Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session H18: Flow Instability: Interfacial and Thin Films II |
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Chair: Satish Kumar, University of Minnesota Room: 206 |
Monday, November 23, 2015 10:35AM - 10:48AM |
H18.00001: Electrohydrodynamic deformation of thin liquid films near surfaces with topography Satish Kumar, Aruna Ramkrishnan Motivated by the use of electrostatic assist to improve liquid transfer in gravure printing, we use theory and experiment to understand how electric fields deform thin liquid films near surfaces with cavity-like topographical features. Lubrication theory is used to describe the film dynamics, and both perfect and leaky dielectric materials are considered. For sinusoidal cavities, we apply asymptotic methods to obtain analytical results that relate the film deformation to the other problem parameters. For trapezoidal-like cavities, we numerically solve evolution equations to study the influence of steep topographical features and the spacing between cavities. Results from flow visualization experiments are in qualitative agreement with the theoretical predictions. In addition to being relevant to printing processes, the model problems we consider are also of fundamental interest in and represent novel contributions to the areas of electrohydrodynamics and thin-liquid-film flows. [Preview Abstract] |
Monday, November 23, 2015 10:48AM - 11:01AM |
H18.00002: Miscible viscous fingering involving production of gel by chemical reactions Yuichiro Nagatsu, Kenichi Hoshino We have experimentally investigated miscible viscous fingering with chemical reactions producing gel. Here, two systems were employed. In one system, sodium polyacrylate (SPA) solution and aluminum ion (Al3$+)$ solution were used as the more and less viscous liquids, respectively. In another system, SPA solution and ferric ion (Fe3$+)$ solution were used as the more and less viscous liquids, respectively. In the case of Al3$+$, displacement efficiency was smaller than that in the non-reactive case, whereas in the case of Fe3$+$, the displacement efficiency was larger. We consider that the difference in change of the patterns in the two systems will be caused by the difference in the properties of the gels. Therefore, we have measured the rheological properties of the gels by means of a rheometer. We discuss relationship between the VF patterns and the rheological measurement. [Preview Abstract] |
Monday, November 23, 2015 11:01AM - 11:14AM |
H18.00003: Sensitivity of Saffman-Taylor fingers to channel-depth variations Andres Franco-Gomez, Alice Thompson, Andrew Hazel, Anne Juel We probe the sensitivity of Saffman--Taylor fingers to small controlled variations in channel depth by investigating the effect of a centred, rectangular occlusion on finger propagation in a Hele-Shaw channel. This geometry supports symmetric, asymmetric and oscillatory propagation states. A previously developed depth-averaged model is in quantitative agreement with laboratory experiments once the aspect ratio (width/height) of the tube's cross-section reaches a value of 40. We find that the multiplicity of solutions at a finite occlusion height arises through interactions of the single stable and multiple unstable solutions already present in the absence of the occlusion: the classic Saffman--Taylor viscous fingering problem. The sequence of interactions that occurs with increasing occlusion height are invariable for all aspect ratios investigated, but the occlusion height required for each interaction decreases with increasing aspect ratio. Thus, the system becomes more sensitive as the aspect ratio increases, in the sense that multiple solutions are provoked for smaller relative depth changes. We estimate that the required depth-changes become of the same order as the typical roughness of the experimental system (1 micron) for aspect ratios beyond 155. [Preview Abstract] |
Monday, November 23, 2015 11:14AM - 11:27AM |
H18.00004: Influence of the contact line velocity on the finger formation of the liquid film expanding on an inclined plate Masatoshi Yamashita, Masato Nishikawa, Takahiro Ito, Yoshiyuki Tsuji When a liquid film flows down on an inclined solid surface, the contact line can be destabilized to finger shape. This phenomenon leads to the non-uniform height of the liquid surface or even to generation of dry patch, and then has a great effect on cooling of energy device and quality of coating. In previous studies, the final finger shapes have been discussed by relating the with capillary (Ca) number and the wetting properties of the liquid for the solid substrate, i.e. the contact angle. However, in the experimental studies, little attention has been paid on the difference between the static contact angle and the dynamic one, the latter which is actually observed when the finger is developing. In this study, we performed three-dimensional measurement of surface geometry of the liquid film to clarify how the dynamic contact angles and the Ca number influence the finger shape by optical method. We observed two different finger shapes depending on the volumes of the working fluid., and verified that the finger shapes depend on the contact angle scaled by Ca number. We found that the local dynamic contact angle and the contact line velocity on the trough part of the wavy contact line can be highly related with the final finger shape. [Preview Abstract] |
Monday, November 23, 2015 11:27AM - 11:40AM |
H18.00005: The Role of Chemical Reactions in Fluid Instabilities: Step-Growth Polymerization Simone Stewart, Daniela Marin, Patrick Bunton Fingering is a fluid instability that occurs when a fluid of high mobility displaces a fluid of lower mobility. When the source of mobility difference is viscosity, viscous fingering occurs. Schlieren imaging is used to view viscous fingering during step-growth polymerization of various dithiol-di-acrylate systems in a Hele-Shaw cell. A dithiol is flowed into various diacrylates of varying viscosity. Systems are characterized in terms of the Damk\"{o}hler number (D$_{\mathrm{a}})$, which is the ratio of the chemical time scale to the hydrodynamic time scale. The reaction rate is tuned by varying the kind and amount of initiator and the flow rate is easily varied with a syringe pump. As a result of these variations, it is possible to gain some degree over control of the fingering that occurs. Results have shown the effects of a low flow rate on a low concentration monomer are comparable to the effects an increase in reactivity has on a flow run at a high rate. Due to the sensitivity of the Schlieren technique and the instability of viscous fingering, gravitational instabilities within the monomer flows are also revealed in this experiment. These are discussed in terms of recent three-dimensional calculations in the literature. [Preview Abstract] |
