pith. sign in

arxiv: 2604.10407 · v1 · submitted 2026-04-12 · ❄️ cond-mat.soft · physics.flu-dyn

On the selection of Saffman-Taylor fingers in a tapered Hele-Shaw cell

Dipa Ghosh , Satyajit Pramanik This is my paper

Pith reviewed 2026-05-10 16:26 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.flu-dyn
keywords Saffman-Taylor fingerHele-Shaw celltapered geometryfinger selectionviscous fingeringsingular perturbationWKB approximationcapillary number
0
0 comments X

The pith

In tapered Hele-Shaw cells with small gap gradients, the Saffman-Taylor finger width deviates from the parallel-cell value by an amount proportional to the gradient times the capillary number to the two-thirds power.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives an analytical prediction for the width of Saffman-Taylor fingers in a tapered Hele-Shaw cell with constant small depth gradient. Using singular perturbation theory and the WKB approximation, it finds that the dimensionless finger width Lambda satisfies Lambda minus one half scales with a function f of alpha times the modified capillary number to the two-thirds as the capillary number goes to zero, where f is linear in alpha and equals one when alpha is zero. This shows that the taper can be used to stabilize or destabilize the single finger state compared to the standard parallel case. The result agrees well with experiments and linear stability calculations.

Core claim

For small gap gradients alpha in a rectilinear tapered Hele-Shaw cell, the selected dimensionless finger width Lambda obeys Lambda - 1/2 ~ f(alpha) Ca_m^{2/3} as Ca_m -> 0 with |alpha| << 1, where f(alpha) is linear in alpha and f(0) = 1, thereby recovering the classic selection law of the parallel cell while showing how the gradient modifies the selection.

What carries the argument

Singular perturbation analysis combined with WKB approximation to solve for the finger shape and selection criterion in the presence of the depth gradient.

If this is right

  • The gap gradient can stabilize or destabilize the single-finger steady state depending on its sign.
  • The finger width can be controlled by adjusting the constant depth gradient.
  • The selection mechanism reduces precisely to the known parallel-cell result when the gradient vanishes.
  • The theoretical finger widths match available experimental data for tapered cells.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Microfluidic channels with controlled tapers could suppress or promote fingering instabilities in applications like oil recovery or inkjet printing.
  • Small linear tapers provide a simple way to perturb the classic selection without requiring full numerical simulation.
  • Similar asymptotic techniques might apply to other controlled geometries such as channels with varying width or surface tension gradients.

Load-bearing premise

The depth gradient must be small enough that singular perturbation and WKB methods stay valid all the way through the finger selection region.

What would settle it

Precise measurements of finger width in a tapered Hele-Shaw cell at very low modified capillary numbers, checking if the deviation from one half scales linearly with the gap gradient alpha.

Figures

Figures reproduced from arXiv: 2604.10407 by Dipa Ghosh, Satyajit Pramanik.

Figure 1
Figure 1. Figure 1: (a) A schematic illustrating the top view of the fluid displacement in a rectilinear tapered Hele-Shaw cell. (b) Schematics of the side view of the cell illustrating a positive and a negative depth gradient along the flow direction. In the present study, we examine the displacement of one fluid by another in a Hele–Shaw cell where the plates are not parallel; instead, they are separated by a slight depth g… view at source ↗
Figure 2
Figure 2. Figure 2: A schematic diagram of a Saffman-Taylor finger in a laboratory frame, assumed symmetric about the ˜x−axis (Top view) 2.1. Derivation of the viscous fingering equations in the physical plane. Since L ≫ W ≫ h(x), the slow flow of an incompressible fluid in a homogeneous porous medium is governed by two-dimensional Darcy’s law and the continuity equation modified to account for the depth gradient ⃗u = − h 2 (… view at source ↗
Figure 3
Figure 3. Figure 3: A schematic diagram of a Saffman-Taylor finger from the physical plane to the potential plane 2.2. Transformation of the tapered cell into an infinite strip. We define ϕ = − h 3 12µ p, where p = pF1 − pF2 such that ⃗u = ∇⃗ ϕ h (2.6) . The scalar function ϕ can be interpreted as a velocity potential that satisfies Darcy’s law (2.1a) in the leading order. The deviation from Darcy’s law is O(α). Here, we disc… view at source ↗
Figure 4
Figure 4. Figure 4: A schematic diagram of a Saffman-Taylor finger from potential plane to confor￾mal plane A natural (dimensionless) complex velocity of magnitude ˜q is given by ˜u − iv˜. We write this complex velocity ˜u − iv˜ in polar coordinates as ˜qe−iθ˜ and study the logarithm of this function, i.e., − ln ˜q + i ˜θ in the complex plane (using the Kirchhoff-Helmholtz free streamline theory), so that it is given by the c… view at source ↗
Figure 5
Figure 5. Figure 5: Contours of integration for the evaluation of the cusp function, C (Definition (3.3)) 3.1.1. Case-I (β < 1 or Λ < 1/2). Here, the branch point ηb = i β is out of the contour of integration for evaluating C. Thus, we can integrate by expanding S0(η) around the point of the stationary phase η = i. Defining ω through η = i + ω, we write S0 as S0 = 2iβ2 (1 + α x0 h0 ) 3/2      Z i 0 (1 + iη′ ) 3/4 (1 − iη… view at source ↗
Figure 6
Figure 6. Figure 6: Variation of Λ with x0 corresponding to 1/B = 100. Using Eq. (4.2), we compute U and vary time t to obtain different values of x0 = U t. This shows that for positive gradient (α = 0.0027), Λ increases, for zero gradient (α = 0), it is approximately 1/2, and for negative gradient (α = −0.0027), it decreases. In this paper, we provide an analytical treatment of the Saffman-Taylor fingers in a non-standard He… view at source ↗
Figure 7
Figure 7. Figure 7: Dependence of Λ on the surface tension parameter 1/B at different time (a) t = 10, (b) t = 50, and (c) t = 100. For a unique 1/B, we obtain a unique U that determines the location of the fingertip. This clearly indicates that for a given value of 1/B, as the finger propagates along the cell, its width increases/decreases as the cell diverges/converges; whereas, the width remains almost half of the cell wid… view at source ↗
read the original abstract

