Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session KG: Instability: Interfacial and Thin Films IV |
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Chair: Paul Steen, Cornell University Room: Salt Palace Convention Center 250 A |
Tuesday, November 20, 2007 8:00AM - 8:13AM |
KG.00001: Dynamics of Circular Contact Lines: Spin Coating under Marangoni forces. Shomeek Mukhopadhyay, Robert Behringer Spin Coating remains one of the most important industrial applications of fluid dynamics, where understanding and controlling the instabilities is very important. The basic configuration consists of a fluid drop that is initially centrally located on a flat horizontal rotating surface. In this work we report on experiments on thin liquid films and fingering instabilities of a liquid drop, over a large range of angular speeds (from 10 mHz to 10Hz) of completely wetting PDMS oils on oxidized silicon wafers. Using a novel experimental setup, we will look at the effect of applying a radial temperature gradient (as opposed to a vertical gradient) on the dynamics of both the drop and the thin liquid film. In this case, the Marangoni forces oppose the centrifugal body forces. Depending on the relative strength of the driving force (angular speeds of 1 to 10 Hz and temparature gradients of 10 K/cm) and the drop size (volume of the drop varies from 1 microlitre to 100 microlitre) nontrivial wave structures and patterns arise. These results will be analyzed in the framework of the lubrication approximation. [Preview Abstract] |
Tuesday, November 20, 2007 8:13AM - 8:26AM |
KG.00002: Marangoni convection in binary and nano-fluids Alla Podolny, Alex Nepomnyashchy, Alex Oron Investigation of the Marangoni convection in binary fluids in the framework of a linear stability theory was started several decades ago. Recently, a new class of fluids, nanofluids, has been successfully applied in heat transfer devices. From the point of view of dynamics and heat/mass transfer, a typical nanofluid behaves as a Newtonian binary fluid with an extremely small Lewis number and anomalously high Soret coefficient. While there is a significant number of publications on the buoyancy convection in nanofluids, including binary nanofluids, the Marangoni convection in nanofluids is still hardly investigated, though an essential influence of nanoparticles on surface tension has been revealed in some experiments. The latter phenomenon can be significant for applications of nanofluids in boiling devices, including those used under microgravity conditions. The present talk describes a unified theoretical description of Marangoni convection, which can be applied for both binary solutions and nanofluids. [Preview Abstract] |
Tuesday, November 20, 2007 8:26AM - 8:39AM |
KG.00003: Rayleigh-Benard-Marangoni instability of a horizontal non-Boussinesq fluid layer with a deformable free surface Tatyana Lyubimova, Dimitri Lyubimov, Nikolai Lobov, Iwan Alexander The stability of the conductive state of a horizontal fluid layer with a deformable free surface, a flat isothermal rigid lower boundary and a convective heat transfer condition at the free surface is considered. The fluid is assumed to be isothermally incompressible. In contrast to the Boussinesq approximation, density variations are accounted for in the continuity equation and in the buoyancy and inertial terms of the momentum equations. Three different types of temperature dependence of the density are considered: linear, exponential and ideal gas. The long-wave instability is studied analytically and instability to perturbations with finite wave number is examined numerically. It is found that there is a decrease in stability of the system with respect to the onset of long-wave Marangoni convection. This result could not be obtained within the framework of the conventional Boussinesq approximation. It is also shown that at \textit{Ma = 0 }the critical Rayleigh number increases with \textit{Ga} (the ratio of gravity to viscous forces or Galilei number). At some value of \textit{Ga,} the Rayleigh-B\`{e}nard instability vanishes. This stabilization occurs for each of the density equations of state. At small values of \textit{Ga }and when deformation of the free surface is important, results predicted using the Boussinesq approximation be misleading. [Preview Abstract] |
Tuesday, November 20, 2007 8:39AM - 8:52AM |
KG.00004: Domains of attraction for volume-scavenging among N coupled capillary droplets Henrik van Lengerich, Paul Steen, Mike Vogel A large number of capillary droplets protruding from a surface can be made to adhere or detach to a substrate by manipulating the volume of the droplets so that they form or break liquid bridges with the substrate. Because such a device is easiest to manufacture with a single liquid reservoir, we are motivated to study the dynamics of N coupled droplets. Experiments and numerical simulations show that the droplets exchange volume in a complicated manner until one droplet has scavenged the volume from all the others. Which of the N droplets becomes largest is sensitive to the total droplet volume, initial droplet volume perturbation, and topology of the coupling; it can be very intuitive, exhibit patterns, or become disordered. To explain these findings we find a Lyapunov function, characterize the fixed points, and find the invariant manifolds using a combination of local and global methods. We show how to combine this information to obtain the domains of attraction for small N and explain phenomenon observed by the numerical computations. [Preview Abstract] |
Tuesday, November 20, 2007 8:52AM - 9:05AM |
KG.00005: Experiment on miscible displacement in capillary tubes varying Korteweg stress. Yuichiro Nagatsu, Yuji Hosokawa, Yoshihito Kato, Yutaka Tada It is known that flow in the miscible displacements in vertically capillary tube is governed by a Peclet number, a gravity parameter, and a viscosity contrast. Additionally, we know that a spike is formed at the displacement tip, depending on these parameters. It is hypothesized that the stress believed to act in the region with a steep concentration gradient between the two miscible fluids, which mimics an interfacial tension acting on two immiscible fluids, plays an important role on the spike formation, in addition to the combination of these parameters. The stress is referred as to Korteweg stress. The present study has established an experimental system which can vary the Korteweg stress effect although these three parameters are unchanged. Experimental results show that under the same condition of these three parameters, the spike is formed or not formed in the cases where the Korteweg stress effect is large or small, respectively. This is the first experimental result that directly shows that the Korteweg stress is responsible for the spike formation. [Preview Abstract] |