Monday, November 23, 2015 11:40AM - 11:53AM |
H18.00006: Impact of Viscous Fingering on Fluid Mixing Jane Chui, Pietro de Anna, Ruben Juanes Viscous fingering is a hydrodynamic instability that occurs when a less viscous fluid displaces a more viscous one. Instead of progressing as a uniform front, the less viscous fluid forms fingers that vary in size and shape to create complex patterns. Understanding how these patterns and their associated gradients evolve over time is of critical importance in characterizing the mixing of two fluids, which in turn is important to applications such as enhanced oil recovery and microfluidics. Mixing relies on the presence of concentration gradients. In this work, we determine the concentration field experimentally during the injection of a fluid into a circular Hele-Shaw cell to displace a more viscous fluid. We use a fluorescent tracer with the injected fluid to obtain high-resolution concentration fields, from which we determine the concentration gradients for different fluid injection rates and various viscosity ratios. Areas where gradients are present constitute the mixing zone, which can be characterized by its length and its thickness. We develop quantitative models of the dynamics of the interface length (previous work) and mixing zone thickness, and propose a scaling theory for the growth of the mixing zone and the overall impact of viscous fingering on mixing. [Preview Abstract] |
Monday, November 23, 2015 11:53AM - 12:06PM |
H18.00007: Influence of fluid dispersion on transient behaviors of miscible viscous fingering Tapan Kumar Hota, Manoranjan Mishra We study the influence of fluid dispersion on miscible viscous fingering (VF) in the framework of non-modal stability theory. Miscible VF has traditionally been investigated by quasi-steady approximation (QSSA), followed by normal mode analysis. However, the results of QSSA poorly predicting the transient behavior and often stability analysis are obscured by the unsteady base flow. The system has been studied by coupling the continuity and Darcy equations with a convection-diffusion equation for the evolution of solute concentration. To measure the fluid dispersion the convective characteristic scales are used. The long time behavior of the response to external excitations and the initial conditions are studied by examining the structure of pseudospectra and the optimal growth function, respectively. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by modal analysis. The results show that there can be substantial transient growth of perturbations when the fluid disperses at a very slow rate. [Preview Abstract] |
Monday, November 23, 2015 12:06PM - 12:19PM |
H18.00008: Fingering patterns induced by precipitation reactions A. De Wit, F. Haudin, P. Shukla, F. Brau When reactants of a precipitation reaction are injected in a given porous medium, a fingering instability deforming the precipitation front can occur due to a change in permeability along the flow. We study the related precipitation patterns by combined experimental and theoretical work. Experiments are performed in confined geometries i.e. so-called Hele-Shaw cells consisting in two horizontal transparent plates separated by a thin gap containing a solution of one reactant B. The solution of the other reactant A is injected radially in the cell through a small hole. Upon displacement, a precipitation reaction between reactants A and B produce a solid phase C in the miscible reactive zone. We show that a wealth of different precipitation patterns (including spirals, flowers or filaments) can be observed depending on the flow rate and relative concentration of the two reactants. We discuss the relative effect of viscous fingering and of the cohesive properties of the precipitate in shaping the patterns. From a theoretical point of view, nonlinear simulations of the problem give insight into the similarities and differences between viscous fingering and precipitation-driven fingering. [Preview Abstract] |
Monday, November 23, 2015 12:19PM - 12:32PM |
H18.00009: Comet-shape deformation and transition to viscous fingering of a miscible circular blob in porous media Manoranjan Mishra, Anne De Wit, Satyajit Pramanik We numerically show that a miscible circular blob of viscosity larger than the ambient fluid features three different instability patterns -- viscous fingering (VF), lump- and comet-shape instabilities. For a given P\'{e}clet number larger than the critical value, VF is observed in a finite range of viscosity contrast between the two fluids. This is in strong contrast to the displacement of a finite slice of miscible fluid in porous media in which instability enhances as viscosity contrast increases. Outside the finite interval of critical viscosity contrast for VF, the circular blob features comet- and lump-shape instabilities. These new dynamics are attributed to competition among the diffusive, convective and viscous forces. Our findings can be very important to understand many physico-chemical dynamics, CO$_{2}$ sequestration, reactive dissolution of porous rocks, etc. [Preview Abstract] |
Monday, November 23, 2015 12:32PM - 12:45PM |
H18.00010: Shock Layer effects on Viscous Fingering instability Chinar Rana, Manoranjan Mishra The displacement flow in a porous media is remarkably influenced by the solute concentration dissolved in the fluids. The equilibrium-dispersive model for the evolution of the solute is numerically investigated which is coupled to Darcy law. In this model the fluid viscosity depends upon the solute concentration with the solute undergoing a non-linear adsorption of Langmuir type. The non-linear adsorption results in the formation of shock layer, which is progressively developed at the interface of the two fluids. The simulation results reveal that as soon as there is viscosity contrast between the interplaying fluids, the steepened profile formed due to Langmuir adsorption speed up the instability phenomena. Thus for fluids having larger viscosity contrast the shock layer is never formed. However, for fluids having less viscosity gradient, the shock layer gets formed but it eventually vanishes at the onset of instability. Hence the viscous fingering instability and shock layer affect the occurrence of each other. [Preview Abstract] |
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