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arxiv: 2603.10942 · v2 · submitted 2026-03-11 · ⚛️ physics.flu-dyn · cond-mat.soft

Spectral methods for wedge and corner flows: The Fourier-Kontorovich-Lebedev integral transform

Abdallah Daddi-Moussa-Ider This is my paper

Pith reviewed 2026-05-15 12:44 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn cond-mat.soft
keywords Stokes flowwedge geometriesKontorovich-Lebedev transformPapkovich-Neuber representationmicrofluidicsStokesletrotletlow-Reynolds hydrodynamics
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The pith

The Fourier-Kontorovich-Lebedev transform combined with the Papkovich-Neuber representation solves Stokes flow problems for point forces and torques in wedge and corner geometries.

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

This paper reviews analytical techniques for solving the Stokes equations in wedge-shaped domains at low Reynolds numbers. It centers on representing the flow via four harmonic functions in the Papkovich-Neuber form and then applying the Fourier-Kontorovich-Lebedev integral transform to obtain explicit solutions for a Stokeslet and a rotlet. The resulting expressions cover a range of wedge angles and boundary conditions. A sympathetic reader would value the approach because it supplies closed-form or efficiently computable velocity and pressure fields that describe particle motion near corners without repeated numerical solves.

Core claim

The paper shows that the Fourier-Kontorovich-Lebedev integral transform applied to the four harmonic functions of the Papkovich-Neuber representation produces solutions to the Stokes equations for a point force and a point torque inside wedge geometries, thereby furnishing a systematic spectral method that works for general opening angles and standard boundary conditions on the walls.

What carries the argument

The Fourier-Kontorovich-Lebedev (FKL) integral transform, which converts the biharmonic problem into integrals involving modified Bessel functions to enforce no-slip or other conditions on the wedge walls.

If this is right

  • Velocity and pressure fields become available in explicit integral form for arbitrary wedge angles.
  • Hydrodynamic interactions between particles confined in wedge geometries can be computed directly from the Stokeslet and rotlet solutions.
  • The same framework supplies the building blocks needed to model transport near corners in microfluidic channels.
  • Both force-driven and torque-driven singularities are treated uniformly within one spectral representation.

Where Pith is reading between the lines

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

  • The transform technique could be extended to time-dependent or weakly inertial flows by adding appropriate unsteady terms to the harmonic potentials.
  • Similar spectral decompositions might handle other corner flows, such as those driven by surface tension or temperature gradients, without changing the core machinery.
  • Once implemented numerically, the integral expressions could serve as fast forward models inside optimization loops for designing wedge-based lab-on-chip devices.

Load-bearing premise

The Papkovich-Neuber representation with four harmonic functions combined with the FKL transform yields practical closed-form or efficiently computable solutions for general wedge angles and boundary conditions.

What would settle it

A high-resolution numerical solution of the Stokes equations for a Stokeslet placed inside a 90-degree wedge that produces velocity or pressure fields measurably different from the FKL-derived expressions would show the method fails for that case.

Figures

Figures reproduced from arXiv: 2603.10942 by Abdallah Daddi-Moussa-Ider.

Figure 1
Figure 1. Figure 1: Schematic of the system representing a fluid confined [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Scaled magnitude of the fluid velocity on the upper [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
read the original abstract

Understanding fluid flow in wedge-shaped geometries is essential for predicting hydrodynamic interactions in confined systems, such as microfluidic devices and near-corner transport phenomena. This article reviews analytical methods and techniques for addressing wedge problems in low-Reynolds-number hydrodynamics, focusing on solutions of the Stokes equations for a point force (Stokeslet) and a point torque (rotlet). The formulation is based on the Papkovich-Neuber representation, which uses four harmonic functions to characterize the fluid flow. A concise overview of the Fourier-Kontorovich-Lebedev (FKL) transform method is provided, highlighting key properties and steps employed in deriving these solutions. This offers a versatile framework for predicting particle dynamics in wedge confinements and for designing microfluidic systems with corner geometries.

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

0 major / 1 minor

Summary. The manuscript reviews analytical methods for solving the Stokes equations in wedge and corner geometries at low Reynolds number, focusing on Stokeslet and rotlet solutions. It centers on the Papkovich-Neuber representation employing four harmonic functions combined with the Fourier-Kontorovich-Lebedev (FKL) integral transform, providing an overview of key properties and derivation steps. The central claim is that this established framework supplies a versatile approach for predicting particle dynamics in wedge confinements and for microfluidic system design.