We present an analytical study for predicting the finger width of the Saffman-Taylor finger in a tapered Hele-Shaw cell. We consider a rectilinear geometry with a constant depth gradient and apply analytical techniques of singular perturbation analysis and WKB approximation to derive an expression for the finger selection mechanism for such tapered Hele-Shaw cells with small depth gradients. We establish \[ \Lambda - \frac{1}{2} \sim f(\alpha) Ca_m^{2/3} \quad \mbox{as} \quad Ca_m \rightarrow 0, \;\;\; \mbox{and} \;\;\; \lvert \alpha \rvert \ll 1.\] Here, $\Lambda$ is the dimensionless finger width, $Ca_m$ denotes the modified Capillary parameter, and $f(\alpha)$ is a linear function of the gap gradient $\alpha$, such that $f(\alpha = 0) = 1$ recovering the results of parallel Hele-Shaw cell (Hong and Langer \cite{hong1986analytic}, Combescot \emph{et al.} \cite{Combescot1986}, Shraiman \cite{shraiman1986velocity}). Our findings indicate that the Hele-Shaw cell gap gradient plays a crucial role in determining $\Lambda$, allowing for control over fingering instabilities such that the single-finger steady state can be stabilised or destabilised depending on the sign of the gradient, compared to the standard Hele-Shaw cell. The theoretical estimates reveal excellent agreement with experimental finger-width data and predictions from linear stability analyses.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives an asymptotic relation for the selected finger width Λ in a rectilinear tapered Hele-Shaw cell of small constant depth gradient α. Using singular perturbation theory and WKB approximation on the free-boundary problem, it obtains Λ − 1/2 ∼ f(α) Ca_m^{2/3} as Ca_m → 0 and |α| ≪ 1, where f(α) is linear in α with f(0) = 1, recovering the classic parallel-cell selection of Hong-Langer, Combescot et al., and Shraiman. The authors report excellent agreement with experimental finger-width data and linear stability predictions, and note that the sign of α can stabilize or destabilize the single-finger state relative to the α = 0 case.

Significance. If the WKB matching and solvability condition are rigorously controlled, the result supplies a parameter-free (within the stated asymptotics) prediction for how a weak taper modifies finger selection. This extends the classic Saffman-Taylor theory to a controllable geometry and offers a concrete mechanism for suppressing or enhancing fingering via the gap gradient, which is potentially useful for microfluidic design and pattern-formation studies. The explicit recovery of the α = 0 limit and the linear dependence on α are clear strengths.

major comments (2)
  1. [§4] §4 (comparison with experiments): The claim of “excellent agreement with experimental finger-width data” is not supported by any tabulation or discussion of the actual values of α and Ca_m realized in the cited experiments. Without explicit verification that those data lie inside the joint regime |α| ≪ 1 and Ca_m ≪ 1, the reported agreement cannot confirm the derived linear f(α) or the validity of the WKB matching procedure.
  2. [§3] §3 (WKB analysis and matching): The derivation assumes that the depth gradient α remains a small perturbation throughout the tip region where the solvability condition is imposed. The manuscript should state the explicit range of α for which the linear term in f(α) is obtained and confirm that no O(α^2) corrections enter the leading 2/3 scaling before the matching is performed.
minor comments (2)
  1. The definition of the modified capillary number Ca_m should be written explicitly (including its relation to the local gap) rather than left implicit.
  2. Figure captions for the stability-analysis comparisons should indicate the precise values of α used in the numerical curves.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and will incorporate the suggested clarifications and additions in the revised version.

read point-by-point responses

  1. Referee: [§4] §4 (comparison with experiments): The claim of “excellent agreement with experimental finger-width data” is not supported by any tabulation or discussion of the actual values of α and Ca_m realized in the cited experiments. Without explicit verification that those data lie inside the joint regime |α| ≪ 1 and Ca_m ≪ 1, the reported agreement cannot confirm the derived linear f(α) or the validity of the WKB matching procedure.

