Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session D9: Interfacial/Thin Film Instability II: Fingering |
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Chair: Sarah Kieweg, University of Kansas Room: 25B |
Sunday, November 18, 2012 2:15PM - 2:28PM |
D9.00001: Viscous fingering with production of surfactant by chemical reaction in a Hele-Shaw cell Masanari Fujimura, Yuichiro Nagastu Viscous fingering experiments have been performed in a radial Hele-Shaw cell for a liquid--liquid system in the presence of a chemical reaction which produces a surfactant. The reaction is a neutralization of a fatty acid by an alkaline material to form a surfactant. Viscous fingering experiments employing the chemical recipe were previously performed by several researchers. The present experiments were done in wider range of the reactant concentrations and the flow rate. Experimental results showed that the reaction made viscous fingers thinner for low flow rate whereas wider for high flow rate in the condition of low reactant concentrations. The reaction made the fingers wider for low reactant concentrations whereas thinner for high reactant concentration in the condition of high flow rate. In summary, we have found the opposite effects of the reaction on the finger width depending on flow rate in the low reactant concentration and depending on reactant concentrations in the high flow rate by employing the wide range of experimental conditions. [Preview Abstract] |
Sunday, November 18, 2012 2:28PM - 2:41PM |
D9.00002: Viscous fingering involving disappearance of precipitation by a chemical reaction in a Hele-Shaw cell Yuki Ishii, Yutaka Tada, Yuichiro Nagatsu Previously, we experimentally studied viscous fingering involving production of a precipitation by a chemical reaction in a Hele-Shaw cell (Nagatsu et al. PRE 77, 067302 (2008)). In the present study, we have conducted experiments on viscous fingering involving disappearance of a precipitation by a chemical reaction in a Hele-Shaw cell. In the present experiments, the more-viscous liquid contains the precipitation. In the reactive case, we used a solution including a reactant which reacts with the precipitation resulting in disappearance of the precipitation. In the non-reactive case, water was used as the less-viscous liquid. Thus, viscous fingering was observed in both the reactive and non-reactive cases. We have found that viscous fingering pattern is changed by disappearance of the precipitation by the reaction. Furthermore, effects of the reactant concentration and the injection rate of the less-viscous liquid on the change in the pattern by the disappearance of the precipitation were examined. [Preview Abstract] |
Sunday, November 18, 2012 2:41PM - 2:54PM |
D9.00003: Experimental Investigation of the Growth of Mixing Zone in Miscible Viscous Fingering Sahil Malhotra, Eric R. Lehman, Mukul M. Sharma An experimental study is performed to study the growth of the mixing zone in miscible viscous fingering. Rectilinear flow displacement experiments are performed in a Hele-Shaw cell over a wide range of viscosity ratios (1 to 700) by injecting water into Glycerol solutions at different flow rates. A linear growth in mixing zone is observed in all the experiments. The mixing zone velocity increases with the viscosity ratio up to viscosity ratios of 330 and the trend is consistent with Koval's model (Koval 1963). However, at higher viscosity ratios the mixing velocity plateaus signifying no further effect of viscosity contrast on the growth of mixing zone. [Preview Abstract] |
Sunday, November 18, 2012 2:54PM - 3:07PM |
D9.00004: ABSTRACT WITHDRAWN |
Sunday, November 18, 2012 3:07PM - 3:20PM |
D9.00005: Anomalous structure formation in the zero surface tension limit of viscous fingering Irmgard Bischofberger, Radha Ramachandran, Sidney R. Nagel The displacement of a more viscous fluid, of viscosity \textit{$\eta $}$_{out}$, by a less viscous one, of viscosity \textit{$\eta $}$_{in}$, in a two-dimensional geometry or a porous medium is unstable and typically produces complex fingering patterns. These fingering patterns are predicted to become sharper as the surface tension between the two fluids is decreased. However, our experiments performed in a radial Hele-Shaw cell suggest the opposite conclusion: fingering is less likely to occur in the limit of low surface tension. When the two fluids are miscible, so that the surface tension is negligible, the instability can be entirely suppressed; when the viscosity ratio of the two fluids, \textit{$\eta $}$_{out}$\textit{/$\eta $}$_{in}$, is greater than, but close to, one, the interface between the fluids is circular. With increasing viscosity ratio, the pattern starts to develop small blunt structures (toes) and when the viscosity ratio is large the pattern consists of highly branched fingers. We measure the amount of external fluid that gets displaced by the less viscous one and find that the displacement across the gap is always incomplete; the fingers form three dimensional structures. We discuss the implications of this 3D nature of the instability on the overall pattern formation. [Preview Abstract] |
Sunday, November 18, 2012 3:20PM - 3:33PM |
