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arxiv: 2505.22799 · v2 · submitted 2025-05-28 · ⚛️ physics.flu-dyn

Theory and simulation of elastoinertial rectification of oscillatory flows in two-dimensional deformable rectangular channels

Uday M. Rade , Shrihari D. Pande , Ivan C. Christov This is my paper

Pith reviewed 2026-05-19 12:47 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords elastoinertial rectificationfluid-structure interactionoscillatory flowdeformable channelstreamingWomersley numberelastoviscous numbercompliance number
0
0 comments X

The pith

Elastoinertial rectification theory predicts cycle-averaged pressure and deformation in oscillatory deformable channels that matches simulations for small compliance.

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

The paper adapts the theory of elastoinertial rectification to a two-dimensional rectangular channel with an elastic top layer. It derives predictions for cycle-averaged quantities under the assumption of small compliance and compares them to direct numerical simulations using an arbitrary Lagrangian-Eulerian method. The theory captures the nonlinear coupling between fluid inertia and structural deformation that leads to streaming effects. This is useful for understanding net fluid transport in flexible conduits driven by periodic flows, such as in microscale devices.

Core claim

By assuming a small compliance number, the adapted elastoinertial rectification theory predicts leading-order cycle-averaged pressure and deformation, next-order cycle-averaged pressures, and nontrivial cycle-averaged vertical and horizontal displacements. These agree well with direct numerical simulations across a range of Womersley and elastoviscous numbers.

What carries the argument

Elastoinertial rectification, the enhancement of streaming due to the nonlinear coupling of flow inertia and deformation-induced asymmetry in the channel cross-section.

If this is right

  • Cycle-averaged pressure shows axial variation determined by the Womersley and elastoviscous numbers.
  • Nontrivial cycle-averaged displacements occur in both vertical and horizontal directions.
  • The leading-order theory provides accurate predictions for pressure and deformation under small compliance.
  • Agreement between theory and simulation holds across tested ranges of the dimensionless groups.

Where Pith is reading between the lines

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

  • Designers of microfluidic systems could use this to create net flow from oscillation without pumps.
  • Similar rectification may appear in other FSI systems like blood flow in elastic vessels.
  • Extensions to larger compliance would require including higher-order terms in the expansion.
  • Three-dimensional versions of the channel could reveal additional effects not seen in 2D.

Load-bearing premise

The compliance number is small enough for the perturbation expansion to hold and produce accurate leading-order results.

What would settle it

Direct numerical simulations performed at a larger compliance number yielding significant differences from the theoretical cycle-averaged pressure and deformation profiles.

Figures

Figures reproduced from arXiv: 2505.22799 by Ivan C. Christov, Shrihari D. Pande, Uday M. Rade.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic of the 2D problem of oscillatory flow in a fluidic channel bounded by a rigid surface below and a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) The reduced complex “wavenumber” [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) The streaming pressure profile from Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The 2D [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Pressure distribution along the fluidic channel over one flow oscillation cycle. As a periodic state has been [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Visualization of the pressure field, [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Visualization of the horizontal component of the velocity field, [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Vertical displacement of the fluid–solid interface. Solid curves represent the theoretical prediction [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Displacement of the fluid–solid interface: the two components, [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Visualization of (a,b,c) the vertical component of the displacement field, [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Streaming (cycle-averaged) pressure distribution, [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Streaming (cycle-averaged) (a) vertical and (b) horizontal displacements along the fluid–solid interface for [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: The (a) vertical displacement of the fluid–solid interface Re[ [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
read the original abstract