    Authors: We agree that an explicit tabulation of the experimental parameters would make the comparison more rigorous. In the revised manuscript we will add a table in §4 listing the approximate values of α and Ca_m extracted from the cited experiments, together with a short discussion confirming that they satisfy |α| ≪ 1 and Ca_m ≪ 1. This will directly substantiate that the data lie inside the joint asymptotic regime and thereby support both the linear f(α) prediction and the underlying WKB matching. revision: yes

  2. Referee: [§3] §3 (WKB analysis and matching): The derivation assumes that the depth gradient α remains a small perturbation throughout the tip region where the solvability condition is imposed. The manuscript should state the explicit range of α for which the linear term in f(α) is obtained and confirm that no O(α^2) corrections enter the leading 2/3 scaling before the matching is performed.

    Authors: The derivation is performed under the joint limit |α| ≪ 1 and Ca_m → 0. Within the tip-region scaling, α enters as a small perturbation to the base parallel-cell problem; the solvability condition is evaluated at leading order in this expansion, yielding a correction linear in α. Any O(α²) terms generated by the gap variation appear only at higher order in the asymptotic series and therefore do not modify the Ca_m^{2/3} scaling or the leading solvability condition prior to matching. We will revise §3 to state the range |α| ≪ 1 explicitly and to include the above ordering argument. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation proceeds from singular perturbation + WKB on the free-boundary problem and recovers the independent parallel-cell limit

full rationale

The central claim Λ − 1/2 ∼ f(α) Ca_m^{2/3} (f linear, f(0)=1) is obtained by applying standard singular-perturbation and WKB techniques to the tapered-cell free-boundary problem under the stated small-α, small-Ca_m assumptions. When α=0 the expression reduces exactly to the known parallel-cell solvability condition already established in the cited external literature (Hong & Langer, Combescot et al., Shraiman). No parameter is fitted to a subset of the target data and then re-labeled a prediction, no self-citation supplies a uniqueness theorem or ansatz that the present derivation relies upon, and the functional form of f(α) is generated by the perturbation calculation rather than imposed by definition. The derivation chain is therefore independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central asymptotic result rests on standard low-capillary-number assumptions and a small-gradient expansion; no new free parameters or invented entities are introduced.

axioms (2)
  • domain assumption Depth gradient is small: |α| ≪ 1
    Required to justify the singular perturbation expansion around the parallel-plate solution.
  • domain assumption Modified capillary number approaches zero: Ca_m → 0
    Enables the WKB and matched-asymptotic treatment of the finger tip and sides.

pith-pipeline@v0.9.0 · 5603 in / 1387 out tokens · 85686 ms · 2026-05-10T16:26:05.034358+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages

  1. [1]

    Analytic theory of the selection mechanism in the saffman-taylor problem.Physical review letters, 56(19):2032, 1986

    DC Hong and JS Langer. Analytic theory of the selection mechanism in the saffman-taylor problem.Physical review letters, 56(19):2032, 1986

    work page 2032

  2. [2]

    Shape selection of saffman-taylor fingers.Physical Review Letters, 56:2036–2039, 1986

    Roland Combescot, Thierry Dombre, Vincent Hakim, Yves Pomeau, and Alain Pumir. Shape selection of saffman-taylor fingers.Physical Review Letters, 56:2036–2039, 1986

    work page 2036

  3. [3]

    Velocity selection and the saffman-taylor problem.Physical review letters, 56(19):2028, 1986

    Boris I Shraiman. Velocity selection and the saffman-taylor problem.Physical review letters, 56(19):2028, 1986

    work page 2028

  4. [4]

    Channeling in packed columns.Chemical Engineering Science, 1(6):247–253, 1952

    S Hill et al. Channeling in packed columns.Chemical Engineering Science, 1(6):247–253, 1952

    work page 1952

  5. [5]

    The penetration of a fluid into a porous medium or hele-shaw cell containing a more viscous liquid.Proceedings of the Royal Society of London

    Philip Geoffrey Saffman and Geoffrey Ingram Taylor. The penetration of a fluid into a porous medium or hele-shaw cell containing a more viscous liquid.Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 245(1242):312–329, 1958

    work page 1958

  6. [6]

    The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media.Transactions of the AIME, 216(01):188–194, 1959

