Modelling the suppression of viscous fingering in elastic-walled Hele-Shaw cells

2013 ◽  
Vol 731 ◽  
pp. 162-183 ◽  
Author(s):  
Draga Pihler-Puzović ◽  
Raphaël Périllat ◽  
Matthew Russell ◽  
Anne Juel ◽  
Matthias Heil
Keyword(s):  
Viscous Fingering ◽  
Base Flow ◽  
Elastic Membrane ◽  
Minor Role ◽  
Viscous Effects ◽  
Flow Rates ◽  
Air Bubble ◽  
Lubrication Equation ◽  
Fingering Instability ◽  
Air Liquid Interface

AbstractRecent experiments by Pihler-Puzovic et al. (Phys. Rev. Lett., vol. 108, 2012, article 074502) have shown that the onset of viscous fingering in circular Hele-Shaw cells in which an air bubble displaces a viscous fluid is delayed considerably when the top boundary of the cell is replaced by an elastic membrane. Non-axisymmetric instabilities are only observed at much larger flow rates, and the large-amplitude fingers that develop are fundamentally different from the highly branched fingers in rigid-walled cells. We explain the mechanism for the suppression of the instability using a combination of linear stability analysis and direct numerical simulations, based on a theoretical model that couples a depth-averaged lubrication equation for the fluid flow to the Föppl–von Kármán equations, which describe the deformation of the elastic membrane. We show that fluid–structure interaction affects the instability primarily via two changes to the axisymmetric base flow: the axisymmetric inflation of the membrane prior to the onset of any instabilities slows down the expansion of the air bubble and forces the air–liquid interface to propagate into a converging fluid-filled gap. Both of these changes reduce the destabilizing viscous effects that drive the fingering instability in a rigid-walled cell. In contrast, capillary effects only play a very minor role in the suppression of the instability.

scholarly journals Viscous fingering in a radial elastic-walled Hele-Shaw cell

2018 ◽  
Vol 849 ◽  
pp. 163-191 ◽  
Author(s):  
Draga Pihler-Puzović ◽  
Gunnar G. Peng ◽  
John R. Lister ◽  
Matthias Heil ◽  
Anne Juel
Keyword(s):  
Stability Analysis ◽  
Flow Rate ◽  
Small Amplitude ◽  
Viscous Fingering ◽  
Flow Rates ◽  
Injection Flow ◽  
Fingering Instability ◽  
Air Liquid Interface ◽  
Hele Shaw Cell ◽  
Axisymmetric Perturbations

We study the viscous-fingering instability in a radial Hele-Shaw cell in which the top boundary has been replaced by a thin elastic sheet. The introduction of wall elasticity delays the onset of the fingering instability to much larger values of the injection flow rate. Furthermore, when the instability develops, the fingers that form on the expanding air–liquid interface are short and stubby, in contrast with the highly branched patterns observed in rigid-walled cells (Pihler-Puzović et al., Phys. Rev. Lett., vol. 108, 2012, 074502). We report the outcome of a comprehensive experimental study of this problem and compare the experimental observations to the predictions from a theoretical model that is based on the solution of the Reynolds lubrication equations, coupled to the Föppl–von-Kármán equations which describe the deformation of the elastic sheet. We perform a linear stability analysis to study the evolution of small-amplitude non-axisymmetric perturbations to the time-evolving base flow. We then derive a simplified model by exploiting the observations (i) that the non-axisymmetric perturbations to the sheet are very small and (ii) that perturbations to the flow occur predominantly in a small wedge-shaped region ahead of the air–liquid interface. This allows us to identify the various physical mechanisms by which viscous fingering is weakened (or even suppressed) by the presence of wall elasticity. We show that the theoretical predictions for the growth rate of small-amplitude perturbations are in good agreement with experimental observations for injection flow rates that are slightly larger than the critical flow rate required for the onset of the instability. We also characterize the large-amplitude fingering patterns that develop at larger injection flow rates. We show that the wavenumber of these patterns is still well predicted by the linear stability analysis, and that the length of the fingers is set by the local geometry of the compliant cell.

