Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session LJ: Surface Tension Effects I |
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Chair: Oliver Jensen, University of Nottingham Room: 101I |
Monday, November 23, 2009 3:35PM - 3:48PM |
LJ.00001: Surfactant spreading on a thin fluid layer: visualization via fluorescence David Fallest, Christopher Fox, Ellen Peterson, Michael Shearer, Karen Daniels We perform quantitative measurements of the spreading of an insoluble surfactant on a thin layer of glycerin. We directly observe both the radial height profile of the spreading droplet and the spatial distribution of the fluorescently-tagged surfactant during the spreading process. The spreading circular layer of surfactant forms a capillary ridge at the leading edge, the peak of which spreads with $R \approx t^{1/4}$, in agreement with predictions based on the lubrication approximation of the Stokes equations (Jensen \& Grotberg, 1992). In addition, the surfactant concentration is observed to have a peak which follows, then lags behind, the capillary ridge during spreading. The companion talk (to follow) will compare these results with numerical simulations and analysis. [Preview Abstract] |
Monday, November 23, 2009 3:48PM - 4:01PM |
LJ.00002: Surfactant spreading on a thin liquid layer: Modeling and Theory Ellen Peterson, Michael Shearer, Karen Daniels, David Fallest To model the spreading of a droplet of insoluble surfactant on a thin liquid layer, we use the lubrication approximation of the Stokes equations. The resulting system of nonlinear PDE describes the height of the fluid surface and the distribution of surfactant on the surface. The flow is driven by the surface tension gradient induced by the surfactant. Ignoring the smoothing effects of capillarity and diffusion of surfactant, the system simplifies to a pair of transport equations. These equations admit a similarity solution characterized by Jensen and Grotberg (1992) that sets the spreading rate of the surfactant layer. We employ finite difference simulations to capture the shape of the free surface and the surfactant distribution. The leading edge of the surfactant layer is treated as a free boundary, with a boundary condition corresponding to a jump in the free surface height first discovered by Gaver and Grotberg (1990). We are able to examine a solution for both the outer region as well as the boundary layer that accounts for the behavior of the film near the center of the surfactant droplet. For the full system, with capillarity, gravity, and diffusion on the surface, the leading shock smooths to a ridge. We compare simulations of the full thin film system with experimental observations of film height profiles, and with the observed spreading rate of the surfactant layer. [Preview Abstract] |
Monday, November 23, 2009 4:01PM - 4:14PM |
LJ.00003: Efficient numerical computation of fluid interfaces with soluble surfactant (I) an inviscid drop Michael Booty, Michael Siegel We address a difficulty in the computation of fluid interfaces with soluble surfactant. At the large values of bulk Peclet number typical of fluid-surfactant systems, a transition layer forms adjacent to the interface in which the surfactant concentration varies rapidly, while its gradient at the interface must be evaluated accurately to determine bulk-interface exchange of surfactant, surface tension, and the drop's dynamics. We present a fast and accurate hybrid numerical method that incorporates a separate singular perturbation reduction of the transition layer into a full numerical solution of the interfacial free boundary problem. Results are presented for an inviscid drop in the Stokes flow limit, where the underlying flow solver for insoluble surfactant uses conformal mapping techniques in two dimensions. This facilitates comparison of the hybrid method with a traditional numerical method at moderately large Peclet number. [Preview Abstract] |
Monday, November 23, 2009 4:14PM - 4:27PM |
LJ.00004: Efficient numerical computation of fluid interfaces with soluble surfactant (II) a viscous drop Kuan Xu, Michael Siegel, Michael Booty We address a difficulty in the computation of fluid interfaces with soluble surfactant. At the large values of bulk Peclet number typical of fluid-surfactant systems, a transition layer forms adjacent to the interface in which the surfactant concentration varies rapidly, while its gradient at the interface must be evaluated accurately to determine bulk-interface exchange of surfactant, surface tension, and the drop's dynamics. We present a fast and accurate hybrid numerical method that incorporates a separate singular perturbation reduction of the transition layer into a full numerical solution of the interfacial free boundary problem. Results are presented for a drop of arbitrary viscosity in the Stokes flow limit, where the underlying flow solver for insoluble surfactant uses a direct (primitive variable) boundary integral method. [Preview Abstract] |
Monday, November 23, 2009 4:27PM - 4:40PM |
LJ.00005: Dynamic contact angles of evaporating liquids on heated surfaces Vladimir Ajaev, Tatiana Gambaryan-Roisman, Jill Klentzman, Pater Stephan We studied dynamic apparent contact angle for gravity-driven flow of volatile liquid down a heated inclined plane. The apparent contact line is modeled as the transition region between the mascroscopic film and ultra-thin adsorbed film dominated by disjoining pressure effects. Three commonly used disjoining pressure models are investigated. The dynamic contact angle follows the Tanner's law remarkably well over a range of evaporation conditions. However, deviations from the predictions based on the Tanner's law are found when interface shape changes rapidly in response to rapid changes of the heater temperature. The Marangoni stresses are shown to result in increase of the values of apparent contact angles. Applications of different models of partial wetting to studies of fingering instability in evaporating liquids are also discussed. [Preview Abstract] |
Monday, November 23, 2009 4:40PM - 4:53PM |