Tuesday, November 20, 2007 9:05AM - 9:18AM |
KG.00006: Capillary penetration into periodically corrugated plates Marina Medina, Fausto Sanchez, Francisco Higuera, Abraham Medina Spontaneous capillary rise of viscous liquid between two sinusoidally corrugated plates, which are vertically placed in a gravitational field, is studied. The effect of geometrical variations perpendicular to the direction of penetration on the rate of capillary penetration is analyzed by using the lubrication theory. Numerical solutions of the Reynolds equations for the local free surface and pressure distribution in the fluid and the spatially-averaged penetration length are given. It was found that the amplitude of corrugation determines the time necessary to reach the equilibrium length when constant average capillary gap width is applied. These results also illustrate some features experimentally observed in spontaneous penetration of liquids into porous materials where the permeability changes spatially. Many geological and technological applications involve this type of anomalies. [Preview Abstract] |
Tuesday, November 20, 2007 9:18AM - 9:31AM |
KG.00007: Destabilization of a Saffman--Taylor finger in a granular suspension Anke Lindner, Christophe Chevalier, Eric Clement We study the Saffman--Taylor instability in a granular suspension formed by micrometric beads immersed in a viscous liquid. We use an effective viscosity for flow of the suspension in the Hele-Shaw cell to define the control parameter of the system. The results for the finger width of stable fingers are then found to be close to the classical results of Saffman--Taylor for a large number of experimental conditions. One observes however an early destabilization of the fingers that can be attributed to the discrete nature of the individual grains. The addition of even a slight fraction of grains to the pure fluid decreases the threshold of destabilization drastically. This destabilization is classically attributed to the noise in the cell and is thus difficult to quantify. We show that the grains represent a ``controlled noise'' and produce an initial perturbation of the interface with an amplitude proportional to the grain size. The finite amplitude instability mechanism proposed by Bensimon {\it et al.} allows to link this perturbation to the value of the threshold observed. [Preview Abstract] |
Tuesday, November 20, 2007 9:31AM - 9:44AM |
KG.00008: Effect of Damkohler number on miscible viscous fingering involving viscosity decrease due to chemical reaction Yusuke Kondo, Yuichiro Nagatsu, Yoshihito Kato, Yutaka Tada When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. We find that a chemical reaction between a polymer solution and a solution including metal ions decreases the viscosity of the polymer solution and that the rate of the decrease in the viscosity (that is the chemical reaction rate) can be changed by variation in the concentrations of the metal ions. By using the liquids and the reaction, we have succeeded in experimentally showing the effect of Damkohler number on miscible viscous fingering pattern involving the viscosity decrease due to chemical reaction in a radial Hele-Shaw cell. Results show that up to threshold value of \textit{Da}, the area occupied by the fingering pattern near the injection hole is increased with \textit{Da}, whereas over the threshold value of \textit{Da}, the area is decreased with \textit{Da}. A physical model to explain these experimental results is proposed. [Preview Abstract] |
Tuesday, November 20, 2007 9:44AM - 9:57AM |
KG.00009: Miscible viscous fingering with chemical reaction involving precipitation. Si-Kyun Bae, Yuichiro Nagatsu, Yoshihito Kato, Yutaka Tada When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. The present study has experimentally examined how precipitation produced by chemical reaction affects miscible viscous fingering pattern. A 97 wt {\%} glycerin solution containing iron(III) nitrate (yellow) and a solution containing potassium hexacyano ferrate(II) (colorless) were used as the more- and less-viscous liquids, respectively. In this case, the chemical reaction instantaneously takes place and produces the precipitation being dark blue in color. The experiments were done by varying reactant concentrations, the cell's gap width, and the displacement speed. We compared the patterns involving the precipitation reaction with those in the non-reactive cases. We have found fylfot-like pattern is observed, depending on the experimental condition, which has never been formed in the non-reactive experiments. As the reactant concentrations are increased or the displacement speed is decreased, the effects of the precipitation on the patterns are more pronounced. [Preview Abstract] |
Tuesday, November 20, 2007 9:57AM - 10:10AM |
KG.00010: The Frankel Law for the Thickness of Vertically Withdrawn Soap Films: Reconsidering the Basic Fluid Dynamical Assumptions E.A. Van Nierop, B. Scheid, H.A. Stone The formation of soap films by vertical withdrawal from a bath is typically described by the Frankel law. This law is based on an assumption of rigid film ``walls,'' with the idea that the dynamics are shear-like (as in the Landau-Levich description of the fluid film produced by plate withdrawal from a liquid bath). Since most soap films have boundaries that are not actually rigid, and as the usual flow in thin free films and fibers is extensional, a revision of the theory of the formation of soap films is provided. We review the old and recent literature on this topic, and present analytical results from a new approach that relies on surface viscosity. Surprisingly, the main result of the Frankel law, namely that film thickness scales as the two-thirds power of the withdrawal speed, is also obtained through this extensional flow characterization with surface viscosity. When bulk viscous stresses are included, the speed dependence can vary between V$^{(2/3)}$ and V$^2$. Comparison with existing data in the literature will be given. [Preview Abstract] |
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