Viscous fingering with a single fluid

2005 ◽  
Vol 83 (5) ◽  
pp. 551-564 ◽  
Author(s):  
Kristi E Holloway ◽  
John R de Bruyn
Keyword(s):  
Numerical Simulations ◽  
Viscous Fingering ◽  
High Flow ◽  
Cell Width ◽  
Flow Rates ◽  
Viscosity Contrast ◽  
Fingering Instability ◽  
Hele Shaw Cell ◽  
Initial Viscosity

We study fingering that occurs when hot glycerine displaces cooler, more viscous glycerine in a radial Hele-Shaw cell. We find that fingering occurs for a sufficiently large initial viscosity contrast and for sufficiently high flow rates of the displacing fluid. The wavelength of the fingering instability is proportional to the cell width for thin cells, but the ratio of wavelength to cell width decreases for our thickest cell. Similar fingering is seen in numerical simulations of this system.PACS Nos.: 47.54.+r, 68.15.+e, 47.20.–k

scholarly journals Viscous-fingering mechanisms under a peeling elastic sheet

2019 ◽  
Vol 864 ◽  
pp. 1177-1207
Author(s):  
Gunnar G. Peng ◽  
John R. Lister
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Cell Walls ◽  
Viscous Fingering ◽  
Base Flow ◽  
Fingering Instability ◽  
Linear Perturbations ◽  
The Stability ◽  
Rigid Walls ◽  
Hele Shaw Cell

We study the mechanisms affecting the viscous-fingering instability in an elastic-walled Hele-Shaw cell by considering the stability of steady states of unidirectional peeling-by-pulling and peeling-by-bending. We demonstrate that the elasticity of the wall influences the steady base state but has a negligible direct effect on the behaviour of linear perturbations, which thus behave like in the ‘printer’s instability’ with rigid walls. Moreover, the geometry of the cell can be very well approximated as a triangular wedge in the stability analysis. We identify four distinct mechanisms – surface tension acting on the horizontal and the vertical interfacial curvatures, kinematic compression in the longitudinal base flow, and the films deposited on the cell walls – that each contribute to stabilizing the system. The vertical curvature is the dominant stabilizing mechanism for small capillary numbers, but all four mechanisms have a significant effect in a large region of parameter space.

scholarly journals COMPARISON OF DIFFERENT HYDRODYNAMIC CHARACTERISTICS OF AIR- WATER SYSTEM USING DISSIMILAR MOTIONLESS MIXERS

2021 ◽  
Author(s):  
Dr. Mazhar Hussain
Keyword(s):  
Mass Transfer ◽  
Power Consumption ◽  
Dissolved Oxygen ◽  
Bubble Diameter ◽  
Water System ◽  
Hydrodynamic Characteristics ◽  
Flow Rates ◽  
Static Mixers ◽  
Air Bubble ◽  
Transfer Study

The hydrodynamic characteristics of mixing fluids are always the points to consider in improvement of their mixing quality especially using motionless mixers normally stated as “Static Mixers”. Motionless mixing technique was adopted for Air-Water system with the advantage of negligible power consumption over dynamic mixers. Different hydrodynamic characteristics were experimented using “Baffle Type” static element and were compared to those of already used in recent studies. Dissolved oxygen content, Static mixer geometry (i.e. Baffle, Blade, Wheel, Plate and Needle), mixing fluids flow rates were chosen as variables and selected in this content as rate of mass transfer study which founds out to be significant using “Baffle Type” static element. Volumetric mass transfer was also achieved at higher scale which gives a clear indication of increase the mass transfer coefficient in between the comparison of “Baffle type” element and other mentioned elements. Pressure droplet and depletion in Air bubble size across static elements were visually perceived using Hg-Manometer and still photography respectively. A mathematical model was also developed portraying the Air bubble diameter at different flow rates for this system. Other hydrodynamics like higher Dissolved Oxygen (DO) Content, Less Power consumption were also found to be more advantageous for “Baffle Type” static element.

