Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session L22: Instability: Interfacial and Thin Films |
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Chair: Patrick Bunton, William Jewell College Room: 2012 |
Monday, November 24, 2014 3:35PM - 3:48PM |
L22.00001: Forced spreading of films and droplets of colloidal suspensions Leonardo Espin, Satish Kumar When a thin film of a colloidal suspension flows over a substrate, uneven distribution of the suspended particles can lead to an uneven coating. Motivated by this phenomenon, we analyse the flow of perfectly wetting films and droplets of colloidal suspensions down an inclined plane. Lubrication theory and the rapid-vertical-diffusion approximation are used to derive a coupled pair of one-dimensional partial differential equations describing the evolution of the interface height and particle concentration. Precursor films are assumed to be present, the colloidal particles are taken to be hard spheres, and particle and liquid dynamics are coupled through a concentration-dependent viscosity and diffusivity. We find that for sufficiently high P\'eclet numbers, even small initial concentration inhomogeneities produce viscosity gradients that cause the film or droplet front to evolve continuously in time instead of travelling without changing shape as happens in the absence of colloidal particles. Our results suggest that particle concentration gradients can have a dramatic influence on interface evolution in flowing films and droplets, a finding which may be relevant for understanding the onset of patterns that are observed experimentally. [Preview Abstract] |
Monday, November 24, 2014 3:48PM - 4:01PM |
L22.00002: Controlling Viscous Fingering Using Time-dependent Strategies Zhong Zheng, Hyoungsoo Kim, Howard Stone Control and stabilization of viscous fingering of immiscible fluids impacts a wide variety of pressure-driven multiphase flows. We report theoretical and experimental results on time-dependent control strategy by manipulating the gap thickness $b(t)$ in a lifting Hele-Shaw cell in the power-law form $b(t) = b_1 t^{1/7}$. Experimental results show good quantitative agreement with the predictions of linear stability analysis. By choosing the value of a single time-independent control parameter we can either totally suppress the viscous fingering instability or maintain a series of non-splitting viscous fingers during the fluid displacement process. Besides the gap thickness of a Hele-Shaw cell, in principle, time-dependent control strategies can also be placed on the injection rate, viscosity of the displaced fluid, and interfacial tension between the two fluids. [Preview Abstract] |
Monday, November 24, 2014 4:01PM - 4:14PM |
L22.00003: Subglacial ice sheet lubrication Katarzyna N. Kowal, M. Grae Worster Large-scale ice-sheet dynamics can be greatly affected by glacial slip, enhanced by subglacial meltwater and water-saturated sediment that acts as a lubricant at the ice-bed contact. Ice streams, for example, are generally lubricated by a layer of water and till at their base and slide up to two orders of magnitude faster than the surrounding ice, making them a major source of discharge of ice into the oceans despite them occupying a relatively small fraction of present-day ice sheets. We present a theoretical and experimental study in which we model the ice and the lubricant as two layers of fluid spreading under their own weight over a smooth, rigid, horizontal surface. The resulting flows are driven by buoyancy and viscous coupling between the layers. Although we are primarily interested in the case in which the underlying fluid has a much smaller viscosity than that of the overlying fluid, the applicability of our model extends to two-layer gravity currents with general viscosity ratios. There is excellent quantitative agreement between our theory and a series of laboratory experiments that we have conducted using simple, Newtonian fluids. A novel fingering instability develops at later stages of our experiments. [Preview Abstract] |
Monday, November 24, 2014 4:14PM - 4:27PM |
L22.00004: A Solutal Fingering Instability during Capillary Imbibition in Fibrous Media Christopher Guido, Nicolas Young, William Ristenpart We report the existence of a solute-driven, humidity-dependent fingering instability that occurs during capillary imbibition into cellulosic fibrous media (e.g., paper). For sufficiently low solute concentrations and sufficiently high ambient humidities, the imbibition front moves forward smoothly; for higher concentrations and lower humidities, however, the imbibition front develops spatially periodic fluctuations that grow with time. We derive and experimentally corroborate a stability criterion based on solute-induced changes in the air/liquid interfacial tension, which are magnified by liquid infiltration into a humidity-dependent precursor film. The results have broad implications for any process involving motion of liquids through fibrous media, including chromatographic separations, paper-based diagnostic assays, and conservation efforts involving aged manuscripts or artwork. [Preview Abstract] |