A slender two-dimensional (2D) channel bounded by a rigid bottom surface and a slender elastic layer above deforms when a fluid flows through it. Hydrodynamic forces cause deformation at the fluid--solid interface, which in turn changes the cross-sectional area of the fluidic channel. The nonlinear coupling between flow and deformation, along with the attendant asymmetry in geometry caused by flow-induced deformation, produces a streaming effect (a nonzero cycle-average despite time-periodic forcing). Surprisingly, flow inertia provides another nonlinear coupling, tightly connected to deformation, that enhances streaming, termed ``elastoinertial rectification'' by Zhang and Rallabandi [J.\ Fluid Mech.\ \textbf{996}, A16 (2024)]. We adapt the latter theory of how two-way coupled fluid--structure interaction (FSI) produces streaming to a 2D rectangular configuration, specifically taking care to capture the deformations of the nearly incompressible slender elastic layer via the combined foundation model of Chandler and Vella [Proc.\ R.\ Soc.\ A \textbf{476}, 20200551 (2020)]. We supplement the elastoinertial rectification theory with direct numerical simulations performed using a stabilized, conforming arbitrary Lagrangian--Eulerian (ALE) FSI formulation, implemented via the open-source computing platform FEniCS. We examine the axial variation of the cycle-averaged pressure as a function of key dimensionless groups of the problem: the Womersley number, the elastoviscous number, and the compliance number. Assuming a small compliance number, we find excellent agreement between theory and simulations for the leading-order pressure and deformation across a range of conditions. At the next order, the cycle-averaged pressures agree well. Finally, the theory also predicts nontrivial cycle-averaged vertical and horizontal displacements, in agreement with the simulations.

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 / 3 minor

Summary. The manuscript adapts the elastoinertial rectification theory of Zhang and Rallabandi to a two-dimensional rectangular channel with a rigid bottom and a slender elastic top layer modeled via the combined foundation approach of Chandler and Vella. Under the assumption of small compliance number, the leading-order cycle-averaged pressure and deformation are derived analytically; next-order cycle-averaged pressures and nontrivial cycle-averaged vertical and horizontal displacements are also obtained. These predictions are compared to direct numerical simulations performed with a stabilized conforming ALE FSI formulation implemented in open-source FEniCS, showing excellent agreement for leading-order quantities and good agreement at next order across a range of Womersley and elastoviscous numbers.

Significance. If the results hold, the work supplies a validated, asymptotically consistent framework for predicting streaming flows driven by the two-way coupling of inertia and deformation in slender compliant channels. The explicit use of an open-source, reproducible FEniCS implementation and the grounding of all predictions in the small-compliance regime constitute clear strengths. The findings are relevant to microfluidic pumping, lab-on-chip devices, and physiological flows where elastoinertial effects may be exploited or must be controlled.

minor comments (3)
  1. Abstract and §1: the compliance number is introduced only by name; an explicit definition (e.g., ratio of elastic to viscous forces) placed before the first use would improve readability for readers outside the immediate FSI community.
  2. §4.2, Figure 7: the vertical scale of the cycle-averaged horizontal displacement field is not labeled with the same nondimensionalization used in the theory; adding the scaling factor would make the comparison with the analytic prediction immediate.
  3. §5: the statement that 'excellent agreement' holds 'across a range of conditions' would be strengthened by a brief quantitative metric (e.g., L2 error norms) rather than qualitative description alone.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our manuscript, as well as for highlighting its strengths in providing a validated asymptotic framework, reproducible open-source implementation, and relevance to microfluidic and physiological applications. We are pleased with the recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper adapts the elastoinertial rectification theory from the external citation Zhang and Rallabandi (J. Fluid Mech. 996, A16, 2024) to a 2D rectangular geometry and incorporates the independent combined foundation model from Chandler and Vella (Proc. R. Soc. A 476, 20200551, 2020). These are non-overlapping external references. Leading-order and next-order cycle-averaged predictions for pressure and deformation are derived under the explicitly stated small-compliance-number assumption and are validated against independent direct numerical simulations via a stabilized ALE FSI formulation in FEniCS. No predictions or results reduce by the paper's own equations to parameters fitted within this work, and no load-bearing step relies on self-citation chains or self-defined quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on established models for fluid inertia and elastic foundation behavior without introducing new fitted parameters or postulated entities; the small compliance number functions as a regime restriction rather than a free parameter.

axioms (2)
  • domain assumption Combined foundation model of Chandler and Vella for deformations of the nearly incompressible slender elastic layer.
    Invoked to capture the fluid-solid interface deformation in the 2D rectangular setup.
  • ad hoc to paper Small compliance number regime for leading-order analysis.
    Stated explicitly to obtain excellent agreement between theory and simulations.