scholarly journals Numerical simulation of bubble dynamics in response to acoustic disturbances

2007 ◽  
Author(s):  
Κωνσταντίνος Τσιγκλιφής
Keyword(s):  
Constitutive Law ◽  
Membrane Properties ◽  
Elastic Membrane ◽  
Shear Stresses ◽  
Additional Parameter ◽  
Viscous Effects ◽  
Membrane Elasticity ◽  
Backscatter Signal ◽  
Acoustic Disturbances ◽  
Bending Modulus

The dynamic behavior and the fashion of collapse of a free bubble play a significant role in the phenomenon of single cavitation bubble luminescence (SCBL) and single bubble sono-luminescence (SBSL), in which light is emitted during its breakdown. In SCBL, the bubble is produced by the application of a laser pulse, in the host liquid, with a duration of 10⁻¹⁵ sec (femtosecond bubbles) and 10⁻⁹ sec (nanosecond bubbles). The resulting bubbles have size of the order of 5 and 500 μm, respectively. The femtosecond bubbles display severe elongation with regards to the axis of symmetry, while light is not emitted during their collapse. In contrast, the nanosecond bubbles exhibit almost spherosymmetric shape initially and collapse producing light. A parametric study is conducted on the fashion of collapse of bubbles, of various sizes, for weak or strong elongation and vanishing small or large internal overpressure, considering axisymmetric oscillations with weak viscous effects. Further, an effort is made to reproduce, as close as possible, respective SCBL and SBSL experiments, aiming to investigate the effect of the initial asymmetry on the fashion of collapse and the velocity of the resulting jet during collapse. Recently, a significant number of applications in diagnostic and therapeutic medicine use the ability of microbubbles, encapsulated by an elastic membrane (contrast agents), to reflect the ultrasound waves. Initially, a model that predicts the backscatter signal of the microbubble as a function of the membrane properties, of the host liquid and the width and the frequency of the acoustic disturbances, is presented. This model predicts with accuracy the effect of the non linear membrane constitutive law on the microbubble response for large acoustic disturbances in comparison to experimental measurements. The control of cohesion of microbubbles is desirable in several applications, such as in quantitative evaluation of heart blood flow (contrast perfusion imaging). In order to gain understanding regarding its cohesion range, the large-amplitude axisymmetric oscillation and collapse of an encapsulated microbubble is examined. The shear stresses that develop on the membrane due to the bending moments are accounted for, based on the shell stability theory, and are determined by the scalar bending modulus. This is a measure of the shell resistance to bending and is introduced as an additional parameter, due to the anisotropy of the membrane elasticity along the interface and perpendicular to it. With the help of stability analysis, it is feasible to estimate the range of the parameters for shape oscillations of the microbubble, as well as for the buckling of the shell. In combination with the model of the spherosymmetric oscillations, a theoretical tool is developed for the characterisation of a microbubble with regards to its membrane elasticity, bending resistance and viscosity. Phase diagrams are constructed where the regions of stable or unstable oscillation of a microbubble are defined. Finally, axisymmetric simulations of the interaction of the external flow field and the encapsulated microbubble are performed, implementing a hybrid boundary-finite element method, in order to determine the conditions under which a jet is created during the oscillation of the microbubble; a phenomenon which is observed when a microbubble oscillates near the walls of neighbouring tissues.