    RL Chuoke, P Van Meurs, and C van der Poel. The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media.Transactions of the AIME, 216(01):188–194, 1959

    work page 1959

  7. [7]

    Viscous fingering in porous media.Annual review of fluid mechanics, 19(1):271–311, 1987

    George M Homsy. Viscous fingering in porous media.Annual review of fluid mechanics, 19(1):271–311, 1987

    work page 1987

  8. [8]

    Nonlinear saffman-taylor instability.Physical review letters, 92(5):054501, 2004

    Enrique ´Alvarez-Lacalle, Jordi Ort´ ın, and J Casademunt. Nonlinear saffman-taylor instability.Physical review letters, 92(5):054501, 2004

    work page 2004

  9. [9]

    The effect of surface tension on the shape of fingers in a hele shaw cell.Journal of Fluid Mechanics, 102:455–469, 1981

    JW McLean and PG Saffman. The effect of surface tension on the shape of fingers in a hele shaw cell.Journal of Fluid Mechanics, 102:455–469, 1981

    work page 1981

  10. [10]

    Pattern selection and tip perturbations in the saffman-taylor problem.Physical Review A, 36(5):2325, 1987

    DC Hong and JS Langer. Pattern selection and tip perturbations in the saffman-taylor problem.Physical Review A, 36(5):2325, 1987

    work page 1987

  11. [11]

    The saffman–taylor instability: From the linear to the circular geometry

    H Thom´ e, Marc Rabaud, V Hakim, and Y Couder. The saffman–taylor instability: From the linear to the circular geometry. Physics of Fluids A: Fluid Dynamics, 1(2):224–240, 1989

    work page 1989

  12. [12]

    Viscous fingering in hele-shaw cells.Journal of Fluid Mechanics, 173:73–94, 1986

    PG Saffman. Viscous fingering in hele-shaw cells.Journal of Fluid Mechanics, 173:73–94, 1986

    work page 1986

  13. [13]

    Penetration of fluid into a hele–shaw cell: The saffman–taylor experiment.Journal of fluid mechanics, 97(1):53–64, 1980

    E Pitts. Penetration of fluid into a hele–shaw cell: The saffman–taylor experiment.Journal of fluid mechanics, 97(1):53–64, 1980

    work page 1980

  14. [14]

    Film draining and the saffman-taylor problem.Physical Review A, 33(1):794, 1986

    P Tabeling and A Libchaber. Film draining and the saffman-taylor problem.Physical Review A, 33(1):794, 1986

    work page 1986

  15. [15]

    An experimental study of the saffman-taylor instability.Journal of Fluid Me- chanics, 177:67–82, 1987

    P Tabeling, G Zocchi, and A Libchaber. An experimental study of the saffman-taylor instability.Journal of Fluid Me- chanics, 177:67–82, 1987

    work page 1987

  16. [16]

    The effect of surface tension on the shape of a hele–shaw cell bubble.The Physics of fluids, 29(11):3537–3548, 1986

    Saleh Tanveer. The effect of surface tension on the shape of a hele–shaw cell bubble.The Physics of fluids, 29(11):3537–3548, 1986

    work page 1986

  17. [17]

    Viscous flows in two dimensions

    David Bensimon, Leo P Kadanoff, Shoudan Liang, Boris I Shraiman, and Chao Tang. Viscous flows in two dimensions. Reviews of Modern Physics, 58(4):977, 1986

    work page 1986

  18. [18]

    Selection mechanism in non-newtonian saffman–taylor fingers.SIAM Journal on Applied Mathematics, 83(2):329–353, 2023

    Diksha Bansal, Dipa Ghosh, and Sarthok Sircar. Selection mechanism in non-newtonian saffman–taylor fingers.SIAM Journal on Applied Mathematics, 83(2):329–353, 2023. SELECTION OF SAFFMAN-TAYLOR FINGERS IN A TAPERED HELE-SHAW CEL 23

    work page 2023

  19. [19]

    A theory of the optimal policy of oil recovery by secondary displacement processes

    Sheldon B Gorell and GM Homsy. A theory of the optimal policy of oil recovery by secondary displacement processes. SIAM Journal on Applied Mathematics, 43(1):79–98, 1983

    work page 1983

  20. [20]

    Enhanced oil recovery

    Larry W Lake. Enhanced oil recovery. 1988

    work page 1988

  21. [21]

    The promise and problems of enhanced oil recovery methods.Journal of Canadian Petroleum Technology, 35(07), 1996

    SM Farouq Ali and Sera Thomas. The promise and problems of enhanced oil recovery methods.Journal of Canadian Petroleum Technology, 35(07), 1996

    work page 1996

  22. [22]

    Experimental and computational advances on the study of viscous fingering: An umbrella review.Heliyon, 7(7), 2021