Significance. As a review synthesizing prior literature on spectral methods for confined Stokes flow, the paper could serve as a compact reference for researchers in microfluidics and low-Re hydrodynamics. Its value lies in consolidating the Papkovich-Neuber plus FKL approach for practical applications, though the absence of new derivations or general-angle existence proofs limits its novelty to improved accessibility of known techniques.

minor comments (1)
  1. [Abstract] Abstract: The assertion that the method 'offers a versatile framework for ... general wedge angles' should be qualified by referencing the specific angle ranges (e.g., 0 < α < π) for which the FKL inversion yields practical closed-form or numerically stable solutions, as implied by the cited literature.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and recommendation of minor revision. We agree with the assessment that the work is a synthesis of established methods and will revise the manuscript to better clarify its scope and contributions to accessibility.

read point-by-point responses

  1. Referee: As a review synthesizing prior literature on spectral methods for confined Stokes flow, the paper could serve as a compact reference for researchers in microfluidics and low-Re hydrodynamics. Its value lies in consolidating the Papkovich-Neuber plus FKL approach for practical applications, though the absence of new derivations or general-angle existence proofs limits its novelty to improved accessibility of known techniques.

    Authors: We appreciate the referee's balanced assessment. The manuscript is intended as a review to consolidate the Papkovich-Neuber representation with the Fourier-Kontorovich-Lebedev transform, providing a unified overview of key properties and derivation steps for Stokeslet and rotlet solutions in wedge geometries. We do not present new derivations or general-angle existence proofs, which are available in the cited prior literature. The contribution lies in making these techniques more accessible for applications in particle dynamics and microfluidic design. We will revise the abstract, introduction, and conclusion to explicitly state the review nature and emphasize the practical framework for confined flows. revision: yes

Circularity Check

0 steps flagged

Review of established methods with no load-bearing self-derived predictions

full rationale

The manuscript is explicitly a review summarizing the Papkovich-Neuber representation (four harmonic functions) and Fourier-Kontorovich-Lebedev transform for Stokeslet/rotlet solutions in wedges, drawing from prior literature rather than advancing new derivations, fitted parameters, or uniqueness theorems. No equations reduce by construction to inputs within the paper itself, and self-citations (if present) are not load-bearing for any claimed prediction. The central claim of versatility for microfluidic design rests on cited external results, keeping circularity minimal.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper is a review and therefore rests on standard assumptions of low-Reynolds-number hydrodynamics and the validity of the Papkovich-Neuber representation; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Stokes equations govern the flow at low Reynolds number
    Invoked throughout the abstract as the governing equations for the wedge problems.
  • domain assumption Papkovich-Neuber representation expresses any Stokes flow using four harmonic functions
    Stated as the basis for the formulation in the abstract.

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Reference graph

Works this paper leans on

96 extracted references · 96 canonical work pages · 1 internal anchor

  1. [1]

    These include the FKL transform of derivatives with respect torandz, operations such as division byrand multiplication byz/r, as well as the FKL transform of the Laplace equation

    Functional relationships Here, we summarize key properties of the FKL transform that are relevant for solving Stokes flow problems involving a point force or point torque singularity. These include the FKL transform of derivatives with respect torandz, operations such as division byrand multiplication byz/r, as well as the FKL transform of the Laplace equ...

    work page

  2. [2]

    For a point force, the harmonic functions are expressed directly in terms of 1/s, whereas for a point torque they are given in terms of partial derivatives of 1/s

    FKL transform of1/s In the context of three-dimensional Stokes flow induced by a force or torque singularity, the FKL transform of 1/sis a fundamental quantity that helps construct the free-space contribution to the solution. For a point force, the harmonic functions are expressed directly in terms of 1/s, whereas for a point torque they are given in term...

    work page

  3. [3]

    (7) and representing the complementary solution, satisfy the Laplace equation

    Representation of the solution in FKL space The four harmonic functionsϕ j,j∈ {x, y, z, w}, defined in Eq. (7) and representing the complementary solution, satisfy the Laplace equation. As shown in the last entry of Tab. I, the Laplace equation takes a remarkably simple form in FKL space, reducing to a linear second-order ordinary differential equation wi...

    work page

  4. [4]

    (18) and (19), the solution for the four harmonic functions can be expressed in real space as a double integral over the radial and axial wavenumbers