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Works this paper leans on

106 extracted references · 106 canonical work pages

  1. [1]

    component

    is theelastoviscous number[41, 52]. The elastoviscous number is the ratio of time scales—the vertical displacement time scale set by uc/(ϵf vc) to the oscillation time scale set byω −1 [61]. Table I summarizes the dimensionless numbers of the problem, the assumptions placed on them in the theory, and their representative values considered in the simulatio...

    work page 2019

  2. [2]

    The plots show a strong agreement between the theoretical predictions, i.e., the primary pressureP 0(Z, T) = Re[P 0,a(Z)eiT ] obtained from Eq

    Fluid pressure and velocity Figure 5 presents the dimensionless pressure distribution,P(Z, T), along the fluidic channel over one flow oscillation cycle for three representative value pairs of the elastoviscous numberγand the Womersley number Wo. The plots show a strong agreement between the theoretical predictions, i.e., the primary pressureP 0(Z, T) = R...

    work page

  3. [3]

    8, we present the vertical displacement of the fluid–solid interface,U Y (Z, T), over one flow oscillation cycle for the same three pairs ofγand Wo as in the previous subsection

    Elastic layer displacements In Fig. 8, we present the vertical displacement of the fluid–solid interface,U Y (Z, T), over one flow oscillation cycle for the same three pairs ofγand Wo as in the previous subsection. Here, the agreement between the combined foundation model,U Y,0(Z, T) = Re[U Y,0,a(Z)eiT ] obtained from Eq. (14a), and the finite element sim...

    work page

  4. [4]

    Fluid pressure A nonzero cycle-averaged (streaming) pressure⟨P 1⟩arises because both the flow-induced wall (geometric nonlin- earity) deformation and the advective inertia (flow nonlinearity) lead to cycle-averages of products of two oscillatory quantities that, while individually having zero mean, yield a nonzero mean over the oscillation cycle, as shown...

    work page

  5. [5]

    if the imposed boundary conditions are incompatible with the displacement field suggested... we expect a boundary layer,

    Fluid–solid interface displacements Figure 12 presents the scaled cycle-averaged displacements, ⟨UY ⟩/β=⟨P 1⟩ −(θ−ϑf 1) d2⟨P1⟩ dZ2 ,(36a) ⟨UZ⟩/β= ϵsh0 CW G f1 −ϵ s ˆϑ d⟨P1⟩ dZ ,(36b) obtained from Eqs. (4), for the representative value ofγ= 1.5 and the three values of Wo. The requisite derivatives of⟨P 1⟩are computed by second-order finite difference from...

    work page doi:10.4231/50c7-hk87

  6. [6]

    Dincau, E

    B. Dincau, E. Dressaire, and A. Sauret, Pulsatile Flow in Microfluidic Systems, Small16, 1904032 (2020)

    work page 2020

  7. [7]

    J. B. Grotberg, Pulmonary flow and transport phenomena, Annu. Rev. Fluid Mech.26, 529 (1994)

    work page 1994

  8. [8]

    J. B. Grotberg and O. E. Jensen, Biofluid mechanics in flexible tubes, Annu. Rev. Fluid Mech.36, 121 (2004)

    work page 2004

  9. [9]

    Heil and A

    M. Heil and A. L. Hazel, Fluid-structure interaction in internal physiological flows, Annu. Rev. Fluid Mech.43, 141 (2011)

    work page 2011

  10. [10]

    T. J. Pedley,The Fluid Mechanics of Large Blood Vessels(Cambridge University Press, Cambridge, 1980)

    work page 1980

  11. [11]

    Y. C. Fung,Biomechanics: Circulation, 2nd ed. (Springer-Verlag, New York, NY, 1997)

    work page 1997

  12. [12]

    P. S. Stewart and A. J. E. Foss, Self-excited oscillations in a collapsible channel with applications to retinal venous pulsation, ANZIAM J.61, 320 (2019)

    work page 2019

  13. [13]

    P. A. R. Bork, A. Ladr´ on-de Guevara, A. H. Christensen, K. H. Jensen, M. Nedergaard, and T. Bohr, Astrocyte endfeet may theoretically act as valves to convert pressure oscillations to glymphatic flow, J. R. Soc. Interface20, 20230050 (2023)

    work page 2023

  14. [14]