    Andr´ es Pinilla, Miguel Asuaje, and Nicol´ as Ratkovich. Experimental and computational advances on the study of viscous fingering: An umbrella review.Heliyon, 7(7), 2021

    work page 2021

  23. [23]

    A comprehensive numerical study of immiscible and miscible viscous fingers during chemical enhanced oil recovery.Fuel, 194:480–490, 2017

    R Vishnudas and Abhijit Chaudhuri. A comprehensive numerical study of immiscible and miscible viscous fingers during chemical enhanced oil recovery.Fuel, 194:480–490, 2017

    work page 2017

  24. [24]

    The fluid mechanics of carbon dioxide sequestration.Annual review of fluid mechanics, 46(1):255–272, 2014

    Herbert E Huppert and Jerome A Neufeld. The fluid mechanics of carbon dioxide sequestration.Annual review of fluid mechanics, 46(1):255–272, 2014

    work page 2014

  25. [25]

    Numerical simulation of saffman-taylor instabilities during co 2-eor in heterogeneous reservoirs.Mas- ter’s thesis, 2018

    UWAYZ Al-Qarani. Numerical simulation of saffman-taylor instabilities during co 2-eor in heterogeneous reservoirs.Mas- ter’s thesis, 2018

    work page 2018

  26. [26]

    Foam assisted co2-eor: A review of concept, challenges, and future prospects.Journal of Petroleum Science and Engineering, 120:202–215, 2014

    Seyedeh Hosna Talebian, Rahim Masoudi, Isa Mohd Tan, and Pacelli Lidio Jose Zitha. Foam assisted co2-eor: A review of concept, challenges, and future prospects.Journal of Petroleum Science and Engineering, 120:202–215, 2014

    work page 2014

  27. [27]

    An optimal viscosity profile in enhanced oil recovery by polymer flooding.International Journal of Engineering Science, 42(19-20):2029–2039, 2004

    Prabir Daripa and G Pa¸ sa. An optimal viscosity profile in enhanced oil recovery by polymer flooding.International Journal of Engineering Science, 42(19-20):2029–2039, 2004

    work page 2029

  28. [28]

    A numerical study of instability control for the design of an optimal policy of enhanced oil recovery by tertiary displacement processes.Transport in Porous Media, 93:675–703, 2012

    Prabir Daripa and Xueru Ding. A numerical study of instability control for the design of an optimal policy of enhanced oil recovery by tertiary displacement processes.Transport in Porous Media, 93:675–703, 2012

    work page 2012

  29. [29]

    An existence theorem for a control problem in oil recovery.Numerical functional analysis and optimization, 17(9-10):911–923, 1996

    Gelu I Pasa. An existence theorem for a control problem in oil recovery.Numerical functional analysis and optimization, 17(9-10):911–923, 1996

    work page 1996

  30. [30]

    Simulation of nonlinear viscous fingering in miscible displacement.The Physics of fluids, 31(6):1330–1338, 1988

    CT Tan and GM Homsy. Simulation of nonlinear viscous fingering in miscible displacement.The Physics of fluids, 31(6):1330–1338, 1988

    work page 1988

  31. [31]

    Density-driven unstable flows of miscible fluids in a hele-shaw cell

    J Fernandez, P Kurowski, P Petitjeans, and E Meiburg. Density-driven unstable flows of miscible fluids in a hele-shaw cell. Journal of Fluid Mechanics, 451:239–260, 2002

    work page 2002

  32. [32]

    Effect of p´ eclet number on miscible rectilinear displacement in a hele-shaw cell.Physical Review E, 91(3):033006, 2015

    Satyajit Pramanik and Manoranjan Mishra. Effect of p´ eclet number on miscible rectilinear displacement in a hele-shaw cell.Physical Review E, 91(3):033006, 2015

    work page 2015

  33. [33]

    The effect of a stabilising gradient on interface morphology

    T Maxworthy. The effect of a stabilising gradient on interface morphology. InInterfaces for the 21st Century: New Research Directions in Fluid Mechanics and Materials Science, pages 3–20. World Scientific, 2002

    work page 2002

  34. [34]

    The instability of uniform viscous flow under rollers and spreaders.Journal of Fluid Mechanics, 7(4):481–500, 1960

    JRA Pearson. The instability of uniform viscous flow under rollers and spreaders.Journal of Fluid Mechanics, 7(4):481–500, 1960

    work page 1960

  35. [35]

    The flow of thin liquid films between rollers.Journal of Fluid Mechanics, 11(1):33–50, 1961

    E Pitts and J Greiller. The flow of thin liquid films between rollers.Journal of Fluid Mechanics, 11(1):33–50, 1961

    work page 1961

  36. [36]

    Hydraulic conductivity of rock fractures.Transport in porous media, 23(1):1–30, 1996

    Robert W Zimmerman and Gudmundur S Bodvarsson. Hydraulic conductivity of rock fractures.Transport in porous media, 23(1):1–30, 1996

    work page 1996

  37. [37]