    Representation of the solution in real space By combining the inverse Fourier and inverse KL transforms, Eqs. (18) and (19), the solution for the four harmonic functions can be expressed in real space as a double integral over the radial and axial wavenumbers. The integration overkcan be performed using tabulated integrals, leaving a single integral overν...

    work page

  5. [5]

    Erd´ elyi, W

    A. Erd´ elyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms, Vol. II (McGraw-Hill, New York, 1954)

    work page 1954

  6. [6]

    Debnath and D

    L. Debnath and D. Bhatta,Integral Transforms and Their Applications(Chapman and Hall/CRC, Boca Raton, Florida, 2016)

    work page 2016

  7. [7]

    Prudnikov, Y

    A. Prudnikov, Y. Brychkov, and O. Marichev,Integrals and Series, Volume 2: Special Functions(Gordon and Breach Science Publishers, London, 1992)

    work page 1992

  8. [8]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions, 5 (Dover, New York, 1972)

    work page 1972

  9. [9]

    I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products(Academic press, London, 2014)

    work page 2014

  10. [10]

    Polyanin and A

    P. Polyanin and A. V. Manzhirov,Handbook of Integral Equations(Chapman and Hall/CRC, Florida, 2008)

    work page 2008

  11. [11]

    Kontorovich and N

    M. Kontorovich and N. Lebedev, On the one method of solution for some problems in diffraction theory and related problems, J. Exp. Theor. Phys. U.S.S.R.8, 1192 (1938)

    work page 1938

  12. [12]

    Kontorovich and N

    M. Kontorovich and N. Lebedev, On a method of solution of some problems of the diffraction theory, J. Phys. Acad. Sci. 14 U.S.S.R.1, 1 (1939)

    work page 1939

  13. [13]

    Lebedev and M

    N. Lebedev and M. Kontorovich, On the application of inversion formulae to the solution of some electrodynamics problems, J. Exp. Theor. Phys. U.S.S.R.9, 729 (1939)

    work page 1939

  14. [14]

    N. N. Lebedev, On an inversion formula, Doklady Akademii Nauk52, 395 (1946); N. Lebedev, Sur une formule d’inversion, CR Acad. Sci. URSS52, 302 (1946)

    work page 1946

  15. [15]

    N. N. Lebedev, On the representation of an arbitrary function by an integral involving cylinder functions of imaginary index and argument, Prikl. Matem. Mekh.13, 465 (1949)

    work page 1949

  16. [16]

    Lebedev and I

    N. Lebedev and I. Skal’skaia, Dual integral equations related to the Kontorovich-Lebedev transform, J. Appl. Math. Mech.38, 1033 (1974)

    work page 1974

  17. [17]

    N. N. Lebedev, I. Skal’skaia, and Y. S. Uflyand,Problems of Mathematical Physics(Prentice Hall, Englewood Cliffs, New Jersey, 1965)

    work page 1965

  18. [18]

    Wimp, A class of integral transforms, Proc

    J. Wimp, A class of integral transforms, Proc. Edinburgh Math. Soc.14, 33 (1964)

    work page 1964

  19. [19]

    S. B. Yakubovich,Index Transforms(World Scientific Publishing, London, 1996)

    work page 1996

  20. [20]

    N. N. Lebedev,Special Functions and Their Applications (Dover Publications, Inc., New York, 1972)

    work page 1972

  21. [21]

    S. B. Yakubovich, On the Kontorovich-Lebedev transformation, J. Integral Equations Appl. , 95 (2003)

    work page 2003

  22. [22]

    S. B. Yakubovich, On a progress in the Kontorovich–Lebedev transform theory and related integral operators, Integral Transforms Spec. Funct.19, 509 (2008)

    work page 2008

  23. [23]

    Yakubovich, An index integral and convolution operator related to the Kontorovich-Lebedev and Mehler-Fock transforms, Complex Anal

    S. Yakubovich, An index integral and convolution operator related to the Kontorovich-Lebedev and Mehler-Fock transforms, Complex Anal. Oper. Theory6, 947 (2012)

    work page 2012

  24. [24]

    Rodrigues, N

    M. Rodrigues, N. Vieira, and S. Yakubovich, A convolution operator related to the generalized Mehler–Fock and Kontorovich–Lebedev transforms, Results Math.63, 511 (2013)

    work page 2013

  25. [25]

