Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session P34: Flow Instability: Interfacial and Thin Film Fingering |
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Chair: Dominique Legendre, IMFT Room: 616 |
Monday, November 25, 2019 5:16PM - 5:29PM |
P34.00001: Linear Stability Analysis of Radial Miscible Viscous Fingering Manoranjan Mishra, Vandita Sharma, Satyajit Pramanik, Ching-Yao Chen Viscous fingering (VF) is a hydrodynamic instability ubiquitous during the displacement of a more viscous fluid by a less viscous one in a porous medium or Hele-Shaw flow. We perform a state-of-the-art linear stability analysis (LSA) of miscible VF with a radial flow. The LSA provides an alternate approach to study time dependent linear system arising in miscible VF. The time dependent base state is calculated numerically using the method of lines. The evolution of the disturbances is studied relative to the time dependent base state using momentary stability. Growth rate is adequately defined to take into account the radial source flow. The LSA captures the competition between advective and diffusive forces during the initial stages of radial VF and gives an insight into the effect of the competition on the onset of instability. The results are verified by performing the experiments and non-linear simulations. [Preview Abstract] |
Monday, November 25, 2019 5:29PM - 5:42PM |
P34.00002: Immiscible Fingering Instability via Alternating Injection: Experiments and Simulations Chi-Chian Chou, Wei-Cheng Huang, Ching-Yao Chen Viscous fingering instability on an immiscible interface via alternating injection is investigated by both experiments and numerical simulations. Multiple fluid annuluses associated with unstable and stable interfaces are resulted by injecting the less and more viscous fluid alternatively. We focus on the influences of two control parameters, e.g., the alternating injection interval and viscosity contrast, to the development of fingering instability. It is interesting to observe less prominent instability, determined by the shorter interfacial length, in the case with higher viscosity ratio by the alternating injection, which is contradictory with the conventional continuous injection. This inconsistent behavior is mainly due to rupture of the fluid annuluses of the less viscous fluid. Because of surface tension, the ruptured less viscous fluids tend to form separated drops, so that the total interfacial length decreases. On the other hand, the fluid annuluses appear more stable in the cases of lower viscosity contrast, so that the annuluses are stretched to prolong the overall interfacial length. [Preview Abstract] |
Monday, November 25, 2019 5:42PM - 5:55PM |
P34.00003: Pattern Formation from Instabilities in Chromonic Liquid Crystals Irmgard Bischofberger, Qing Zhang, Shuang Zhou The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. In isotropic systems, disordered dense-branching morphologies arise from repeated tip-splitting of the evolving finger. In anisotropic systems, by contrast, the growth morphology changes to a highly ordered dendritic growth characterized by stable needle-like protrusions decorated with regular side-branches. We investigate such morphology transitions between dendritic growth and dense-branching growth in an intrinsically anisotropic liquid; a lyotropic chromonic liquid crystal in the nematic phase. We show that the transition is remarkably sensitive to the interface velocity and the viscosity ratio between the less-viscous inner fluid and the more-viscous outer liquid crystal. We discuss the importance of a stable shear alignment of the liquid crystal in governing the morphology transition to dendritic growth. [Preview Abstract] |
Monday, November 25, 2019 5:55PM - 6:08PM |
P34.00004: Rivulet formation in falling liquid films Gianluca Lavalle, Julien Sebilleau, Dominique Legendre When a thin liquid film falls down an inclined or vertical plane, a capillary ridge develops behind the advancing contact line. For sufficiently thick ridges, rivulets appear as a result of the contact-line instability. The formation of such complex liquid structures might degrade the performances of several industrial applications, such as coating, aerodynamic efficiency and chemical processes. We investigate the dynamics of liquid films of partially wetting fluids falling down a vertical plane. We are particularly interested in the fingering instability and the distribution of rivulets. Based on direct numerical simulations, we study the influence of initial contact-line perturbations and pre-existing surface contaminations upon the fingering topology. Interestingly, varying the wave-number of the initial sinusoidal contact-line perturbation leads to different rivulet topologies and root velocities. Meanwhile, the presence of a pre-existing sufficiently large drop forces the formation of a rivulet where the drop and the contact line interact, thus destroying the symmetry of the flow. Finally, we discuss the wetted area for several surface contaminations in the form of pre-existing random drops. [Preview Abstract] |
Monday, November 25, 2019 6:08PM - 6:21PM |
P34.00005: Stability and fingering of radial flows John Lister, Frederik Dauck A pool of honey spreading on a horizontal surface becomes axisymmetric, but radial flow in a Hele-Shaw cell is unstable to fingering if the injected fluid is sufficiently less viscous than the ambient. Why the difference? Radial geometries offer a distinct advantage for the analysis of fingering instabilities of spreading flows in that the azimuthal wavenumber remains constant and thus self-similarity methods can be employed. Several problems of this sort are described. For example, it is shown analytically that viscous gravity currents, with power-law injection and power-law flux relationship $q=-h^n\nabla h$, are stable. And it is shown by analysis of a self-similar kinematic wave that Hele-Shaw flows of miscible fluids at infinite Peclet number are unstable if and only if the viscosity ratio exceeds 3/2. [Preview Abstract] |