D9.00006: Fingering instabilities for a thin liquid film flowing down the outside of a vertical cylinder Scott McCue, Lisa Mayo, Timothy Moroney The flow of a thin film of viscous fluid down an inclined plane is well-studied, with much progress made by applying the lubrication approximation to derive a governing evolution equation for the film height. This equation is a fourth-order pde with a nonlinear degenerate diffusion term. Here we generalise this approach to apply for the problem of a thin film flowing down the outside of a vertical cylinder. In this context, a recent linear stability analysis of Smolka \& SeGall [1] provides a relationship between the growth rate and wavenumber of each mode, predicting the number of fingers that form on the surface of the cylinder as a function of the fluid properties and the cylinder's radius. To complement these results, we solve the full nonlinear problem numerically and analyse the manner in which nonlinear modes grow and interact for longer times. We also consider the problem of a single large droplet spreading and sliding down the vertical cylinder, studying the effect that the cylinder curvature has on the flow.\\[4pt] [1] L.B. Smolka and M. SeGall, ``Fingering instability down the outside of a vertical cylinder,'' Phys. Fluids \textbf{23}, 092103 (2011) [Preview Abstract] |
Sunday, November 18, 2012 3:33PM - 3:46PM |
D9.00007: Contact line instability of gravity-driven flow of power-law fluids Bin Hu, Sarah Kieweg In our previous studies, we developed 2D and 3D models to simulate a power-law fluid flowing down an incline. This study is intended to examine how the shear-thinning effect of the fluid can influence the fingering instability for arbitrary wavenumbers in gravity-driven thin film flow. We apply the linear stability analysis method on our 3D power-law model and use Taylor series to approximate the power terms in the power-law evolution equation. The perturbation and the growth rate are obtained numerically for different wavenumbers. Parametric study is performed to investigate the impact of shear-thinning index on the growth rate of perturbation. For the assessment of this study, we compare the result of this study with the existing result for Newtonian fluids in literature. The wavelength and growth rate obtained in this study are also compared to our previous 3D simulation results and experimental results. [Preview Abstract] |
Sunday, November 18, 2012 3:46PM - 3:59PM |
D9.00008: Inhibition of viscous fluid fingering: A variational scheme for optimal flow rates Jose Miranda, Eduardo Dias, Enrique Alvarez-Lacalle, Marcio Carvalho Conventional viscous fingering flow in radial Hele-Shaw cells employs a constant injection rate, resulting in the emergence of branched interfacial shapes. The search for mechanisms to prevent the development of these bifurcated morphologies is relevant to a number of areas in science and technology. A challenging problem is how best to choose the pumping rate in order to restrain growth of interfacial amplitudes. We use an analytical variational scheme to look for the precise functional form of such an optimal flow rate. We find it increases linearly with time in a specific manner so that interface disturbances are minimized. Experiments and nonlinear numerical simulations support the effectiveness of this particularly simple, but not at all obvious, pattern controlling process. [Preview Abstract] |
Sunday, November 18, 2012 3:59PM - 4:12PM |
D9.00009: Modelling the suppression of radial fingering in elastic Hele-Shaw cells Draga Pihler-Puzovic, Raphael Perillat, Matthias Heil, Anne Juel We find a surprisingly effective means of suppressing the fingering instabilities at the interface of air and a viscous fluid in the narrow gap between two parallel plates, by replacing one of the plates with an elastic membrane. Experiments show that the resulting fluid-structure interaction considerably delays the onset of fingering and fundamentally alters the large-amplitude interfacial patterns that develop subsequently. We present the results of a linear stability analysis which assesses how the stability of the axisymmetrically expanding air bubble to non-axisymmetric perturbations is affected by the presence of the elastic membrane, and perform direct numerical simulations to follow the evolution of the instabilities into the large-amplitude regime. The theoretical/computational predictions are then compared against the experimental results. [Preview Abstract] |
Sunday, November 18, 2012 4:12PM - 4:25PM |
D9.00010: Thin-film flows without precursors Ruben Juanes, Luis Cueto-Felgueroso, Michael Szulczewski The flow of thin films over flat surfaces has been the subject of much theoretical, experimental and computational research. Under the lubrication approximation, the classical mathematical model for these flows takes the form of a nonlinear fourth-order PDE, where the fourth-order term models the effect of surface tension. This classical model, however, effectively assumes that the film is perfectly wetting to the substrate and, therefore, does not capture the partial wetting regime. Partial wetting is responsible for stopping the spread of a liquid puddle, and for pinning the contact line of a viscous liquid down an incline, controlling the morphology of the fingering pattern that ensues. Here, we extend our recent work on macroscopic phase-field modeling of two-phase flow in a capillary tube to thin-film flows with partial wetting. Our model naturally accounts for the dynamic contact angle at the contact line, and therefore permits modeling thin-film flows without invoking a precursor film, leading to compactly-supported solutions. We model the statics and dynamics of a liquid puddle, and the fingering behavior of flow down an incline. We compare model predictions with experiments of thin-film flows both on a horizontal plane and down an incline, for different contact angles. [Preview Abstract] |
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