Monday, November 24, 2014 4:27PM - 4:40PM |
L22.00005: Non-modal disturbances growth of miscible viscous fingering in porous media Tapan Kumar Hota, Manoranjan Mishra The transient amplification of disturbances in a pressure driven rectilinear flow of two miscible fluids with varying viscosity in porous media are examined. The system has been studied by coupling the continuity and Darcy equations with a convection-diffusion equation for the evolution of solute concentration. Since the base state is time dependent, the common techniques used in the literatures for studying the linear stability are either quasi-steady state approach or initial value approach with random initial disturbance or both. To overcome difficulties in these approaches, the non-modal analysis (NMA) has been employed to study the amplification of disturbances. The Runge-Kutta method has been used to solve the matrix differential equation obtained by NMA from the linearized equations. The optimum amplification and structures of the disturbances are found by singular value decomposition. Initial disturbances that lead to the optimum amplifications are found to be localized within the diffusive layers, unlike the random disturbances used in the initial value technique. It has also been observed that the optimum growth obtained by NMA decays at early time due to the diffusion before it starts amplifying, unlike the results of modal analysis. [Preview Abstract] |
Monday, November 24, 2014 4:40PM - 4:53PM |
L22.00006: Elastic viscous fingering John Lister, Gunnar Peng The Saffman--Taylor viscous-fingering instability in a circular Hele-Shaw cell can be suppressed by replacing one of the rigid walls with an elastic sheet (Pihler-Puzovic, Illien, Heil, Juel, 2012). We successfully reproduce these results numerically by considering linear non-axisymmetric perturbations to an axisymmetric evolving base state. Our calculations show that, in the relevant parameter regime, the non-axisymmetric perturbations to the elastic sheet are negligible. Instead, the elastic suppression of the fingering instability is due to changes to the axisymmetric base state. We identify four physical mechanisms that affect the stability of the system, and find that the contribution from each one is significant. [Preview Abstract] |
Monday, November 24, 2014 4:53PM - 5:06PM |
L22.00007: What the geometry of a river network says about its growth Olivier Devauchelle, Yossi Cohen, Hansjoerg F. Seybold, Robert S. Yi, Piotr Szymczak, Daniel H. Rothman The growth of a river network is governed by the flow of rainwater towards it. When the streams drain groundwater, this flow conforms to a harmonic field, thus turning the network growth into an analogue of Saffman-Taylor fingering and diffusion-limited aggregation. A theoretical description of this process should specify (i) how fast a river grows, (ii) in which direction and (iii) when it bifurcates. Simple physical reasoning suggests that a river grows along the groundwater flow lines (geodesic growth). In a harmonic field, this hypothesis sets the branching angle of the network to 72$^{\circ}$, regardless of the other growth rules. This geometrical property appears unambiguously in nature. Inspired by fracture mechanics, we reformulate the geodesic growth in terms of local symmetry: as it cuts into the landscape, a river maintains a symmetric groundwater flow around its tip. Based on this principle, we reconstruct the history of the network by growing it backwards from its present geometry. We then use this history to infer the network's dynamics. [Preview Abstract] |
Monday, November 24, 2014 5:06PM - 5:19PM |