    Dowson and Z.-M

    D. Dowson and Z.-M. Jin, Micro-Elastohydrodynamic Lubrication of Synovial Joints, Eng. Med.15, 63 (1986)

    work page 1986

  15. [15]

    Parthasarathy, Y

    T. Parthasarathy, Y. Bhosale, and M. Gazzola, Elastic solid dynamics in a coupled oscillatory Couette flow system, J. Fluid Mech.946, A15 (2022)

    work page 2022

  16. [16]

    Coyle, Forward roll coating with deformable rolls: A simple one-dimensional elastohydrodynamic model, Chem

    D. Coyle, Forward roll coating with deformable rolls: A simple one-dimensional elastohydrodynamic model, Chem. Eng. Sci.43, 2673 (1988)

    work page 1988

  17. [17]

    Carvalho and L

    M. Carvalho and L. Scriven, Flows in Forward Deformable Roll Coating Gaps: Comparison between Spring and Plane- Strain Models of Roll Cover, J. Comput. Phys.138, 449 (1997)

    work page 1997

  18. [18]

    Yin and S

    X. Yin and S. Kumar, Lubrication flow between a cavity and a flexible wall, Phys. Fluids17, 063101 (2005). 19

    work page 2005

  19. [19]

    J. M. Skotheim and L. Mahadevan, Soft Lubrication, Phys. Rev. Lett.92, 245509 (2004)

    work page 2004

  20. [20]

    J. A. Greenwood, Elastohydrodynamic Lubrication, Lubricants8, 51 (2020)

    work page 2020

  21. [21]

    Karan, J

    P. Karan, J. Chakraborty, and S. Chakraborty, Small-scale flow with deformable boundaries, J. Indian Inst. Sci.98, 159 (2018)

    work page 2018

  22. [22]

    Bureau, G

    L. Bureau, G. Coupier, and T. Salez, Lift at low Reynolds number, Eur. Phys. J. E46, 111 (2023)

    work page 2023

  23. [23]

    Rallabandi, Fluid-Elastic Interactions Near Contact at Low Reynolds Number, Annu

    B. Rallabandi, Fluid-Elastic Interactions Near Contact at Low Reynolds Number, Annu. Rev. Fluid Mech.56, 491 (2024)

    work page 2024

  24. [24]

    Chakraborty and S

    J. Chakraborty and S. Chakraborty, Influence of streaming potential on the elastic response of a compliant microfluidic substrate subjected to dynamic loading, Phys. Fluids22, 122002 (2010)

    work page 2010

  25. [25]

    Pandey, S

    A. Pandey, S. Karpitschka, C. H. Venner, and J. H. Snoeijer, Lubrication of soft viscoelastic solids, J. Fluid Mech.799, 433 (2016)

    work page 2016

  26. [26]

    S. B. Elbaz, H. Jacob, and A. D. Gat, Transient gas flow in elastic microchannels, J. Fluid Mech.846, 460 (2018)

    work page 2018

  27. [27]

    D. A. Dillard, B. Mukherjee, P. Karnal, R. C. Batra, and J. Frechette, A review of Winkler’s foundation and its profound influence on adhesion and soft matter applications, Soft Matter14, 3669 (2018)

    work page 2018

  28. [28]

    M. H. Essink, A. Pandey, S. Karpitschka, C. H. Venner, and J. H. Snoeijer, Regimes of soft lubrication, J. Fluid Mech. 915, A49 (2021)

    work page 2021

  29. [29]

    T. G. J. Chandler and D. Vella, Validity of Winkler’s mattress model for thin elastomeric layers: beyond Poisson’s ratio, Proc. R. Soc. A476, 20200551 (2020)

    work page 2020

  30. [30]

    H. M. Xia, J. W. Wu, J. J. Zheng, J. Zhang, and Z. P. Wang, Nonlinear microfluidics: device physics, functions, and applications, Lab Chip21, 1241 (2021)

    work page 2021

  31. [31]

    Battat, D

    S. Battat, D. A. Weitz, and G. M. Whitesides, Nonlinear Phenomena in Microfluidics, Chem. Rev.122, 6921 (2022)

    work page 2022

  32. [32]

