Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session D27: Focus Session: Unanswered Questions in Viscous Fingering IInstabilities
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Chair: Irmgard Bischofberger, Massachusetts Institute of Technology Room: 709 |
Sunday, November 19, 2017 2:15PM - 2:28PM |
D27.00001: Propagation of a finite bubble in a Hele-Shaw channel of variable depth Anne Juel, Andres Franco-Gomez, Alice Thompson, Andrew Hazel We study the propagation of finite bubbles in a Hele-Shaw channel, where a centred rail is introduced to provide a small axially-uniform depth constriction. We demonstrate experimentally that this channel geometry can be used as a passive sorting device. Single air bubbles carried within silicone oil are generally transported on one side of the rail. However, for flow rates marginally larger than a critical value, a narrow band of bubble sizes on the order of the rail width can propagate over the rail, while bubbles of other sizes segregate to the side of the rail. The width of this band of bubble sizes increases with flow rate and the size of the most stable bubble can be tuned by varying the rail width. We present a depth-averaged theory which reveals that the mechanism relies on a non-trivial interaction between capillary and viscous forces that is fully dynamic, rather than being a simple modification of capillary static solutions. In contrast, for larger bubbles and sufficiently large imposed flow rates, we find that initially centred bubbles do not converge onto a steady mode of propagation. Instead they transiently explore weakly unstable steady modes, an evolution which results in their break-up and eventual settling into a steady state of changed topology. [Preview Abstract] |
Sunday, November 19, 2017 2:28PM - 2:41PM |
D27.00002: Viscous Fingering in Deformable Systems Jian Hui Guan, Chris MacMinn Viscous fingering is a classical hydrodynamic instability that occurs when an invading fluid is injected into a porous medium or a Hele-Shaw cell that contains a more viscous defending fluid. Recent work has shown that viscous fingering in a Hele-Shaw cell is supressed when the flow cell is deformable. However, the mechanism of suppression relies on a net volumetric expansion of the flow area. Here, we study flow in a novel Hele-Shaw cell consisting of a rigid bottom plate and a flexible top plate that deforms in a way that is volume-conserving. In other words, fluid injection into the flow cell leads to a local expansion of the flow area (outward displacement of the flexible surface) that must be coupled to non-local contraction (inward displacement of the flexible surface). We explore the impact of this volumetric confinement on steady viscous flow and on viscous fingering. [Preview Abstract] |
Sunday, November 19, 2017 2:41PM - 2:54PM |
D27.00003: An experimental study of miscible viscous fingering of annular ring Yuichiro Nagatsu, Hamirul Bin Othman, Manoranjan Mishra Understanding the viscous fingering (VF) dynamics of finite width sample is important in the fields especially such as liquid chromatography and groundwater contamination and mixing in microfluidics. In this paper, we experimentally investigate such hydrodynamical morphology of VF using a Hele-Shaw flow system in which a miscible annular ring of fluid is displaced radially. Experiments are performed to investigate the effects of the sample volume, the effects of dispersion and log mobility ratio $R$ on the dynamics of VF pattern and onset of such instability. Depending whether the finite width ring is more or less viscous than the carrier fluid, the log mobility ratio R becomes positive or negative respectively. The experiments are successfully conducted to obtain the VF patterns for $R $\textgreater 0 and $R $\textless 0, of the finite annular ring at the inner and outer radial interfaces, respectively. It is found that in the radial displacement, the inward finger moves slower than the outward finger. The experimental results are found to be qualitatively in good agreement with the corresponding linear stability analysis and non-linear simulations results available in the literature. [Preview Abstract] |
Sunday, November 19, 2017 2:54PM - 3:07PM |
D27.00004: Repeated bubble breakup and coalescence in perturbed Hele-Shaw channels Alice Thompson, Andres Franco-Gomez, Andrew Hazel, Anne Juel The introduction of an axially-uniform, centred constriction in a Hele-Shaw channel leads to multiple propagation modes for both air fingers and bubbles, including symmetric and asymmetric steadily propagating modes along with oscillations. These multiple modes correspond to a non-trivial bifurcation structure, and relate to the plethora of steadily propagating bubbles and fingers which exist in the Saffman-Taylor system. In both experiments and depth-averaged computations, a very small centred occlusion can be enough to trigger bubble breakup, with a single large centred bubble splitting into two smaller bubbles which propagate along each side of the channel. We present numerical simulations for the depth-averaged model, implementing geometric criteria for pinchoff and coalescence in order to track the bubble before and beyond breakup. We find that the two-bubble state is itself unstable, with finger competition causing one bubble to move ahead; the trailing bubble then moves across the channel to merge with the leading bubble. However, the story is not always so simple, enabling complicated cascades of splitting and merging bubbles. We compare the general dynamical behaviour, basins of attraction, and the details of merging and splitting, to experimental observations. [Preview Abstract] |
Sunday, November 19, 2017 3:07PM - 3:20PM |
D27.00005: Self-similarity in particle accumulation on the fluid-fluid interface Yun Chen, Feng Xu, Sungyon Lee When the mixture of viscous oil and non-colloidal particles displaces air between two parallel plates, the shear-induced migration of particles leads to the gradual accumulation of particles on the advancing oil-air interface. This particle accumulation results in the fingering of an otherwise stable fluid-fluid interface. While the previous works by Xu and colleagues have focused on the resultant instability, one unexplored yet striking feature of the experiments is the self-similarity in the concentration profile of the accumulating particles. In this talk, we model the self-similar particle profiles mathematically, by considering the depth-averaged particle transport equations and the suspension balance model. The method of asymptotic matching is used to combine the key physical effects -- the shear-induced migration far upstream of the interface and the secondary flow near the interface, in a mathematically tractable way. [Preview Abstract] |