L22.00008: Schlieren Imaging of Viscous-Fingering in a Horizontal Hele-Shaw Cell Patrick Bunton, Gabrielle Brooks, Simone Stewart, Anne De Wit Viscous fingering (VF) occurs when a fluid of high mobility displaces a fluid of lower mobility. Recent increased interest is motivated by applications to enhanced petroleum recover, pollutant dispersal, and climatological issues along with increased computational capability. Most often VF is observed in a Hele-Shaw (HS) cell consisting of two transparent plates separated by a narrow gap. For the typical case of transparent fluids, dyes are used for observation. Chemical indicators are used for reactive studies. Other techniques have been used such as interferometry, Schlieren, shadowgraph, fluorescence, and MRI. Here is reported a modification of Schlieren for use in imaging horizontal flows in a HS cell. The technique requires no dyes or chemical indicators that might complicate interpretation or even alter the dynamics. It is exquisitely sensitive, readily yielding information about 3D flows in gaps under a mm. Schlieren imaging is particularly useful in that it allows one to image flows within the fingers, rather than merely imaging the boundary. Following a description of the technique, data for water-glycerol systems are presented revealing previously unobserved internal detail. This detail is interpreted in terms of recently published 3D models of VF. [Preview Abstract] |
Monday, November 24, 2014 5:19PM - 5:32PM |
L22.00009: A new Saffman-Taylor growth rate formula Prabir Daripa In this talk, we discuss modification of the classical Saffman-Taylor growth rate formula when the dynamic Laplace law including viscous stress tensor on the interface is included in the linear stability analysis for the displacement of a Newtonian fluid by air. In particular, we derive a new formula for the growth rate and show that the problem is linearly well-posed for all values of surface tension. This is a joint work with Gelu Pasa. [Preview Abstract] |
Monday, November 24, 2014 5:32PM - 5:45PM |
L22.00010: Experimental study on effects of effective interfacial tension on miscible viscous fingering Fu Wei Quah, Yu Qi, Yuichiro Nagatsu We experimentally investigate effects of effective interfacial tension (EIT) on miscible viscous fingering (VF). To do so, we prepare two miscible liquid systems in which the viscosity contrast between the more- and less viscous liquids is the same but the EIT between the two liquids is different. We confirm that the viscosity is the same in both the systems but EIT is different by means of the measurements of viscosity and EIT. We perform VF experiment by using a Hele-Shaw cell. We find that the typical width of the fingers is larger in the system involving larger EIT. This experimental result has a good agreement with recent numerical studies of the related issue. [Preview Abstract] |
Monday, November 24, 2014 5:45PM - 5:58PM |
L22.00011: Characteristics of proportionate growth observed in instability patterns of miscible fluids Irmgard Bischofberger, Radha Ramachandran, Sidney R. Nagel As a baby mammal grows, different parts of its body develop at the nearly the same rate and thus to a good approximation in direct proportion to one another. This type of growth is called proportionate growth. As familiar as it appears to us, it is very rarely found in physical systems outside of the biological world. We here show an example of proportionate growth that occurs in the instability formed when a less viscous liquid, of viscosity $\eta_{in}$ displaces a more viscous miscible one, of viscosity $\eta _{out}$. We investigate the growth of these patterns in a quasi-two-dimensional geometry. Within a range of viscosity ratios 0.1 \textless $\eta_{in}$ /$\eta_{out}$ \textless 0.3, we observe the formation of small blunt structures that form at the edges of an inner circular region devoid of fingers. As the pattern grows, the size of these structures increases in proportion to the size of the inner circle, such that even small details in the shape of the pattern remain essentially unchanged during growth. These characteristics of proportionate growth are reflected in the shape of the interface in the third dimension as well. [Preview Abstract] |
Monday, November 24, 2014 5:58PM - 6:11PM |
L22.00012: Shear-induced morphology in mixed phospholipid films Amir Hirsa, James Young, David Posada, Juan Lopez Flow of mixed phospholipid films on liquid surfaces plays a significant role in biological processes ranging from lipid bilayer fluidity and the associated behavior of cellular membranes, to flow on the liquid lining in the lungs. Phospholipid films are also central to the process of two-dimensional protein crystallization below a ligand-bearing film. Here, we study a binary mixture of phospholipids that form an insoluble monolayer on the air-water interface. Brewster angle microscopy reveals that a shearing flow induces a phase separation in the binary film, resulting in the appearance of 10 micron-scale dark domains. Hydrodynamic response of the binary film is quantified at the macro-scale by measurements of the surface shear viscosity, via a deep-channel surface viscometer. Reynolds number was shown to be a state variable, along with surface pressure, controlling the surface shear viscosity of a biotinylated lipid film. [Preview Abstract] |
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