Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session EY: Instability: Interfacial and Thin Film III |
Hide Abstracts |
Chair: George M. Homsy, University of British Columbia Room: Hyatt Regency Long Beach Regency E |
Sunday, November 21, 2010 4:10PM - 4:23PM |
EY.00001: Surface temperature reconstruction based on the thermocapillary effect Mathieu Sellier, Satyananda Panda A thin liquid film subject to a temperature gradient is known to deform under the action of thermocapillary stresses which induce convective cells. The free surface deformation can be thought of as the signature of the imposed temperature gradient and this study investigates the inverse problem of trying to reconstruct the temperature field from known free surface variations. The present work builds on the analysis of Tan et al. [Phys. Fluids A {\bf 2}, 313 (1990)] which provides a long- wave evolution equation for the fluid film thickness variation on non-uniformly heated substrates and proposes a solution strategy for the plane flow version of this inverse problem. The analysis reveals a particular case for which there exists an explicit, closed-form solution expressing the local surface temperature in terms of the local film thickness and its spatial derivatives. With some simplifications, the analysis also shows that this solution applies to three-dimensional flows. The temperature reconstruction strategies are successfully tested against ``artificial'' experimental data (obtained by solving the direct problem for known temperature profiles) and actual experimental ones from Burelbach et al., [Phys. Fluids A {\bf 2}, 322 (1990)]. [Preview Abstract] |
Sunday, November 21, 2010 4:23PM - 4:36PM |
EY.00002: Oscillatory surface patterns in a heated thin film of a binary mixture Michael Bestehorn We study a thin liquid film with a free surface on a uniformly heated substrate. The film consists of a mixture of two arbitrarily miscible fluids. The surface tension depends both on temperature and on relative concentration of the mixture. Using lubrication approximation, a systematic derivation of the extended thin film equation is performed. The resulting coupled system of two conservation equations (mean thickness and mean concentration) is discussed by a linear stability analysis of the flat film. It turns out that for a large region in parameter space oscillatory (Hopf) instabilities are obtained which are long-wave. Numerical solutions of the non-linear problem finally show a rich spatio-temporal behavior of the film's surface in form of traveling spots and holes or mazes having an intrinsic time dependence. [Preview Abstract] |
Sunday, November 21, 2010 4:36PM - 4:49PM |
EY.00003: Influence of vibration on thermocapillary instability in a binary mixture with Soret effect Irina Fayzrakhmanova, Sergey Shklyaev, Alexander A. Nepomnyashchy Influence of vibration on the onset of Marangoni convection in a layer of a binary mixture with the Soret effect is studied in the framework of the linear stability theory. At the rigid bottom boundary of the layer a fixed heat flux is specified; the free top boundary is assumed to be nondeformable. The vibration frequency is low, the amplitude is sufficiently large to provide finite values of the inertia force. Formerly, the stability with respect to longwave disturbances was studied [1]. In the present talk, the analysis is extended to the case of arbitrary wavenumbers. The Wentzel-Kramers-Brillouin (WKB) method is applied for the computation of growth rates of disturbances with finite wavenumbers. It is shown that the longwave mode is critical only within a certain interval of the Soret number. Outside of that interval, either monotonic or oscillatory mode with a finite value of the wavenumber is critical. The authors acknowledge the support of joint grants of IMS (No. 3-5799) and RFBR (No.09-01-92472); grant of the EU PITN- GA-2008-214919 (MULTIFLOW) and ISF (No. 680/10). [1] I.S. Fayzrakhmanova, S. Shklyaev, A.A. Nepomnyashchy, (submitted to Phys. Fluids). [Preview Abstract] |
Sunday, November 21, 2010 4:49PM - 5:02PM |
EY.00004: Convection and evaporation rate of planar liquid films subjected to impulsive superheating J.T. Kimball, J.C. Hermanson, J.S. Allen The interfacial stability, convective structure, and evaporation rate of upward-facing, thin liquid films were studied experimentally. Four different working fluids were used. Films initially 5 mm to 100 $\mu $m thick were subjected to impulsive superheating. The films resided on a temperature controlled, gold-plated copper surface in a closed, initially degassed test chamber. Superheating was achieved by suddenly dropping the pressure of the saturated pure vapor in the test chamber. The dynamic film thickness was measured at multiple points using ultrasound, and instability wavelength and convective structure information was obtained by schlieren imaging. Considering previous quasi-steady results, the observed convection patterns in many cases suggest an initial, limited penetration of the convection structures into the film. The initial convection patterns and measured evaporation rate in these films are independent of the thermal boundary condition of the substrate. After a sufficiently long time, the convection pattern changes and approaches the previously observed quasi-steady condition. [Preview Abstract] |
Sunday, November 21, 2010 5:02PM - 5:15PM |
