Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session KF: Interfacial and Thin Film Instabilities III |
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Chair: Alexander Golovin, Northwestern University Room: Hilton Chicago Continental C |
Monday, November 21, 2005 4:10PM - 4:23PM |
KF.00001: Nonlinear Stability Analysis of a Two-Layer Thin Liquid Film: Dewetting and Autophobicity Lael Fisher, Alexander Golovin The nonlinear analysis of a two-layer thin liquid film on a solid substrate is performed. Weakly nonlinear stability analysis of nonlinear evolution equations for the two interfaces reveals that coupling of van der Waals interactions in the layers can lead to an autophobic behavior of the film, similar to spinodal decomposition. Numerical simulations of the strongly nonlinear evolution equations confirm this conclusion. The effect of both soluble and insoluble surfactants on the film stability is also studied. It is shown that the presence of surfactants can lead to an osillatory instability of a two-layer film that manifests itself as dewetting waves. [Preview Abstract] |
Monday, November 21, 2005 4:23PM - 4:36PM |
KF.00002: Instability of an interface, with large viscosity-contrast, under tangentially oscillatory motion Harunori N. Yoshikawa, Jos\'{e} E. Wesfreid We shall present here an instability which initiates a pattern formation on the interface between two viscous fluids, with very strong viscosity contrast, subjected to tangential oscillatory motion at a moderate frequency. We carried out experiments and theoretical studies. Experimental results showed that the first selected wavelength, which is far from the capillary one, is controlled by the oscillation amplitude. A quasi static model is elaborated, predicting the instability threshold and the wavelength dependence on the amplitude, in agreement with the experiments. A detailed analysis reveals that the origin of the instability is not a simple Kelvin Helmholtz type, because the pressure perturbation distribution is different. This difference lies in the contribution of the streaming effect. [Preview Abstract] |
Monday, November 21, 2005 4:36PM - 4:49PM |
KF.00003: Longwave Marangoni instability in a binary-liquid layer with deformable interface in the presence of Soret effect. The case of a finite Biot number A. Oron, A. Podolny, A. A. Nepomnyashchy We investigate the long-wave Marangoni
instability in a binary-liquid layer with a deformable
interface in the limit
of a finite Biot number $B$ and a specified heat flux at
the solid substrate and in the presence of
the Soret effect.
In the fundamental case (a) of both finite Galileo
and Lewis numbers, $G$ and $L$, respectively,
and a large inverse capillary number $S$, both
monotonic and oscillatory instabilities are present.
The monotonic instability takes place with
the critical Marangoni number $M_{mon}=48\,L\,\chi^{-1}$,
where $\chi$ is the Soret (separation) number when $-1<\chi<0$.
When $(1+\chi)/\chi >0$, this instability emerges if $L |
Monday, November 21, 2005 4:49PM - 5:02PM |
KF.00004: Strongly nonlinear interfacial-surfactant instability and diffusion Alexander Frenkel, David Halpern The nonlinear stages of the recently uncovered instability due to insoluble surfactant at the interface between two fluids in a creeping plane Couette flow are investigated for the case when one of the fluids is a thin film and the other is semi- infinite in the cross-flow direction. Numerical simulation of strongly nonlinear longwave evolution equations which couple the film thickness and the surfactant concentration, assuming the latter sufficiently small, reveals that the instability saturation is only possible when the surfactant diffusion exceeds a threshold strength whose value depends on the interfacial shear rate and other parameters. The disturbance of surfactant concentration never remains small, so the evolution never can be completely described by weakly nonlinear equations. The evolution time scale appears to grow indefinitely as the interfacial shear goes to zero and/or the surfactant diffusion strength increases. [Preview Abstract] |
Monday, November 21, 2005 5:02PM - 5:15PM |
KF.00005: Monolayer phase coarsening using oscillatory flow J. Leung, A.H. Hirsa, J.M. Lopez, M.J. Vogel The co-existing phase domains of monolayers commonly observed via microscope are examined on flowing systems. Recent evidence shows that co-existing phase domains have profound effects on monolayer response to bulk flow. The present flow geometry consists of an open-top rectangular cavity in which the flow is driven by the periodic oscillation of the floor in its own plane. The oscillation of the floor dilates and compresses any film at the gas/liquid interface while still maintaining an essentially flat interface. A range of flow conditions (oscillation frequency and amplitude) is chosen so that the flow remains essentially two-dimensional. Measurements at the interface, initially covered by an insoluble monolayer (vitamin K$_{1}$ or stearic acid), are made using a Brewster angle microscope system with a pulsed laser. Various phenomena such as fragmentation (breaking up of co-existing domains into finer ones) had previously been observed in sheared monolayer flows. In this new flow regime, we have seen dramatic coarsening of the domains. Interesting relaxation behavior at short and long time scales will also be discussed. [Preview Abstract] |
Monday, November 21, 2005 5:15PM - 5:28PM |
KF.00006: Starbursts and Wispy Drops : Surfactants Spreading on Gel Substrates Shomeek Mukhopadhyay, Karen Daniels, Robert Behringer We report a phase diagram for a novel instability seen in drops of nonionic surfactant solution (Triton X-305) spreading on viscoelastic agar gel substrate . This system allows us to examine the effect of varying the effective fluidity/stiffness of aqueous substrates. The morphology is strongly affected by the substrate fluidity, ranging from spreading starbursts of arms on weak gels, to wispy drops on intermediate strength gels, to circular drops on stiff gels. We analyze the dynamics of spreading in the starburst phase, where the arm length grows as t $^{3/4 }$at early times, independent of the gel strength and surfactant concentration. The number of arms is proportional to the surfactant concentration and inversely proportional to the gel strength. Ongoing work is exploring the effects of changing the drop volume. [Preview Abstract] |
Monday, November 21, 2005 5:28PM - 5:41PM |