Sunday, November 19, 2017 3:20PM - 3:33PM |
D27.00006: Enhancement of particle-induced viscous fingering in bidisperse suspensions Feng Xu, Sungyon Lee The novel particle-induced fingering instability is observed when bidisperse particle suspensions displace air in a Hele-Shaw cell. Leading to the instability, we observe that larger particles consistently enrich the fluid-fluid interface at a faster rate than the small particles. This size-dependent enrichment of the interface leads to an earlier onset of the fingering instability for bidisperse suspensions, compared to their monodisperse counterpart. Careful experiments are carried out by either systematically varying the ratio of large to small particles at fixed total concentrations, or by changing the total concentrations while the large particle concentrations are held constant. Experimental results show that the presence of large particle causes the instability to occur at concentrations as much as 5\% lower than the pure small particle case. We also discuss the physical mechanism that drives the enrichment and the subsequent instability based on the modified suspension balance model. [Preview Abstract] |
Sunday, November 19, 2017 3:33PM - 3:46PM |
D27.00007: Deformation of interface in a partially miscible system during favorable displacement Ryuta Suzuki, Yuichiro Nagatsu, Manoranjan Mishra, Takahiko Ban The Saffman-Taylor instability triggers a well-known viscous fingering (VF, called unfavorable displacement), occurring when a less viscous fluid displaces a more viscous one in porous media or in a Hele-Shaw cell because the boundary of the two fluids becomes hydrodynamically unstable. In the reverse situation (called favorable displacement) in which a more viscous fluid displaces a less viscous one, no instabilities occur due to hydrodynamically stable system. It has been reported that the favorable displacements become unstable by several physicochemical effects. So far, studies of both displacements have focused on fluids that are either fully miscible or immiscible. However, little attention has been paid to displacements in partially miscible system. Here, we have discovered that a partial miscibility triggers fingering instability in a favorable displacement without any chemical reactions. The occurrence of this new instability is induced by not hydrodynamic effects but a thermodynamic effect that is so-called Korteweg effect in which convection is induced during phase separation process in a partially miscible system. [Preview Abstract] |
Sunday, November 19, 2017 3:46PM - 3:59PM |
D27.00008: A transition in the viscous fingering instability in miscible fluids Thomas Videbaek, Sidney R. Nagel The viscous fingering instability in a quasi-two dimensional Hele-Shaw cell is an example of complex structure formation from benign initial conditions. When the invading fluid has the lesser viscosity, the interface between the two fluids is unstable to finger formation. Here, we study the instability between pairs of miscible fluids in a circular cell with fluid injected at its center. As the injection rate is decreased, diffusion will smooth out the discontinuity in the gap-averaged viscosity at the interface between the fluids. At high injection rates (i.e., high P\'eclet number, Pe), fingering is associated with three-dimensional structure within the gap between the confining plates. On lowering Pe, we find a sharp transition in the finger morphology at a critical value, $\mathrm{Pe}_c\sim(\eta_i/\eta_o)^{1/2}$, with $\eta_i$ ( $\eta_o$) being the viscosity of the inner (outer) fluid; at this point, the width of the fingers jumps, the length of the fingers shrinks towards zero and the three-dimensional structure goes from half filling to fully filling the gap. Thus, by controlling the viscosity contrast at the interface, one can alter and even completely suppress the instability. [Preview Abstract] |
Sunday, November 19, 2017 3:59PM - 4:12PM |
D27.00009: Stabilization of miscible viscous fingering by a step-growth polymerization reaction Patrick Bunton, Simone Stewart, Daniela Marin, Michael Tullier, Eckart Meiburg, John Pojman Viscous fingering is a hydrodynamic instability that occurs when a more mobile fluid displaces a fluid of lower mobility. Viscous fingering is often undesirable in industrial processes such as secondary petroleum recovery where it limits resource recovery. Linear stability analysis by Hejazi et al. (2010) has predicted that a non-monotonic viscosity profile at an otherwise unstable interface can in some instances stabilize the flow. We use step-growth polymerization at the interface between two miscible monomers as a model system. A dithiol monomer displacing a diacrylate react to form a linear polymer that behaves as a Newtonian fluid. Viscous fingering was imaged in a horizontal Hele-Shaw cell via Schlieren, which is sensitive to polymer conversion. By varying reaction rate via initiator concentration along with flow rate, we demonstrated increasing stabilization of the flow with increasing Damkohler number (ratio of the reaction rate to the flow rate). Results were compared with regions of predicted stability from the results of Hejazi et al. (2010). When the advection outran the reaction, viscous fingering occurred as usual. However, when the reaction was able to keep pace with the advection, the increased viscosity at the interface stabilized the flow. [Preview Abstract] |
Sunday, November 19, 2017 4:12PM - 4:25PM |
D27.00010: Osmosis-driven viscous fingering of oil-in-water emulsions Ying Liu, Bhargav Rallabandi, Mrudhula Baskaran, Howard Stone Viscous fingering occurs when a low viscosity fluid invades a more viscous fluid. Fingering of two miscible fluids is more complicated than that of immiscible fluids in that there is no sharp fluid-fluid interface and diffusion occurs between the phases. We experimentally studied the fingering of two miscible fluids: an oil-in-water emulsion and a sodium chloride solution. When the concentration of sodium chloride in the water phase in the emulsion exceeds that in the sodium chloride solution, the consequent osmotic flow automatically facilitates the occurrence of the fingering. On the contrary, when the sodium chloride solution has higher concentration, the spreading of emulsion is more uniform than the case without the concentration difference. We provide a model to rationalize and quantify these observations. [Preview Abstract] |
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