    Courier Corporation, 2013

    Jacob Bear.Dynamics of fluids in porous media. Courier Corporation, 2013

    work page 2013

  38. [38]

    Control of interfacial instabilities using flow geometry.Nature Physics, 8(10):747–750, 2012

    Talal T Al-Housseiny, Peichun A Tsai, and Howard A Stone. Control of interfacial instabilities using flow geometry.Nature Physics, 8(10):747–750, 2012

    work page 2012

  39. [39]

    Controlling viscous fingering in tapered hele-shaw cells.Physics of Fluids, 25(9), 2013

    Talal T Al-Housseiny and Howard A Stone. Controlling viscous fingering in tapered hele-shaw cells.Physics of Fluids, 25(9), 2013

    work page 2013

  40. [40]

    Perturbing hele-shaw flow with a small gap gradient.Physical Review A, 45(4):2455, 1992

    H Zhao, J Casademunt, C Yeung, and JV Maher. Perturbing hele-shaw flow with a small gap gradient.Physical Review A, 45(4):2455, 1992

    work page 1992

  41. [41]

    Finger tip behavior in small gap gradient hele-shaw flows.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 82(5):056319, 2010

    Eduardo O Dias and Jos´ e A Miranda. Finger tip behavior in small gap gradient hele-shaw flows.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 82(5):056319, 2010

    work page 2010

  42. [42]

    Taper-induced control of viscous fingering in variable-gap hele-shaw flows.Physical Review E, 87(5):053015, 2013

    Eduardo O Dias and Jos´ e A Miranda. Taper-induced control of viscous fingering in variable-gap hele-shaw flows.Physical Review E, 87(5):053015, 2013

    work page 2013

  43. [43]

    Computational analysis of interfacial dynamics in angled hele-shaw cells: instability regimes.Transport in Porous Media, 131(3):907–934, 2020

    Daihui Lu, Federico Municchi, and Ivan C Christov. Computational analysis of interfacial dynamics in angled hele-shaw cells: instability regimes.Transport in Porous Media, 131(3):907–934, 2020

    work page 2020

  44. [44]

    Two-phase fluid displacement and interfacial instabilities under elastic membranes.Physical review letters, 111(3):034502, 2013

    Talal T Al-Housseiny, Ivan C Christov, and Howard A Stone. Two-phase fluid displacement and interfacial instabilities under elastic membranes.Physical review letters, 111(3):034502, 2013

    work page 2013

  45. [45]

    Suppression of complex fingerlike patterns at the interface between air and a viscous fluid by elastic membranes.Physical review letters, 108(7):074502, 2012

    D Pihler-Puzovi´ c, Pierre Illien, Matthias Heil, and Anne Juel. Suppression of complex fingerlike patterns at the interface between air and a viscous fluid by elastic membranes.Physical review letters, 108(7):074502, 2012

    work page 2012

  46. [46]

    Modelling the suppression of viscous fingering in elastic-walled hele-shaw cells.Journal of Fluid Mechanics, 731:162–183, 2013

    Draga Pihler-Puzovi´ c, Rapha¨ el P´ erillat, Matthew Russell, Anne Juel, and Matthias Heil. Modelling the suppression of viscous fingering in elastic-walled hele-shaw cells.Journal of Fluid Mechanics, 731:162–183, 2013

    work page 2013

  47. [47]

    On the role of stokes lines in the selection of saffman–taylor fingers with small surface tension.European Journal of Applied Mathematics, 10(6):513–534, 1999

    SJ Chapman. On the role of stokes lines in the selection of saffman–taylor fingers with small surface tension.European Journal of Applied Mathematics, 10(6):513–534, 1999

    work page 1999

  48. [48]

    Selection of a hele-shaw bubble via exponential asymp- totics.SIAM Journal on Applied Mathematics, 80(1):289–311, 2020

    Christopher J Lustri, Christopher C Green, and Scott W McCue. Selection of a hele-shaw bubble via exponential asymp- totics.SIAM Journal on Applied Mathematics, 80(1):289–311, 2020

    work page 2020

  49. [49]

    The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics

    S Jonathan Chapman, Michael C Dallaston, Serafim Kalliadasis, Philippe H Trinh, and Thomas P Witelski. The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics. Physica D: Nonlinear Phenomena, 453:133802, 2023

    work page 2023

  50. [50]

    On the selection of saffman–taylor viscous fingers for divergent flow in a wedge.Journal of Fluid Mechanics, 987:A42, 2024

    Cecilie Andersen, Christopher J Lustri, Scott W McCue, and Philippe H Trinh. On the selection of saffman–taylor viscous fingers for divergent flow in a wedge.Journal of Fluid Mechanics, 987:A42, 2024

    work page 2024

  51. [51]