    A. F. Loureiro and S. Yakubovich, Central factorials under the Kontorovich–Lebedev transform of polynomials, Integral Transforms Spec. Funct.24, 217 (2013)

    work page 2013

  26. [26]

    S. Yakubovich, An index transform method for solutions of the boundary value problems in a wedge, inDirect and Inverse Problems with Applications, and Related Topics: A Comprehensive Summer School in Mathematical Analysis (Springer, 2024) pp. 155–160

    work page 2024

  27. [27]

    L. D. Landau and E. M. Lifshitz,The Classical Theory of Fields(Butterworth-Heinemann, Oxford, 1975)

    work page 1975

  28. [28]

    L. D. Landau, E. Lifshitz, and L. Pitaevskii,Electrodynamics of Continuous Media(Pergamon Press, Oxford, 1984)

    work page 1984

  29. [29]

    Lowndes, An application of the Kontorovich-Lebedev transform, Proc

    J. Lowndes, An application of the Kontorovich-Lebedev transform, Proc. Edinb. Math. Soc.11, 135 (1959)

    work page 1959

  30. [30]

    D. S. Jones,The Theory of Electromagnetism(Pergamon Press, Oxford, 1964)

    work page 1964

  31. [31]

    D. S. Jones,Acoustic and Electromagnetic Waves (Clarendon Press, Oxford, 1989)

    work page 1989

  32. [32]

    G. Z. Forristall,Elastodynamics of a Wedge, Ph.D. Thesis, Rice University (1970)

    work page 1970

  33. [33]

    A. M. Davis, Two-dimensional acoustical diffraction by a penetrable wedge, J. Acoust. Soc. Am.100, 1316 (1996)

    work page 1996

  34. [34]

    M. A. Biot and I. Tolstoy, Formulation of wave propagation in infinite media by normal coordinates with an application to diffraction, J. Acoust. Soc. Am.29, 381 (1957)

    work page 1957

  35. [35]

    A. M. Davis and R. W. Scharstein, The complete extension of the Biot–Tolstoy solution to the density contrast wedge with sample calculations, J. Acoust. Soc. Am.101, 1821 (1997)

    work page 1997

  36. [36]

    R. W. Scharstein and A. M. Davis, Time-domain three- dimensional diffraction by the isorefractive wedge, IEEE Trans. Antennas Propag.46, 1148 (1998)

    work page 1998

  37. [37]

    Rawlins, Diffraction by, or diffusion into, a penetrable wedge, Proc

    A. Rawlins, Diffraction by, or diffusion into, a penetrable wedge, Proc. R. Soc. Lond. A Math. Phys. Eng. Sci.455, 2655 (1999)

    work page 1999

  38. [38]

    Knockaert, F

    L. Knockaert, F. Olyslager, and D. De Zutter, The diaphanous wedge, IEEE Trans. Antennas Propag.45, 1374 (2002)

    work page 2002

  39. [39]

    Y. A. Antipov, Diffraction of a plane wave by a circular cone with an impedance boundary condition, SIAM J. Appl. Math.62, 1122 (2002)

    work page 2002

  40. [40]

    M. A. Salem, A. H. Kamel, and A. V. Osipov, Electromagnetic fields in the presence of an infinite dielectric wedge, Proc. R. Soc. A Math. Phys. Eng. Sci.462, 2503 (2006)

    work page 2006

  41. [41]

    R. W. Scharstein, Green’s function for the harmonic potential of the three-dimensional wedge transmission problem, IEEE Trans. Antennas Propag.52, 452 (2004)

    work page 2004

  42. [42]

    K. C. Hwang, Scattering from a grooved conducting wedge, IEEE Trans. Antennas Propag.57, 2498 (2009)

    work page 2009

  43. [43]

    J. J. Kim, H. J. Eom, and K. C. Hwang, Electromagnetic scattering from a slotted conducting wedge, IEEE Trans. Antennas Propag.58, 222 (2009)

    work page 2009

  44. [44]

    Shanin and V

    A. Shanin and V. Y. Valyaev, The modified Kontorovich- Lebedev transform and its application to solving canonical problems of diffraction, Acoust. Phys.57, 772 (2011)

    work page 2011

  45. [45]

    Lyalinov, Diffraction by a highly contrast transparent wedge, J

    M. Lyalinov, Diffraction by a highly contrast transparent wedge, J. Phys. A: Math. Gen.32, 2183 (1999)

    work page 1999

  46. [46]

