Electrocapillary drop actuation and fingering instability in a planar Hele-Shaw cell

2015 ◽  
Vol 91 (1) ◽  
Author(s):  
Thomas Ward ◽  
Matthew Walrath
Keyword(s):  
Fingering Instability ◽  
Hele Shaw Cell

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 Solute transport by suspended buoyant particles

2021 ◽  
Vol 249 ◽  
pp. 09002
Author(s):  
Iván Colecchio ◽  
Natalia Arze ◽  
Georgina Flores ◽  
Ana Quijandria ◽  
Alejandro Boschan
Keyword(s):  
Solute Transport ◽  
Solid Fraction ◽  
Light Transmission ◽  
Solute Concentration ◽  
Suspended Particles ◽  
Sharp Interface ◽  
Transmission Technique ◽  
Fingering Instability ◽  
Mass Discharge ◽  
Hele Shaw Cell

The transport of a colouring solute, driven by the buoyant displacement of microscopic suspended particles, and in the absence of net flow, is studied experimentally in a Hele Shaw cell. Initially, a sharp interface between a transparent fluid without particles and an underlying coloured suspension is obtained. From this situation, the suspended particles rise, carrying the solute in the form of a fingering instability across the interface, where a light transmission technique is used to measure the local solute concentration. This one attains an asymptotic value that increases with the solid fraction ϕ of suspended particles, and decreases with the distance to the interface. The solute mass discharge also increases with ϕ, always being relatively small (< 3%). The onset and development of the instability as the mechanism driving the transport of the solute is discussed.

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.

The Taylor–Saffman problem for a non-Newtonian liquid

1990 ◽  
Vol 220 ◽  
pp. 413-425 ◽  
Author(s):  
S. D. R. Wilson
Keyword(s):  
Shear Thinning ◽  
Newtonian Liquid ◽  
Power Law Model ◽  
Oldroyd Fluid ◽  
Partial Explanation ◽  
Oldroyd Model ◽  
Fingering Instability ◽  
Newtonian Liquids ◽  
Hydrodynamical Theory ◽  
Hele Shaw Cell

The Taylor–Saffman problem concerns the fingering instability which develops when one liquid displaces another, more viscous, liquid in a porous medium, or equivalently for Newtonian liquids, in a Hele-Shaw cell. Recent experiments with Hele-Shaw cells using non-Newtonian liquids have shown striking qualitative differences in the fingering pattern, which for these systems branches repeatedly in a manner resembling the growth of a fractal. This paper is an attempt to provide the beginnings of a hydrodynamical theory of this instability by repeating the analysis of Taylor & Saffman using a more general constitutive model. In fact two models are considered; the Oldroyd ‘Fluid B’ model which exhibits elasticity but not shear thinning, and the Ostwald–de Waele power-law model with the opposite combination. Of the two, only the Oldroyd model shows qualitatively new effects, in the form of a kind of resonance which can produce sharply increasing (in fact unbounded) growth rates as the relaxation time of the fluid increases. This may be a partial explanation of the observations on polymer solutions; the similar behaviour reported for clay pastes and slurries is not explained by shear-thinning and may involve a finite yield stress, which is not incorporated into either of the models considered here.

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.

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