LJ.00006: The effect of evaporation and Marangoni stresses on contact line instability Jill Klentzman, Vladimir Ajaev We investigate the contact line instability for the flow of viscous liquid on a heated inclined plane. Numerical simulations are conducted based on a model of the flow derived in our previous work using a lubrication-type approach including the effects of evaporation of the liquid. The impact of Marangoni stresses on the instability development is examined, and the value of the inclination angle of the solid surface is varied to study its effect. Unlike evaporation, which was shown in our previous work to inhibit the instability, Marangoni stresses promote the instability. Stability criteria for different inclination angles are expressed in terms of the modified Marangoni number and the evaporation number, a nondimensional measure of the mass flow rate across the interface. As a result of the development of instability, a finger-like structure is formed. The fingers grow initially, but then saturate at a length which depends on the evaporation conditions. [Preview Abstract] |
Monday, November 23, 2009 4:53PM - 5:06PM |
LJ.00007: A Numerical Method for Variable Surface Tension Effects in Non-Isothermal Atomization Peter Brady, Juan Lopez, Marcus Herrmann Atomization often occurs in non-isothermal environments, such as in combustion devices. There, thermal fluctuations can be significant on length scales associated with the liquid atomization process. Since the surface tension force is a function of local temperature, these thermal fluctuations may result in large local variations of the surface tension force, thereby potentially impacting the atomization process. Here, we present a numerical technique to incorporate these thermal Marangoni forces into the balanced force Refined Level Set Grid (RLSG) approach. With it, the liquid/gas phase interface is tracked by a level set method using an auxiliary high resolution equidistant Cartesian grid. This not only allows for application of higher-order WENO schemes retaining their full order of accuracy both for advecting and reinitializing the level set scalar, but it also provides the necessary high resolution of the phase interface geometry during topology change events in an efficient manner. Verification and validation test cases geared towards testing the applicability of the proposed methods to the case of secondary spray drop atomization will be presented. [Preview Abstract] |
Monday, November 23, 2009 5:06PM - 5:19PM |
LJ.00008: The flow induced dynamic surface tension effects at nanoscale Alex Lukyanov The aim of this report is to describe in general the effects of dynamic surface tension solely induced by the flow over nanoscale topography of the substrates. Capillary effects of similar nature induced by chemical modifications of the substrates or by temperature gradients (Marangoni effect) at the solid walls, have already found many applications in microfluidic actuation. The flow induced surface tension effects are examined on the basis of a sharp interface model. It is demonstrated how nanoscale objects placed at the boundary of the flow domain result in generation of substantial surface forces acting on the bulk flow. The effect, studied in general for arbitrary two-dimensional obstacles, is shown to be the strongest for a lattice of one-dimensional threads. [Preview Abstract] |
Monday, November 23, 2009 5:19PM - 5:32PM |
LJ.00009: Electromagnetically-driven capillary switches and oscillators Bernard Malouin, Amir Hirsa, Michael Vogel By designing pinned-contact, coupled droplet pairs at the appropriate length scale to promote surface tension as the dominant force, one can create bi-stable capillary switches and natural oscillators. These systems have been triggered by pressure pulses, electrochemistry, and electroosmosis. These methods are typically accompanied by bulky setups or slow response times. An alternate approach exploits electromagnetic activation. Our device consists of a millimeter scale orifice, overfilled with an aqueous ferrofluid, in proximity to a wire coil that generates a magnetic field. Experimental evidence of such capillary switches and energy efficient oscillators is presented here. Comparisons to a simplified model are also presented. This activation method is shown to have relatively fast response times, low driving voltages, and individual addressability. Electromagnetically activated capillary switches and oscillators offer many applications ranging from high-speed adaptive optics to micro-actuators, with possible circuit board integration. [Preview Abstract] |
Monday, November 23, 2009 5:32PM - 5:45PM |
LJ.00010: Dynamics of pinned-contact oscillating gas/liquid lenses Amir Hirsa, Bernard Malouin, Joseph Olles, Carlos Lopez, Michael Vogel Liquid lenses are a natural solution for applications in adaptive optics requiring a fast response. Existing liquid lenses use large disturbances to overcome liquid inertia and subsequently utilize the lens after the oscillations have dampened. An alternate strategy was demonstrated recently: a harmonically-driven liquid lens with an oscillating focal length that allows the capture of any plane in a given range by grabbing the image `in sync' with the oscillations. Hence, by continuously oscillating the lens, the task of changing the focal length is effectively transformed from a mechanical manipulation to the electronic timing of image capture by the sensor, which can be achieved much faster. Good optical quality is possible by designing the liquid lens to traverse states where capillarity produces spherical interfaces. Energy efficiency is achieved through pinned contact lines and operation at resonance. We present experimental results along with predictions for the dynamics of such oscillatory driven lenses, including the effects of liquid volume, driving frequency and amplitude on droplet shapes and resultant optical characteristics. High fidelity imaging was demonstrated at 100 Hz for a millimeter scale liquid lens. [Preview Abstract] |
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