    Mudugamuwa, U

    A. Mudugamuwa, U. Roshan, S. Hettiarachchi, H. Cha, H. Musharaf, X. Kang, Q. T. Trinh, H. M. Xia, N. Nguyen, and J. Zhang, Periodic Flows in Microfluidics, Small20, 2404685 (2024)

    work page 2024

  33. [33]

    I. C. Christov, Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits, J. Phys.: Condens. Matter34, 063001 (2022)

    work page 2022

  34. [34]

    Kumaran and P

    V. Kumaran and P. Bandaru, Ultra-fast microfluidic mixing by soft-wall turbulence, Chem. Eng. Sci.149, 156 (2016)

    work page 2016

  35. [35]

    D. C. Leslie, C. J. Easley, E. Seker, J. M. Karlinsey, M. Utz, M. R. Begley, and J. P. Landers, Frequency-specific flow control in microfluidic circuits with passive elastomeric features, Nat. Phys.5, 231 (2009)

    work page 2009

  36. [36]

    Mosadegh, C.-H

    B. Mosadegh, C.-H. Kuo, Y.-C. Tung, Y.-s. Torisawa, T. Bersano-Begey, H. Tavana, and S. Takayama, Integrated elas- tomeric components for autonomous regulation of sequential and oscillatory flow switching in microfluidic devices, Nat. Phys.6, 433 (2010)

    work page 2010

  37. [37]

    Stoecklein and D

    D. Stoecklein and D. Di Carlo, Nonlinear Microfluidics, Anal. Chem.91, 296 (2019)

    work page 2019

  38. [38]

    S. N. Bhatia and D. E. Ingber, Microfluidic organs-on-chips, Nat. Biotechnol.32, 760 (2014)

    work page 2014

  39. [39]

    J. U. Lind, T. A. Busbee, A. D. Valentine, F. S. Pasqualini, H. Yuan, M. Yadid, S. J. Park, A. Kotikian, A. P. Nesmith, P. H. Campbell, J. J. Vlassak, J. A. Lewis, and K. K. Parker, Instrumented cardiac microphysiological devices via multimaterial three-dimensional printing, Nat. Mat.16, 303 (2017)

    work page 2017

  40. [40]

    Dalsbecker, C

    P. Dalsbecker, C. Beck Adiels, and M. Goks¨ or, Liver-on-a-chip devices: the pros and cons of complexity, Am. J. Physiol. - Gastrointest.323, G188 (2022)

    work page 2022

  41. [41]

    C. M. Leung, P. de Haan, K. Ronaldson-Bouchard, G.-A. Kim, J. Ko, H. S. Rho, Z. Chen, P. Habibovic, N. L. Jeon, S. Takayama, M. L. Shuler, G. Vunjak-Novakovic, O. Frey, E. Verpoorte, and Y.-C. Toh, A guide to the organ-on-a-chip, Nat. Rev. Methods Primers2, 33 (2022)

    work page 2022

  42. [42]

    Amselem, C

    G. Amselem, C. Clanet, and M. Benzaquen, Valveless Pumping at Low Reynolds Numbers, Phys. Rev. Appl.19, 024017 (2023)

    work page 2023

  43. [43]

    Y. Pang, H. Kim, Z. Liu, and H. A. Stone, A soft microchannel decreases polydispersity of droplet generation, Lab Chip 14, 4029 (2014)

    work page 2014

  44. [44]

    M. D. Biviano, M. V. Paludan, A. H. Christensen, E. V. Østergaard, and K. H. Jensen, Smoothing Oscillatory Peristaltic Pump Flow with Bioinspired Passive Components, Phys. Rev. Appl.18, 064013 (2022)

    work page 2022

  45. [45]

    Polygerinos, N

    P. Polygerinos, N. Correll, S. A. Morin, B. Mosadegh, C. D. Onal, K. Petersen, M. Cianchetti, M. T. Tolley, and R. F. Shep- herd, Soft Robotics: Review of Fluid-Driven Intrinsically Soft Devices; Manufacturing, Sensing, Control, and Applications in Human-Robot Interaction, Adv. Eng. Mater.19, 1700016 (2017)

    work page 2017

  46. [46]

    S. B. Elbaz and A. D. Gat, Dynamics of viscous liquid within a closed elastic cylinder subject to external forces with application to soft robotics, J. Fluid Mech.758, 221 (2014)

    work page 2014

  47. [47]