    Computations of viscous fingering in a wedge: selection mechanisms and capillarity-driven ripples in the small surface tension limit.Journal of Fluid Mechanics, 1013:A18, 2025

    Cecilie Andersen, Philippe H Trinh, and Jean-Marc Vanden-Broeck. Computations of viscous fingering in a wedge: selection mechanisms and capillarity-driven ripples in the small surface tension limit.Journal of Fluid Mechanics, 1013:A18, 2025

    work page 2025

  52. [52]

    Viscous fingering in a wedge.Physical Review A, 44(6):3673, 1991

    Martine Ben Amar. Viscous fingering in a wedge.Physical Review A, 44(6):3673, 1991. 24 DIPA GHOSH AND SATYAJIT PRAMANIK

    work page 1991

  53. [53]

    Numerical investigation of viscous fingering in hele-shaw cell with spatially periodic variation of depth.Applied Mathematics and Mechanics, 37(1):45–58, 2016

    Jiangping Hu, Bofu Wang, and Dejun Sun. Numerical investigation of viscous fingering in hele-shaw cell with spatially periodic variation of depth.Applied Mathematics and Mechanics, 37(1):45–58, 2016

    work page 2016

  54. [54]

    The stability of immiscible viscous fingering in hele-shaw cells with spatially varying permeability.Computer Methods in Applied Mechanics and Engineering, 320:606–632, 2017

    SJ Jackson, H Power, D Giddings, and D Stevens. The stability of immiscible viscous fingering in hele-shaw cells with spatially varying permeability.Computer Methods in Applied Mechanics and Engineering, 320:606–632, 2017

    work page 2017

  55. [55]

    Manipulation of viscous fingering in a radially tapered cell geometry.Physical Review E, 97(6):061101, 2018

    Gr´ egoire Bongrand and Peichun Amy Tsai. Manipulation of viscous fingering in a radially tapered cell geometry.Physical Review E, 97(6):061101, 2018

    work page 2018

  56. [56]

    Inertia-induced dendriticlike patterns in lifting hele-shaw flows

    Pedro HA Anjos, Eduardo O Dias, and Jos´ e A Miranda. Inertia-induced dendriticlike patterns in lifting hele-shaw flows. Physical Review Fluids, 2(1):014003, 2017

    work page 2017

  57. [57]

    Finger velocities in the lifting hele–shaw cell.Physica A: Statistical Mechanics and its Applications, 328(3-4):305–314, 2003

    Subrata K Kabiraj and Sujata Tarafdar. Finger velocities in the lifting hele–shaw cell.Physica A: Statistical Mechanics and its Applications, 328(3-4):305–314, 2003

    work page 2003

  58. [58]

    Numerical investigation of controlling interfacial instabilities in non-standard hele-shaw configurations.Journal of Fluid Mechanics, 877:1063–1097, 2019

    Liam C Morrow, Timothy J Moroney, and Scott W McCue. Numerical investigation of controlling interfacial instabilities in non-standard hele-shaw configurations.Journal of Fluid Mechanics, 877:1063–1097, 2019

    work page 2019

  59. [59]

    A review of one-phase hele-shaw flows and a level-set method for nonstandard configurations.The ANZIAM Journal, 63(3):269–307, 2021

    Liam C Morrow, Timothy J Moroney, Michael C Dallaston, and Scott W McCue. A review of one-phase hele-shaw flows and a level-set method for nonstandard configurations.The ANZIAM Journal, 63(3):269–307, 2021

    work page 2021

  60. [60]

    Electrokinetic control of viscous fingering.Physical review letters, 119(17):174501, 2017

    Mohammad Mirzadeh and Martin Z Bazant. Electrokinetic control of viscous fingering.Physical review letters, 119(17):174501, 2017

    work page 2017

  61. [61]

    Minimization of viscous fluid fingering: a variational scheme for optimal flow rates.Physical review letters, 109(14):144502, 2012

    Eduardo O Dias, Enrique Alvarez-Lacalle, M´ arcio S Carvalho, and Jos´ e A Miranda. Minimization of viscous fluid fingering: a variational scheme for optimal flow rates.Physical review letters, 109(14):144502, 2012

    work page 2012

  62. [62]

    Stability results for multi-layer radial hele-shaw and porous media flows.Physics of Fluids, 27(1), 2015

    Craig Gin and Prabir Daripa. Stability results for multi-layer radial hele-shaw and porous media flows.Physics of Fluids, 27(1), 2015

    work page 2015

  63. [63]

    Time-dependent injection strategies for multilayer hele-shaw and porous media flows.Physical Review Fluids, 6(3):033901, 2021

    Craig Gin and Prabir Daripa. Time-dependent injection strategies for multilayer hele-shaw and porous media flows.Physical Review Fluids, 6(3):033901, 2021

    work page 2021

  64. [64]