EY.00005: Influence of Gas Rarefaction on Thermocapillary Flow and Instability in Confined Nanofilms Nan Liu, Sandra Troian We have previously conducted a linear stability analysis of a fluid bilayer system sandwiched in between flat solid substrates held at different temperature [1,2]. The bilayer consists of a warm molten viscous nanofilm overlay by a cooler nanofilm of quiescent gas. Lubrication analysis showed how thermocapillary stresses along the viscous film promote formation of fluid elongations resembling nanopillar arrays no matter how small the initial transverse temperature difference. It was assumed in these studies that the rate of heat transfer through the gas layer is well described by Fourier's law of thermal conduction. For sufficiently thin gas layers, however, the mean free path for gas molecules is comparable to or can exceed the thickness of the gas layer. Collisions of the gas molecules with the cooler substrate as well as the warmer evolving viscous film can dominate intermolecular collisions in the gas film leading to temperature jump conditions first described by von Smoluchowski. In this presentation, we show how gas rarefaction effects can increase the growth rate and magnitude of the fastest growing wavelength by as much as 50{\%} for parameter values relevant to experiment. \newline [1] M. Dietzel and S. M. Troian, Phys. Rev. Lett. \textbf{103}, 074501 (2009). [2] M. Dietzel and S. M. Troian, J. Appl. Phys., in press (2010). [Preview Abstract] |
Sunday, November 21, 2010 5:15PM - 5:28PM |
EY.00006: Thermocapillary convection in a cylindrical liquid bridge -- Effect of the ambient gas Michael Lukasser, Daniel Lanzerstorfer, Hendrik Kuhlmann The influence of the ambient gas phase on the stability of the two- dimensional axisymmetric steady flow in a cylindrical liquid bridge is investigated by a numerical linear stability analysis. The computational domain includes an annular gas channel which concentrically surrounds the liquid bridge. The stability boundaries strongly depend on the geometry and the material parameters. We consider a liquid bridge of ${\rm Pr} = 67$ and focus on the effect of the gas-channel width and the thermophysical properties of the ambient gas. Stability boundaries, critical modes and mechanisms will be discussed. [Preview Abstract] |
Sunday, November 21, 2010 5:28PM - 5:41PM |
EY.00007: Influence of adsorption kinetics on the Marangoni convection in a binary liquid layer with a soluble surfactant Alexander A. Nepomnyashchy, Sergey Shklyaev We consider dynamics of a heated binary liquid in a horizontal layer. The solute is a soluble surfactant, which forms a surface phase and a bulk phase. Both the Soret effect and the adsorption kinetics are taken into account. Within the linear stability problem we demonstrate that the adsorption kinetics leads to a significant stabilization of the quiescent state with respect to oscillatory and monotonic longwave modes and a short-wave oscillatory mode. For the latter mode the stabilization is especially strong. Weakly-nonlinear analysis is carried out for the longwave modes, it results in an ill-posed set of amplitude equations. A subcritical bifurcation for both longwave modes is predicted, no nonlinear saturation takes place in the supercritical region. In a number of limiting cases more intricate amplitude equations are obtained; for the fast adsorption kinetics a transition between supercritical and subcritical bifurcations is found. [Preview Abstract] |
Sunday, November 21, 2010 5:41PM - 5:54PM |
EY.00008: Thermocapillary fluid pumping using traveling thermal waves Alex Oron, Wenbin Mao, Alexander Alexeev We use direct numerical simulations of the full Navier-Stokes and energy equations and the analysis based on the long-wave approximation to examine the dynamics of thin liquid films on substrates with periodic heating. Substrate temperature varies according to a sinusoidal law and creates periodic thermal waves that propagate unidirectionally along the substrate. Using the two modeling techniques, we probe how the traveling thermal waves can be harnessed to induce and regulate directed fluid flows in the liquid film. We examine emerging flow structures, film deformation, and characterize the fluid flow in terms of relevant dimensionless parameters. Furthermore, we identify the optimal parameters leading to the efficient fluid pumping. The results of our studies can be useful for designing open microfluidic devices, in which the thermocapillary pumping is employed for controlled transport of samples in free-surface liquid films. [Preview Abstract] |
Sunday, November 21, 2010 5:54PM - 6:07PM |
EY.00009: On the unsteady Benard -- Marangoni problem Itzchak Frankel, Michael Weidenfeld The Benard -- Marangoni instability originating from the coupling between a non-uniform liquid -- surface temperature and convection across a favorable temperature gradient is a classic problem in hydrodynamic stability theory. We study the linear temporal stability problem focusing on short times when perturbations evolve on the background of a non-linear unsteady temperature distribution across the liquid layer. Accordingly, we analyze the initial -- value (rather than the standard eigenvalue) problem and obtain a Volterra -- type integral equation governing the evolution of perturbations. The results indicate that the onset of convection at short times is effectively confined to the narrow thermal boundary layer developing next to the liquid surface and is dominated by short -- wavelength perturbations. Increasing the Prandtl number is found to be destabilizing. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700