    Matia, T

    Y. Matia, T. Elimelech, and A. D. Gat, Leveraging internal viscous flow to extend the capabilities of beam-shaped soft robotic actuators, Soft Robotics4, 126 (2017)

    work page 2017

  48. [48]

    Matia, G

    Y. Matia, G. H. Kaiser, R. F. Shepherd, A. D. Gat, N. Lazarus, and K. H. Petersen, Harnessing Nonuniform Pressure Distributions in Soft Robotic Actuators, Adv. Intell. Syst.5, 2200330 (2023)

    work page 2023

  49. [49]

    Maroundik, D

    N. Maroundik, D. Ilssar, and E. Boyko, Diffusioosmotic flow in a soft microfluidic configuration induces fluid-structure instability, Phys. Rev. Fluids10, 104203 (2025)

    work page 2025

  50. [50]

    Poulain, T

    S. Poulain, T. Koch, L. Mahadevan, and A. Carlson, Hovering of an Actively Driven Fluid-Lubricated Foil, Phys. Rev. Lett.135, 214002 (2025)

    work page 2025

  51. [51]

    Poulain, T

    S. Poulain, T. Koch, L. Mahadevan, and A. Carlson, Viscous adhesion in vibrating sheets: elastohydrodynamics with inertia and compressibility effects, J. Fluid Mech.1031, A9 (2026)

    work page 2026

  52. [52]

    A. Jha, Y. Amarouchene, and T. Salez, Taylor’s swimming sheet near a soft boundary, Soft Matter21, 826 (2025)

    work page 2025

  53. [53]

    Trevino, T

    A. Trevino, T. R. Powers, R. Zenit, and M. Rodriguez, Low Reynolds number pumping near an elastic half space, Phys. Rev. Fluids10, 054003 (2025). 20

    work page 2025

  54. [54]

    Riley, Steady streaming, Annu

    N. Riley, Steady streaming, Annu. Rev. Fluid Mech.33, 43 (2001)

    work page 2001

  55. [55]

    Bhosale, T

    Y. Bhosale, T. Parthasarathy, and M. Gazzola, Soft streaming – flow rectification via elastic boundaries, J. Fluid Mech. 945, R1 (2022)

    work page 2022

  56. [56]

    S. Cui, Y. Bhosale, and M. Gazzola, Three-dimensional soft streaming, J. Fluid Mech.979, A7 (2024)

    work page 2024

  57. [57]

    Zhang and B

    X. Zhang and B. Rallabandi, Elasto-inertial rectification of oscillatory flow in an elastic tube, J. Fluid Mech.996, A16 (2024)

    work page 2024

  58. [58]

    S. D. Pande, X. Wang, and I. C. Christov, Oscillatory flows in compliant conduits at arbitrary Womersley number, Phys. Rev. Fluids8, 124102 (2023)

    work page 2023

  59. [59]

    T. C. Inamdar, X. Wang, and I. C. Christov, Unsteady fluid-structure interactions in a soft-walled microchannel: A one-dimensional lubrication model for finite Reynolds number, Phys. Rev. Fluids5, 064101 (2020)

    work page 2020

  60. [60]

    ˇCani´ c, C

    S. ˇCani´ c, C. J. Hartley, D. Rosenstrauch, J. Tambaˇ ca, G. Guidoboni, and A. Mikeli´ c, Blood flow in compliant arteries: An effective viscoelastic reduced model, numerics, and experimental validation, Ann. Biomed. Eng.34, 575 (2006)

    work page 2006

  61. [61]

    Peir´ o and A

    J. Peir´ o and A. Veneziani, Reduced models of the cardiovascular system, inCardiovascular Mathematics, Modeling, Simu- lation and Applications, Vol. 1, edited by L. Formaggia, A. Quarteroni, and A. Veneziani (Springer, Milano, 2009) Chap. 10, pp. 347–394

    work page 2009

  62. [62]

    Quarteroni, A

    A. Quarteroni, A. Veneziani, and C. Vergara, Geometric multiscale modeling of the cardiovascular system, between theory and practice, Comput. Methods Appl. Mech. Engrg.302, 193 (2016)

    work page 2016

  63. [63]