Freshwater input into a low-Arctic Fjord in West Greenland: Timing, drivers and model evaluation

2021 ◽  
Author(s):  
Jakob Abermann ◽  
Kirsty Langley ◽  
Sille Myreng ◽  
Dorthe Petersen ◽  
Kerstin Rasmussen ◽  
...  
Keyword(s):  
Large Scale ◽  
Temporal Trends ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Base Flow ◽  
Minor Role ◽  
Freshwater Flux ◽  
Freshwater Input ◽  
West Greenland ◽  
Specific Discharge

<p>The majority of the freshwater input from Greenland stems from the Greenland Ice Sheet. Despite its importance in terms of freshwater totals, there is a much higher number of individual catchments disconnected from the ice sheet contributing on average about 26% of the total Greenland freshwater flux. Most of those catchments have local glacier cover, only very few of them are instrumented and little scientific literature exists. We present a dataset of 12 years of discharge of four catchments less than 15 km apart, that are different in size (between 7 and 32 km²), local glacier coverage (4-11%) and lake cover (0-5%). They all drain into Kobbefjord, a well-studied fjord in West Greenland, near Greenland’s capital Nuuk. We find that annual specific discharge totals vary greatly (between 1.2 and 1.9 m/yr on a 12-year average within 15 km) due to a general climatic gradient and different strengths of orographic shading. The seasonal cycle differs among the sites mainly due to different exposure to solar radiation as a driver for major snowmelt; small ice coverage in the catchments plays only a minor role in discharge variability. Dry years generally increase the magnitude of spatial gradients in specific discharge and no significant temporal trends have been found in the studied catchments. On the sub-daily scale, the presence and elevation of lakes determines the catchment’s response during sunny days, leading to a difference in the timing of maximum discharge of between 7 and 12 hours depending on the site and the time of the year. The response of discharge to major precipitation events is discussed, where uniform reaction is found for the catchments with no lakes near the gauge and a delay of between 5 and 7 hours in the catchment with low-lying lakes. A comparison with a recently published modelled discharge time series on individual catchment scale shows the model’s capability of reproducing both snowmelt and large-scale storm events; however, the strong spatial heterogeneity of discharge magnitude and timing as well as the presence and variability of base-flow is not captured. We discuss methods to combine observational data with existing model output in order to improve the potential of their combined usage on the Greenland-scale.</p>

NUMERICAL ANALYSIS OF VISCOUS FINGERING INSTABILITY DUE TO MISCIBLE DISPLACEMENT

2020 ◽  
Vol 61 (4) ◽  
pp. 539-545
Author(s):  
A. Nemati ◽  
H. Saffari ◽  
B. Z. Vamerzani ◽  
R. Azizi ◽  
S. M. Hosseinalipoor ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Viscous Fingering ◽  
Miscible Displacement ◽  
Fingering Instability

Influence of Fluid-Dynamics on Heat Transfer in a Pre-Swirl Rotating-Disc System

2004 ◽  
Author(s):  
Gary D. Lock ◽  
Michael Wilson ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Gas Turbines ◽  
Fluid Dynamic ◽  
Impinging Jets ◽  
Coolant Flow ◽  
Viscous Effects ◽  
Rotating Disc ◽  
Scaled Model ◽  
Flow Rates

Modern gas turbines are cooled using air diverted from the compressor. In a “direct-transfer” pre-swirl system, this cooling air flows axially across the wheel-space from stationary pre-swirl nozzles to receiver holes located in the rotating turbine disc. The distribution of the local Nusselt number, Nu, on the rotating disc is governed by three non-dimensional fluid-dynamic parameters: pre-swirl ratio, βp, rotational Reynolds number, Reφ, and turbulent flow parameter, λT. This paper describes heat transfer measurements obtained from a scaled model of a gas turbine rotor-stator cavity, where the flow structure is representative of that found in the engine. The experiments reveal that Nu on the rotating disc is axisymmetric except in the region of the receiver holes, where significant two-dimensional variations have been measured. At the higher coolant flow rates studied, there is a peak in heat transfer at the radius of the pre-swirl nozzles, associated with the impinging jets from the pre-swirl nozzles. At lower coolant flow rates, the heat transfer is dominated by viscous effects. The Nusselt number is observed to increase as either Reφ or λT increases.

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