limit in which the kinetic undercooling parameter vanishes, the fraction for each family approaches 1/2, suggesting that this "selection" of 1/2 by kinetic undercooling is qualitatively similar to the well-known analog with surface tension. We treat the numerical problem of computing these Saffman-Taylor fingers with kinetic undercooling, which turns out to be more subtle than the analog with surface tension, since kinetic undercooling permits finger shapes which are corner-free but not analytic. We provide numerical evidence for the selection mechanism by setting up a problem with both kinetic undercooling and surface tension and numerically taking the limit that the surface tension vanishes.

Energy spectrum of buoyancy-driven turbulence

Kumar, Abhishek; Chatterjee, Anando G.; Verma, Mahendra K. (Physical Review E, American Physical Society (APS), 2014-08-25) [Article]

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux Πu, we demonstrate that, for stably stratified flows, the kinetic energy spectrum Eu(k)∼k-11/5, the potential energy spectrum Eθ(k)∼k-7/5, and Πu(k)∼k-4/5 are consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence Eu(k) follows Kolmogorov's spectrum with a constant energy flux. For Rayleigh-Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing Πu(k) with k, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant Πu(k) and Eu(k)∼k-5/3 for a narrow band of wave numbers. © 2014 American Physical Society.

Single-bubble dynamics in pool boiling of one-component fluids

Xu, Xinpeng; Qian, Tiezheng (Physical Review E, American Physical Society (APS), 2014-06-04) [Article]

We numerically investigate the pool boiling of one-component fluids with a focus on the effects of surface wettability on the single-bubble dynamics. We employed the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], a diffuse-interface model for liquid-vapor flows involving liquid-vapor transition in nonuniform temperature fields. We first perform simulations for bubbles on homogeneous surfaces. We find that an increase in either the contact angle or the surface superheating can enhance the bubble spreading over the heating surface and increase the bubble departure diameter as well and therefore facilitate the transition into film boiling. We then examine the dynamics of bubbles on patterned surfaces, which incorporate the advantages of both hydrophobic and hydrophilic surfaces. The central hydrophobic region increases the thermodynamic probability of bubble nucleation while the surrounding hydrophilic region hinders the continuous bubble spreading by pinning the contact line at the hydrophobic-hydrophilic intersection. This leads to a small bubble departure diameter and therefore prevents the transition from nucleate boiling into film boiling. With the bubble nucleation probability increased and the bubble departure facilitated, the efficiency of heat transfer on such patterned surfaces is highly enhanced, as observed experimentally [Int. J. Heat Mass Transfer 57, 733 (2013)]. In addition, the stick-slip motion of contact line on patterned surfaces is demonstrated in one-component fluids, with the effect weakened by surface superheating.

Elastic fingering in rotating Hele-Shaw flows

Carvalho, Gabriel D.; Gadêlha, Hermes; Miranda, José A. (Physical Review E, American Physical Society (APS), 2014-05-21) [Article]

The centrifugally driven viscous fingering problem arises when two immiscible fluids of different densities flow in a rotating Hele-Shaw cell. In this conventional setting an interplay between capillary and centrifugal forces makes the fluid-fluid interface unstable, leading to the formation of fingered structures that compete dynamically and reach different lengths. In this context, it is known that finger competition is very sensitive to changes in the viscosity contrast between the fluids. We study a variant of such a rotating flow problem where the fluids react and produce a gellike phase at their separating boundary. This interface is assumed to be elastic, presenting a curvature-dependent bending rigidity. A perturbative weakly nonlinear approach is used to investigate how the elastic nature of the interface affects finger competition events. Our results unveil a very different dynamic scenario, in which finger length variability is not regulated by the viscosity contrast, but rather determined by two controlling quantities: a characteristic radius and a rigidity fraction parameter. By properly tuning these quantities one can describe a whole range of finger competition behaviors even if the viscosity contrast is kept unchanged. © 2014 American Physical Society.

Far-from-equilibrium sheared colloidal liquids: Disentangling relaxation, advection, and shear-induced diffusion

Lin, Neil Y. C.; Goyal, Sushmit; Cheng, Xiang; Zia, Roseanna N.; Escobedo, Fernando A.; Cohen, Itai (Physical Review E, American Physical Society (APS), 2013-12) [Article]

Using high-speed confocal microscopy, we measure the particle positions in a colloidal suspension under large-amplitude oscillatory shear. Using the particle positions, we quantify the in situ anisotropy of the pair-correlation function, a measure of the Brownian stress. From these data we find two distinct types of responses as the system crosses over from equilibrium to far-from-equilibrium states. The first is a nonlinear amplitude saturation that arises from shear-induced advection, while the second is a linear frequency saturation due to competition between suspension relaxation and shear rate. In spite of their different underlying mechanisms, we show that all the data can be scaled onto a master curve that spans the equilibrium and far-from-equilibrium regimes, linking small-amplitude oscillatory to continuous shear. This observation illustrates a colloidal analog of the Cox-Merz rule and its microscopic underpinning. Brownian dynamics simulations show that interparticle interactions are sufficient for generating both experimentally observed saturations. © 2013 American Physical Society.

Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study

Carvalho, Gabriel D.; Miranda, José A.; Gadêlha, Hermes (Physical Review E, American Physical Society (APS), 2013-11-11) [Article]

We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.

Intrinsic viscosity of a suspension of cubes

Mallavajula, Rajesh K.; Koch, Donald L.; Archer, Lynden A. (Physical Review E, American Physical Society (APS), 2013-11-06) [Article]

We report on the viscosity of a dilute suspension of cube-shaped particles. Irrespective of the particle size, size distribution, and surface chemistry, we find empirically that cubes manifest an intrinsic viscosity [η]=3.1±0.2, which is substantially higher than the well-known value for spheres, [η]=2.5. The orientation-dependent intrinsic viscosity of cubic particles is determined theoretically using a finite-element solution of the Stokes equations. For isotropically oriented cubes, these calculations show [η]=3.1, in excellent agreement with our experimental observations. © 2013 American Physical Society.

Shape-dependent orientation of thermophoretic forces in microsystems

Li, Qi; Liang, Tengfei; Ye, Wenjing (Physical Review E, American Physical Society (APS), 2013-09-24) [Article]

It is generally acknowledged that the direction of the thermophoretic force acting on microparticles is largely determined by the imposed temperature gradient, and the shape of the microparticle has little influence on its direction. We show that one type of thermophoretic force, emerged due to the advent of microfabrication techniques, is highly sensitive to object shape, and it is feasible to tune force orientation via proper shape design. We reveal the underlying mechanism by an asymptotic analysis of the Boltzmann equation and point out the reason why the classical thermophoretic force is insensitive to the particle shape, but the force in microsystems is. The discovered phenomenon could find its applications in methods for microparticle manipulation and separation.

Transitions through critical temperatures in nematic liquid crystals

Majumdar, Apala; Ockendon, John; Howell, Peter; Surovyatkina, Elena (Physical Review E, American Physical Society (APS), 2013-08-06) [Article]

We obtain estimates for critical nematic liquid crystal (LC) temperatures under the action of a slowly varying temperature-dependent control variable. We show that biaxiality has a negligible effect within our model and that these delay estimates are well described by a purely uniaxial model. The static theory predicts two critical temperatures: the supercooling temperature below which the isotropic phase loses stability and the superheating temperature above which the ordered nematic states do not exist. In contrast to the static problem, the isotropic phase exhibits a memory effect below the supercooling temperature in the dynamic framework. This delayed loss of stability is independent of the rate of change of temperature and depends purely on the initial value of the temperature. We also show how our results can be used to improve estimates for LC material constants. © 2013 American Physical Society.

Performance evaluation of Maxwell and Cercignani-Lampis gas-wall interaction models in the modeling of thermally driven rarefied gas transport

Liang, Tengfei; Li, Qi; Ye, Wenjing (Physical Review E, American Physical Society (APS), 2013-07-16) [Article]

A systematic study on the performance of two empirical gas-wall interaction models, the Maxwell model and the Cercignani-Lampis (CL) model, in the entire Knudsen range is conducted. The models are evaluated by examining the accuracy of key macroscopic quantities such as temperature, density, and pressure, in three benchmark thermal problems, namely the Fourier thermal problem, the Knudsen force problem, and the thermal transpiration problem. The reference solutions are obtained from a validated hybrid DSMC-MD algorithm developed in-house. It has been found that while both models predict temperature and density reasonably well in the Fourier thermal problem, the pressure profile obtained from Maxwell model exhibits a trend that opposes that from the reference solution. As a consequence, the Maxwell model is unable to predict the orientation change of the Knudsen force acting on a cold cylinder embedded in a hot cylindrical enclosure at a certain Knudsen number. In the simulation of the thermal transpiration coefficient, although all three models overestimate the coefficient, the coefficient obtained from CL model is the closest to the reference solution. The Maxwell model performs the worst. The cause of the overestimated coefficient is investigated and its link to the overly constrained correlation between the tangential momentum accommodation coefficient and the tangential energy accommodation coefficient inherent in the models is pointed out. Directions for further improvement of models are suggested.

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