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Nov 2011

Volume 23, Issue 11, Articles (11xxxx)

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Phys. Fluids 23, 111701 (2011); http://dx.doi.org/10.1063/1.3651269 (4 pages)

A. Mashayek and W. R. Peltier
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back to top Interfacial Flows

Shock-wave solutions in two-layer channel flow. II. Linear and nonlinear stability

A. Mavromoustaki, O. K. Matar, and R. V. Craster

Phys. Fluids 23, 112101 (2011); http://dx.doi.org/10.1063/1.3654191 (20 pages) | Cited 1 time

Online Publication Date: 1 November 2011

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We investigate the flow of two immiscible fluids in an inclined channel, building on the work presented in Part I of this study. In this paper, we examine the stability of the flow to spanwise perturbations in both the linear and nonlinear regimes. The evolution equation governing the interfacial dynamics, derived using lubrication theory in Part I, is linearised to study the effect of system parameters on the linear stability of the interface. A transient growth analysis of the linearised equation is carried out with no-flux conditions in the spanwise direction. The results of this analysis reveal that increasing the density and/or the viscosity of the upper layer, and/or increasing the counter-current nature of the flow configuration exerts a stabilising influence. Inspection of the flow profiles indicates that single Lax-shocks and the trailing Lax-shocks in Lax-undercompressive double-shocks are unstable to finger formation; undercompressive shocks and rarefaction waves are stable. In unstably stratified cases, increasing the channel inclination away from verticality, such that a denser upper layer overhangs a less dense lower one, is found to be destabilising. These results are used to guide our transient numerical simulations aimed at studying the nonlinear development of fingering phenomena.
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47.40.Nm Shock wave interactions and shock effects
47.85.mf Lubrication flows
47.60.Dx Flows in ducts and channels
02.60.Cb Numerical simulation; solution of equations
47.11.-j Computational methods in fluid dynamics
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)

Optical interference effect on pattern formation in thin liquid films on solid substrates induced by irradiative heating

Fumihiro Saeki, Shigehisa Fukui, and Hiroshige Matsuoka

Phys. Fluids 23, 112102 (2011); http://dx.doi.org/10.1063/1.3657433 (14 pages)

Online Publication Date: 9 November 2011

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The pattern formation in thin liquid films on solid substrates induced by irradiative heating is investigated. A model to describe the evolution of both the film surface profile and temperature field in the system is developed, in which the energy absorption into the film and substrate, and the energy reflection to which optical absorption and interference contribute are taken into account. The model consists of a thin film equation that describes the time evolution of the film surface profile and a heat equation for the substrate. The former is obtained within the framework of the long-wave approximation, in which the fluid layer is assumed to be sufficiently thin compared to the lateral length scale, while the latter is unconstrained by the substrate thickness. In order to examine the interference effects on the pattern formation, focus is placed on a transparent film/absorbable substrate system irradiated by a monochromatic wave with laterally uniform intensity distribution. In such a case, the energy reflectance varies periodically with the film thickness due to optical interference. Numerical simulation results show that the stability of the film depends on the first derivative of the energy reflectance with respect to the film thickness at a reference point, and the resultant surface patterns, which include phase separation and periodic wavy patterns, differ depending on the reference thickness and initial perturbation. The stability revealed by the numerical results is confirmed by linear stability analysis of a simplified model.
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47.54.Bd Theoretical aspects
68.15.+e Liquid thin films
47.20.-k Flow instabilities
47.35.-i Hydrodynamic waves

Maximum speed of dewetting on a fiber

Tak Shing Chan, Thomas Gueudré, and Jacco H. Snoeijer

Phys. Fluids 23, 112103 (2011); http://dx.doi.org/10.1063/1.3659018 (9 pages) | Cited 2 times

Online Publication Date: 11 November 2011

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A solid object can be coated by a nonwetting liquid since a receding contact line cannot exceed a critical speed. We theoretically investigate this forced wetting transition for axisymmetric menisci on fibers of varying radii. First, we use a matched asymptotic expansion and derive the maximum speed of dewetting. For all radii, we find the maximum speed occurs at vanishing apparent contact angle. To further investigate the transition, we numerically determine the bifurcation diagram for steady menisci. It is found that the meniscus profiles on thick fibers are smooth, even when there is a film deposited between the bath and the contact line, while profiles on thin fibers exhibit strong oscillations. We discuss how this could lead to different experimental scenarios of film deposition.
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68.03.Cd Surface tension and related phenomena
68.15.+e Liquid thin films

Molecular dynamics study of the processes in the vicinity of the n-dodecane vapour/liquid interface

Jian-Fei Xie, Sergei S. Sazhin, and Bing-Yang Cao

Phys. Fluids 23, 112104 (2011); http://dx.doi.org/10.1063/1.3662004 (11 pages) | Cited 2 times

Online Publication Date: 29 November 2011

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Molecular dynamics (MD) simulation is used to study the evaporation and condensation of n-dodecane (C12H26), the closest approximation to Diesel fuel. The interactions in chain-like molecular structures are modelled using an optimised potential for liquid simulation (OPLS). The thickness of the transition layer between the liquid and vapour phases at equilibrium is estimated. It is shown that molecules at the liquid surface need to obtain relatively large translational energy to evaporate. The vapour molecules with large translational energy can easily penetrate deeply into the transition layer and condense in the liquid phase. The evaporation/condensation coefficient is estimated and the results are shown to be compatible with the previous estimates based on the MD analysis and the estimate based on the transition state theory. The velocity distribution functions of molecules at the liquid-vapour equilibrium state are found in the liquid phase, interface, and the vapour phase. These functions in the liquid phase and at the interface are shown to be close to isotropic Maxwellian for all velocity components. The velocity distribution function in the vapour phase is shown to be close to bi-Maxwellian with the temperature for the distribution normal to the interface being larger than the one for the distribution parallel to the interface.
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47.55.Ca Gas/liquid flows
68.03.Fg Evaporation and condensation of liquids
02.70.Ns Molecular dynamics and particle methods
47.11.Mn Molecular dynamics methods
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