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

Numerical simulations of a viscous-fingering instability in a fluid with a temperature-dependent viscosity

2006 ◽  
Vol 84 (4) ◽  
pp. 273-287 ◽  
Author(s):  
Kristi E Holloway ◽  
John R Bruyn
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Viscosity Ratio ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cell Width ◽  
Inlet Velocity ◽  
Fingering Instability ◽  
Dependent Viscosity ◽  
Hele Shaw Cell

We have performed numerical simulations of the flow of hot glycerine as it displaces colder, more viscous glycerine in a radial Hele–Shaw cell. We find that fingering occurs for sufficiently high inlet velocities and viscosity ratios. The wavelength of the instability is independent of inlet velocity and viscosity ratio, but depends weakly on cell width. The growth rate of the fingers is found to increase with inlet velocity and decrease with the cell width. We compare our results with those from experiments.PACS No.: 47.54.–r

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We study the viscous-fingering instability in a radial Hele-Shaw cell in which the top boundary has been replaced by a thin elastic sheet.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.

scholarly journals Application of High Flow Rate Gas in the Process of Argon Blowing Trough Steel

2017 ◽  
Vol 62 (2) ◽  
pp. 905-910
Author(s):  
T. Merder ◽  
J. Pieprzyca ◽  
M. Warzecha ◽  
P. Warzecha
Keyword(s):  
Numerical Simulations ◽  
Flow Rate ◽  
High Flow ◽  
High Flow Rate ◽  
Water Model ◽  
Steel Ladle ◽  
Metal Bath ◽  
Flow Rates ◽  
Nominal Capacity ◽  
Additional Support

AbstractThe article demonstrates results of modelling research tests concerning the analysis of possibilities of blowing gas into the metal bath at high flow rates in a steel ladle with a nominal capacity of 50 Mg. Various configurations concerning of gas introduction into the steel ladle were analysed. There were considered cases of blowing into the metal bath via one, two or three purging plugs, being installed on the bottom and via additional support for blowing the gas from the top through the lance.Results obtained from the water model of the reactor were verified with the results of numerical simulations.

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 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.

Monitoring Effects of Catchment Management Practices on Phosphorus Loads into the Eutrophic Peel-Harvey Estuary, Western Australia

1986 ◽  
Vol 18 (4-5) ◽  
pp. 53-61 ◽  
Author(s):  
P. B. Birch ◽  
G. G. Forbes ◽  
N. J. Schofield
Keyword(s):  
Management Practices ◽  
Major Change ◽  
High Flow ◽  
Catchment Management ◽  
Flow Rates ◽  
Early Results ◽  
Phosphorus Loads ◽  
Time Of Year ◽  
High Runoff

Early results from monitoring runoff suggest that the programme to reduce application of superphosphate to farmlands in surrounding catchments has been successful in reducing input of phosphorus to the eutrophic Peel-Harvey estuary. In the estuary this phosphorus fertilizes algae which grow in abundance and accumulate and pollute once clean beaches. The success of the programme has been judged from application of an empirical statistical model, which was derived from 6 years of data from the Harvey Estuary catchment prior to a major change in fertilizer practices in 1984. The model relates concentration of phosphorus with rate of flow and time of year. High phosphorus concentrations were associated with high flow rates and with flows early in the high runoff season (May-July). The model predicted that the distribution of flows in 1984 should have resulted in a flow-weighted concentration of phosphorus near the long-term average; the observed concentration was 25% below the long-term average. This means that the amount of phosphorus discharged into the Harvey Estuary could have been about 2 5% less than expected from the volume of runoff which occurred. However several more years of data are required to confirm this trend.

scholarly journals ‘Tanned’ gelatin spheres and granules for exclusion chromatography

1968 ◽  
Vol 108 (4) ◽  
pp. 641-646 ◽  
Author(s):  
A. Polson ◽  
W. Katz
Keyword(s):  
Molecular Weight ◽  
Polyethylene Glycol ◽  
High Molecular Weight ◽  
Weight Fraction ◽  
High Flow ◽  
High Molecular Weight Fraction ◽  
Flow Rates ◽  
Protein Molecules ◽  
Exclusion Chromatography

1. The preparation of tanned gelatin spheres and granules from high-molecular-weight gelatin is described. This material is comparatively hard, giving high flow rates, is insoluble in water at temperatures between 0° and 100° and is resistant to digestion by trypsin and chymotrypsin. The high-molecular-weight fraction of gelatin was prepared by precipitation with polyethylene glycol, and the spheres and granules prepared from this fraction were hardened and insolubilized by tanning with either formalin or chromium salts or both. 2. The spheres and granules were used successfully for the separation of protein molecules and other protein-aceous materials ranging in molecular weight from 200 to greater than 6000000. This gel exclusion material has several properties superior to those of other products used for similar purposes. Further, it was noticed that the porosity of the spheres differed considerably from that of the granules.

Sign in / Sign up

Export Citation Format

Share Document