KF.00007: Domain Relaxation in Polymer Langmuir Layers Andrew J. Bernoff, James C. Alexander, Elizabeth Mann, J. Adin Mann, Jr., Jacob M. Pugh, Lu Zou We report on an experimental, theoretical and computational study of a molecularly thin polymer Langmuir layer on the surface of a subfluid. When stretched (by a transient stagnation flow), the monolayer takes the form of a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape relaxes to the minimum energy configuration of a circular domain. The tether is never observed to rupture, even when it is more than a hundred times as long as it is thin. We model these experiments by taking previous descriptions of the full hydrodynamics (primarily those of Stone \& McConnell and Lubensky \& Goldstein ), identifying the dominant effects via dimensional analysis, and reducing the system to a more tractable form. The result is a free boundary problem where motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. The problem has a boundary integral formulation which allows us to numerically simulate the tether relaxation; comparison with the experiments allows us to estimate the line tension in the system. [Preview Abstract] |
Monday, November 21, 2005 5:41PM - 5:54PM |
KF.00008: Dynamics of a reactive falling film Serafim Kalliadasis, Philip Trevelyan We study the dynamics of a falling film in the presence of a first-order (exothermic or endothermic) chemical reaction. The heat released or absorbed by the reaction alters the surface tension, which in turn affects the evolution of the film, which in turn affects the rate of reaction and therefore the heat released by the reaction (feedback). Our analysis is based on an integral-boundary-layer approximation of the equations of motion, energy and concentration and associated free-surface boundary conditions. The heat/mass transport P\'eclet numbers are taken sufficiently large so that to take into account the convective terms of the heat/mass transport equations. Perticular emphasis is given to permanent-form traveling solitary waves. We show that the solitary waves can be dispersive and the size of dispersion depends on the size of the Prandtl and Schmidt numbers while its sign can change from positive to negative leading to negative-hump solitary waves. For large dispersion and for a sufficiently large region of Reynolds numbers, the liquid layer can be excited in the form of nondissipative solitary pulses which close to criticality assume the form of Kortweg-de Vries solitons. [Preview Abstract] |
Monday, November 21, 2005 5:54PM - 6:07PM |
KF.00009: Dynamics of a falling film in the presence of surfactants Antonio Pereira, Serafim Kalliadasis We investigate the dynamics of a falling film in the presence of surfactants. As a first step we consider insoluble surfactants thus ignoring diffusion from the bulk and desorption to the gas phase. We utilize an integral-boundary-layer approximation of the momentum and concentration equations and free-surface boundary conditions. We construct bifurcation diagrams for single-hump solitary wave solutions and we show that for vanishing Marangoni numbers the surfactants concentration becomes singular. The singularity appears at the front stagnation point of a solitary pulse due to accumulation of surfactants. [Preview Abstract] |
Monday, November 21, 2005 6:07PM - 6:20PM |
KF.00010: Flow down an inclined plane with soluble surfactant Barry Edmonstone, Richard Craster, Omar K. Matar We study the flow of a thin film down an inclined plane in the presence of dilute concentrations of soluble surfactant. Lubrication theory and cross-sectional averaging are used to derive a coupled set of two-dimensional (2-D) evolution equations for the film thickness and surfactant surface and bulk concentrations in the limit of rapid vertical diffusion. These equations are closed by a linear equation of state and parameterized by bulk and surface Peclet numbers, and dimensionless solubility and sorption kinetics parameters; the contact-line singularity is relieved via use of a thin precursor layer. The results of our transient growth analysis and transient numerical simulations of the nonlinear 2-D equations reveal the presence of a fingering instability that targets the thickened advancing ridge where the film adjusts onto the precursor layer. Although these fingering phenomena are present in the surfactant-free case, the presence of surfactant enhances the instability over an intermediate range of solubilities. [Preview Abstract] |
Monday, November 21, 2005 6:20PM - 6:33PM |
KF.00011: Marangoni instability of thin films on horizontal and inclined substrates Alain Bergeon, Edgar Knobloch Nonlinear evolution of the Marangoni instability of thin liquid films is studied via direct integration of the thin film equation to identify the states selected dynamically by the instability. On a horizontal substrate the instability is subcritical and proceeds to rupture. On slightly inclined substrates rupture may occur depending on parameter values and initial conditions. In other cases the instability evolves into arrays of solitary waves with both periodic and nonperiodic time-dependence. The results extend earlier work (U. Thiele and E. Knobloch, Physica D 190, 213, 2004) into the dynamical regime. [Preview Abstract] |
Monday, November 21, 2005 6:33PM - 6:46PM |
KF.00012: Density Effects on Immiscible Interface Breakup and Drop Formation Process Chiyoon Song The interface dynamics of a single immiscible interface at varying density ratios with the viscosity ratio order of one in the presence of vortical flow is examined through Front-Tracking/Finite difference method to solve unsteady Navier-Stokes equations for both the disperse and continuous phase flow. It is observed that as the density ratio of both phases decreases the larger density difference prohibits the formation and growth of surface waves and results in the formation of a longer column, which persists for a longer time until first breakup occurs. In contrast, the numerical simulations show that the change of density ratio is accompanied by the relative small variation in the detached volume of column. In this work, we also show that there exist the upper and lower limits of density ratio. Moreover, the small density ratio effects on the viscosity ratio are investigated. Although the density ratio is responsible for the interface deformation and breakup process when the viscosity of dispersed phase is greater than that of the continuous phase, the small density ratio effects on the dynamics is not observed for the case that the dispersed phase is less viscous than the continuous phase. [Preview Abstract] |
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