    M. A. Lyalinov and N. Y. Zhu, Acoustic scattering by a circular semi-transparent conical surface, J. Eng. Math.59, 385 (2007)

    work page 2007

  47. [47]

    Lyalinov, The far field asymptotics in the problem of diffraction of an acoustic plane wave by an impedance cone, Russ

    M. Lyalinov, The far field asymptotics in the problem of diffraction of an acoustic plane wave by an impedance cone, Russ. J. Math. Phys.16, 277 (2009)

    work page 2009

  48. [48]

    Lyalinov, Integral equations and the scattering diagram in the problem of diffraction by two shifted contacting wedges with polygonal boundary, J

    M. Lyalinov, Integral equations and the scattering diagram in the problem of diffraction by two shifted contacting wedges with polygonal boundary, J. Math. Sci.214, 322 (2016)

    work page 2016

  49. [49]

    Lyalinov, Eigenoscillations in an angular domain and spectral properties of functional equations, Euro

    M. Lyalinov, Eigenoscillations in an angular domain and spectral properties of functional equations, Euro. J. Appl. Math.33, 538 (2022)

    work page 2022

  50. [50]

    H. J. Eom, Integral transforms in electromagnetic formulation, J. Electromagn. Eng. Sci.14, 273 (2014)

    work page 2014

  51. [51]

    L. D. Landau and E. M. Lifshitz,Theory of Elasticity (Butterworth-Heinemann, Oxford, 1986)

    work page 1986

  52. [52]

    M. K. Kassir and G. C. Sih, Application of Papkovich- Neuber potentials to a crack problem, Int. J. Solids Struct. 9, 643 (1973)

    work page 1973

  53. [53]

    M. K. Kassir, Thermal stresses in an elastic solid containing a plane crack, Int. J. Eng. Sci.13, 703 (1975)

    work page 1975

  54. [54]

    Pozharskii, B

    D. Pozharskii, B. Sobol, and P. Vasiliev, Periodic crack system in a layered elastic wedge, Mech. Adv. Mater. Struct. 27, 318 (2020)

    work page 2020

  55. [55]

    Aleksandrov and D

    V. Aleksandrov and D. Pozharskii, Problems of cuts in a composite elastic wedge, J. Appl. Math. Mech.73, 103 (2009)

    work page 2009

  56. [56]

    Hanson and L

    M. Hanson and L. Keer, Analysis of edge effects on rail-wheel contact, Wear144, 39 (1991)

    work page 1991

  57. [57]

    Hanson, Y

    M. Hanson, Y. Xu, and L. Keer, Stress analysis for a 15 three-dimensional incompressible wedge under body force or surface loading, Q. J. Mech. Appl. Math.47, 141 (1994)

    work page 1994

  58. [58]

    Aleksandrov and D

    V. Aleksandrov and D. Pozharskii, The problem of an inclusion in a three-dimensional elastic wedge, J. Appl. Math. Mech.66, 617 (2002)

    work page 2002

  59. [59]

    Aleksandrov and D

    V. Aleksandrov and D. Pozharskii, The three-dimensional problem of a thin inclusion in a composite elastic wedge, J. Appl. Math. Mech.75, 589 (2011)

    work page 2011

  60. [60]

    Daddi-Moussa-Ider, L

    A. Daddi-Moussa-Ider, L. Fischer, M. Pradas, and A. M. Menzel, Elastic displacements and viscous hydrodynamic flows in wedge-shaped geometries with a straight edge: Green’s functions for parallel forces, Proc. R. Soc. A481, 20250353 (2025)

    work page 2025

  61. [61]

    Daddi-Moussa-Ider and A

    A. Daddi-Moussa-Ider and A. M. Menzel, Elastic displacements and viscous flows in wedge-shaped geometries with a straight edge: Green’s functions for perpendicular forces, J. Elast.157, 54 (2025)

    work page 2025

  62. [62]

    Sano and H

    O. Sano and H. Hasimoto, Slow motion of a spherical particle in a viscous fluid bounded by two perpendicular walls, J. Phys. Soc. Japan40, 884 (1976)

    work page 1976

  63. [63]

    Sano and H

    O. Sano and H. Hasimoto, Slow motion of a small sphere in a viscous fluid in a corner i. motion on and across the bisector of a wedge, J. Phys. Soc. Jpn.42, 306 (1977)

    work page 1977

  64. [64]