    Universal stability properties for multilayer hele-shaw flows and application to instability control.SIAM Journal on Applied Mathematics, 72(5):1667–1685, 2012

    Prabir Daripa and Xueru Ding. Universal stability properties for multilayer hele-shaw flows and application to instability control.SIAM Journal on Applied Mathematics, 72(5):1667–1685, 2012

    work page 2012

  65. [65]

    Viscous fingering with permeability heterogeneity.Physics of Fluids A: Fluid Dynamics, 4(6):1099–1101, 1992

    C-T Tan and GM Homsy. Viscous fingering with permeability heterogeneity.Physics of Fluids A: Fluid Dynamics, 4(6):1099–1101, 1992

    work page 1992

  66. [66]

    Radial fingering under arbitrary viscosity and density ratios

    Pedro HA Anjos, Eduardo O Dias, and Jos´ e A Miranda. Radial fingering under arbitrary viscosity and density ratios. Physical Review Fluids, 2(8):084004, 2017

    work page 2017

  67. [67]

    Particle-induced viscous fingering.Journal of Non-Newtonian Fluid Mechanics, 238:92–99, 2016

    Feng Xu, Jungchul Kim, and Sungyon Lee. Particle-induced viscous fingering.Journal of Non-Newtonian Fluid Mechanics, 238:92–99, 2016

    work page 2016

  68. [68]

    Stability analysis of a particle band on the fluid–fluid interface.Journal of Fluid Mechanics, 869:R2, 2019

    Alireza Hooshanginejad, Benjamin C Druecke, and Sungyon Lee. Stability analysis of a particle band on the fluid–fluid interface.Journal of Fluid Mechanics, 869:R2, 2019

    work page 2019

  69. [69]

    Controlling fingering instabilities in rotating ferrofluids.Physical Review E, 67(1):017301, 2003

    David P Jackson and Jos´ e A Miranda. Controlling fingering instabilities in rotating ferrofluids.Physical Review E, 67(1):017301, 2003

    work page 2003

  70. [70]

    Systematic weakly nonlinear analysis of radial viscous fingering.Physical Review E, 68(2):026308, 2003

    Enrique Alvarez-Lacalle, E Paun´ e, J Casademunt, and Jordi Ort´ ın. Systematic weakly nonlinear analysis of radial viscous fingering.Physical Review E, 68(2):026308, 2003

    work page 2003

  71. [71]

    Viscosity contrast effects on fingering formation in rotating hele-shaw flows

    Jos´ e A Miranda and Enrique Alvarez-Lacalle. Viscosity contrast effects on fingering formation in rotating hele-shaw flows. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 72(2):026306, 2005

    work page 2005

  72. [72]

    Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes.Physical Review Fluids, 3(4):044002, 2018

    Pedro HA Anjos, S´ ergio A Lira, and Jos´ e A Miranda. Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes.Physical Review Fluids, 3(4):044002, 2018

    work page 2018

  73. [73]

    Controlling radial fingering patterns in miscible confined flows.Physical Review E, 82(5):056308, 2010

    Ching-Yao Chen, C-W Huang, L-C Wang, and Jos´ e A Miranda. Controlling radial fingering patterns in miscible confined flows.Physical Review E, 82(5):056308, 2010

    work page 2010

  74. [74]

    Control of radial miscible viscous fingering.Journal of Fluid Mechanics, 884:A16, 2020

    Vandita Sharma, Sada Nand, Satyajit Pramanik, Ching-Yao Chen, and Manoranjan Mishra. Control of radial miscible viscous fingering.Journal of Fluid Mechanics, 884:A16, 2020

    work page 2020

  75. [75]

    Anisotropic viscous fingering.Ph

    Eugenia Corvera-Poire. Anisotropic viscous fingering.Ph. D. Thesis, 1995

    work page 1995

  76. [76]

    Steady states for viscous fingers with anisotropic surface tension.Physical Review E, 52(4):4063, 1995

    Eugenia Corvera, Hong Guo, and David Jasnow. Steady states for viscous fingers with anisotropic surface tension.Physical Review E, 52(4):4063, 1995

    work page 1995

  77. [77]

    Saffman-taylor fingers with anisotropic surface tension.Physica A: Statistical Mechanics and its Applications, 220(1-2):48–59, 1995

    Eugenia Corvera, Hong Guo, and David Jasnow. Saffman-taylor fingers with anisotropic surface tension.Physica A: Statistical Mechanics and its Applications, 220(1-2):48–59, 1995

    work page 1995

  78. [78]

    Viscous fingering in complex fluids.Journal of Physics: Condensed Matter, 12(8A):A477, 2000

    Anke Lindner, Daniel Bonn, and Jacques Meunier. Viscous fingering in complex fluids.Journal of Physics: Condensed Matter, 12(8A):A477, 2000. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781039, Assam, India Email address:dipamath@iitg.ac.in Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781...

    work page 2000