    G. E. Neighbor, H. Zhao, M. Saraeian, M. C. Hsu, and D. Kamensky, Leveraging code generation for transparent immer- sogeometric fluid–structure interaction analysis on deforming domains, Eng. Comput.39, 1019 (2023)

    work page 2023

  64. [64]

    I. C. Christov, V. Cognet, T. C. Shidhore, and H. A. Stone, Flow rate–pressure drop relation for deformable shallow microfluidic channels, J. Fluid Mech.814, 267 (2018)

    work page 2018

  65. [65]

    J. R. Womersley, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J. Physiol.127, 553 (1955)

    work page 1955

  66. [66]

    Huang, S

    A. Huang, S. D. Pande, J. Feng, and I. C. Christov, Oscillatory flows in three-dimensional deformable microchannels, J. Fluid Mech.1022, A38 (2025)

    work page 2025

  67. [67]

    I. D. Johnston, D. K. McCluskey, C. K. L. Tan, and M. C. Tracey, Mechanical characterization of bulk Sylgard 184 for microfluidics and microengineering, J. Micromech. Microeng.24, 35017 (2014)

    work page 2014

  68. [68]

    Ramachandra Rao, Oscillatory flow in an elastic tube of variable cross-section, Acta Mech.46, 155 (1983)

    A. Ramachandra Rao, Oscillatory flow in an elastic tube of variable cross-section, Acta Mech.46, 155 (1983)

    work page 1983

  69. [69]

    T. J. Ward and R. J. Whittaker, Effect of base-state curvature on self-excited high-frequency oscillations in flow through an elastic-walled channel, Phys. Rev. Fluids4, 113901 (2019)

    work page 2019

  70. [70]

    Bar-Haim and H

    C. Bar-Haim and H. Diamant, Structured viscoelastic substrates as linear foundations, Phys. Rev. E105, 025005 (2022)

    work page 2022

  71. [71]

    A. N. Gent and E. A. Meinecke, Compression, bending, and shear of bonded rubber blocks, Polym. Eng. Sci10, 48 (1970)

    work page 1970

  72. [72]

    D. A. Dillard, Bending of Plates on Thin Elastomeric Foundations, ASME J. Appl. Mech.56, 382 (1989)

    work page 1989

  73. [73]

    Anand and I

    V. Anand and I. C. Christov, Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory, Z. Angew. Math. Mech. (ZAMM)101, e201900309 (2021)

    work page 2021

  74. [74]

    Boyko, H

    E. Boyko, H. A. Stone, and I. C. Christov, Flow rate-pressure drop relation for deformable channels via fluidic and elastic reciprocal theorems, Phys. Rev. Fluids7, L092201 (2022)

    work page 2022

  75. [75]

    C. A. Dragon and J. B. Grotberg, Oscillatory flow and mass transport in a flexible tube, J. Fluid Mech.231, 135 (1991)

    work page 1991

  76. [76]

    R. Yang, I. C. Christov, I. M. Griffiths, and G. Z. Ramon, Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid, Phys. Rev. Fluids5, 094501 (2020)

    work page 2020

  77. [77]

    Kierzenka and L

    J. Kierzenka and L. F. Shampine, A BVP solver based on residual control and the Matlab PSE, ACM Trans. Math. Softw. 27, 299 (2001)

    work page 2001

  78. [78]

    Mederos, J

    G. Mederos, J. Arcos, O. Bautista, and F. M´ endez, Taylor dispersion in an oscillatory squeeze flow of an Oldroyd-B fluid between hydrophobic disks, Phys. Rev. E112, 055106 (2025)

    work page 2025

  79. [79]

    Bazilevs, V

    Y. Bazilevs, V. M. Calo, T. J. Hughes, and Y. Zhang, Isogeometric fluid-structure interaction: Theory, algorithms, and computations, Comput. Mech.43, 3 (2008)

    work page 2008

  80. [80]

    Bazilevs, J

    Y. Bazilevs, J. Gohean, T. Hughes, R. Moser, and Y. Zhang, Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device, Comput. Meth. Appl. Mech. Engng198, 3534 (2009)

    work page 2000

Showing first 80 references.