Monday, November 25, 2019 6:21PM - 6:34PM |
P34.00006: Fingering Instabilities in Oxidizing Eutectic Gallium-Indium Keith Hillaire, William Llanos, Michael Dickey, Karen Daniels Eutectic gallium-indium (eGaIn), a room-temperature liquid metal alloy, has the largest tension of any liquid at room temperature, and yet can nonetheless undergo fingering instabilities. This effect arises because, under an applied voltage, an oxide builds up on the surface of the metal. The oxide acts like a surfactant, lowering the surface tension and allowing spreading under gravity. In the experiments described here, we examine the hypothesis that fingering instabilities, including tip-splitting, arise due to Marangoni instabilities. Our experiments are performed with eGaIn droplets placed in an electrolyte bath of sodium hydroxide; by placing the eGaIn on copper electrodes, which eGaIn readily wets, we are able to impose a fingering wavelength on the spreading. Two transitions are observed as a function of current: (1) a minimum current at which EGaIn spreads out from the copper electrode; (2) the current at which the fingers become unstable to shorter wavelengths and spread inhomogeneously. We present a phase diagram as a function of current and initial wavelength, and identify a minimum wavelength below which single tip-splitting does not occur. [Preview Abstract] |
Monday, November 25, 2019 6:34PM - 6:47PM |
P34.00007: Delayed onset in viscous fingering Thomas Videbaek, Sidney Nagel The viscous fingering instability occurs at the evolving interface between two viscous fluids confined to a thin gap. We investigate the onset of the instability in both radial and rectilinear geometries for both miscible and immiscible pairs of fluids. In all four cases we observe a region of stable growth, $L_{\mathrm{stable}}$, before fingers start to develop. While the initial stability in the radial cell has been ascribed to the velocity profile associated with point-source injection, this explanation is much too small to explain our observations. The region of stable growth before onset that we observe in the linear cell is unexpected. For miscible fluids, $L_{\mathrm{stable}}$ can be tied to the distance it takes to form steady-state, interfacial structures in the gap. For immiscible fluids, where no internal structure is apparent, there is no obvious explanation for $L_{\mathrm{stable}}$, which we find also depends on the capillary number. These results are not accounted for by current analyses of fingering dynamics. We suggest that this is because the experiments are by nature always quasi-two dimensional with an important length set by the gap size. [Preview Abstract] |
Monday, November 25, 2019 6:47PM - 7:00PM |
P34.00008: Stabilization of viscous fingering in a partially miscible system Ryuta Suzuki, Shoji Seya, Takahiko Ban, Manoranjan Mishra, Yuichiro Nagatsu Viscous fingering (VF) or Saffman-Taylor instability occurs when a less viscous fluid displaces a more viscous one in porous media or in Hele-Shaw cells. The classical VF can be divided into two; miscible and immiscible systems depending on whether two fluids are miscible or immiscible. In addition, it has been recently reported that a partially miscible VF has experimentally shown to change to multiple droplets pattern. However, in the present study, we have experimentally shown a partially miscible VF can have the potential to stabilize the interface more effectively, namely, leading to circular-like pattern in a radial geometry. This is considered to be caused by the two factors; a convection induced by spinodal decomposition directed from the more viscous fluid to the less viscous one and a high rate of the spinodal decomposition. [Preview Abstract] |
Monday, November 25, 2019 7:00PM - 7:13PM |
P34.00009: Deviation from capillary number scaling of nonlinear viscous fingering formed by the injection of Newtonian surfactant solution Ryohei Tanaka, Reiko Tsuzuki, Takahiko Ban, Yuichiro Nagatsu An experimental study of immiscible viscous fingering (VF) with Newtonian fluids is explored in this research. Previous studies show that immiscible VF is dominated by the capillary number defined as the ratio between the viscous force and the interfacial tension, and that the finger width decreases with increasing capillary number. However, in the present study, phenomena contrary to these rules were observed: wider fingers occurred in the surfactant solution system compared to those in the water system, in the nonlinear stage of VF evolution, despite the fact that the capillary number had the same value for both systems. In addition, even though the surfactant system had a higher capillary number than the water system, wider surfactant fingers were observed. A possible mechanism explaining this is discussed by comparing with previous studies regarding VF with surfactants. The present study indicates that the capillary number does not control the nonlinear VF width in the surfactant system. Our results and discussion can be used to contribute to the establishment of well-controlled processes for surfactant flooding and the recovery of residual NAPL in aquifers. [Preview Abstract] |
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