    Sano and H

    O. Sano and H. Hasimoto, The effect of two plane walls on the motion of a small sphere in a viscous fluid, J. Fluid Mech. 87, 673 (1978)

    work page 1978

  65. [65]

    Hasimoto and O

    H. Hasimoto and O. Sano, Stokeslets and eddies in creeping flow, Ann. Rev. Fluid Mech.12, 335 (1980)

    work page 1980

  66. [66]

    Sano,Slow motion of a small sphere in a viscous fluid bounded by two plane walls, Ph.D

    O. Sano,Slow motion of a small sphere in a viscous fluid bounded by two plane walls, Ph.D. Thesis, University of Tokyo (1977)

    work page 1977

  67. [67]

    Hasimoto, M.-U

    H. Hasimoto, M.-U. Kim, and T. Miyazaki, The effect of a semi-infinite plane on the motion of a small particle in a viscous fluid, J. Phys. Soc. Jpn.52, 1996 (1983)

    work page 1996

  68. [68]

    Kim, The effect of a salient wedge on the motion of a small particle in a viscous fluid, J

    M.-U. Kim, The effect of a salient wedge on the motion of a small particle in a viscous fluid, J. Phys. Soc. Jpn.52, 3790 (1983)

    work page 1983

  69. [69]

    Sano and H

    O. Sano and H. Hashimoto, Three-dimensional Moffatt-type eddies due to a Stokeslet in a corner, J. Phys. Soc. Jpn.48, 1763 (1980)

    work page 1980

  70. [70]

    Shankar, On Stokes flow in a semi-infinite wedge, J

    P. Shankar, On Stokes flow in a semi-infinite wedge, J. Fluid Mech.422, 69 (2000)

    work page 2000

  71. [71]

    Dauparas and E

    J. Dauparas and E. Lauga, Leading-order Stokes flows near a corner, IMA J. Appl. Math.83, 590 (2018)

    work page 2018

  72. [72]

    Dauparas,Stokes flows near boundaries: bacteria, corners, and pumps, Ph.D

    J. Dauparas,Stokes flows near boundaries: bacteria, corners, and pumps, Ph.D. Thesis (2018)

    work page 2018

  73. [73]

    A. R. Sprenger and A. M. Menzel, Microswimming under a wedge-shaped confinement, Phys. Fluids35, 123119 (2023)

    work page 2023

  74. [74]

    Daddi-Moussa-Ider, J

    A. Daddi-Moussa-Ider, J. Mihatsch, M. J. Mitchell, E. Tjhung, and A. M. Menzel, Hydrodynamic flows induced by localized torques (rotlets) in wedge-shaped geometries, Phys. Rev. Fluids11, 034101 (2026)

    work page 2026

  75. [75]

    Self-diffusiophoretic propulsion in wedge confinement: The role of phoretic interactions

    A. Daddi-Moussa-Ider and R. Golestanian, Toward a theoretical framework for self-diffusiophoretic propulsion near a wedge, arXiv preprint arXiv:2601.00258 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  76. [76]

    Kim and S

    S. Kim and S. J. Karrila,Microhydrodynamics: Principles and Selected Applications(Dover Publications, Inc. Mineola, New York, 2005)

    work page 2005

  77. [77]

    P. F. Papkovich, The representation of the general integral of the fundamental equations of elasticity theory in terms of harmonic functions, Izv. Akad. Nauk. SSSR Ser. Mat.10, 1425 (1932)

    work page 1932

  78. [78]

    Neuber, Ein neuer Ansatz zur L¨ osung r¨ aumlicher Probleme der Elastizit¨ atstheorie, Z

    H. Neuber, Ein neuer Ansatz zur L¨ osung r¨ aumlicher Probleme der Elastizit¨ atstheorie, Z. Angew. Math. Mech. 14, 203 (1934)

    work page 1934

  79. [79]

    Tran-Cong and J

    T. Tran-Cong and J. R. Blake, General solutions of the Stokes’ flow equations, J. Math. Anal. Appl.90, 72 (1982)

    work page 1982

  80. [80]

    Imai,Ryutai Rikigaku/Fluid Dynamics (in Japanese) (Syokabo, Tokyo, 1973)

    I. Imai,Ryutai Rikigaku/Fluid Dynamics (in Japanese) (Syokabo, Tokyo, 1973)

    work page 1973

Showing first 80 references.