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Thin-gap approximations for microfluidic device design.

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Title: Thin-gap approximations for microfluidic device design.
Authors: Ding, Lingyun1 dingly@g.ucla.edu, Wang, Terry1, Roper, Marcus1,2
Source: Journal of Fluid Mechanics. 3/25/2026, Vol. 1031, p1-17. 17p.
Subjects: Microfluidic devices, Potential flow, Microfluidics, Orthogonal polynomials, Numerical analysis, Flow simulations
Abstract: Over 125 years ago, Henry Selby Hele-Shaw realised that the depth-averaged flow in thingap geometries can be closely approximated by two-dimensional (2-D) potential flow, in a surprising marriage between the theories of viscous-dominated and inviscid flows. Hele-Shaw approximation allows visualisation of potential flows over 2-D aerofoils and also undergirds important discoveries in the dynamics of interfacial instabilities and convection, yet it has found little use in modelling flows in microfluidic devices, although these devices often have thin-gap geometries. Here, we derive a Hele-Shaw approximation for the flow in the kinds of thin-gap geometries created within microfluidic devices. Using the method of weighted residuals, we reinterpret the Hele-Shaw approximation as the leading term of an orthogonal polynomial expansion that can be systematically extended to higher-order corrections. The resulting leading-order equation coincides with the previously derived 2-D approximations, but our derivation is shorter and more direct. By extending the expansion beyond leading order, we obtain a new reduced model that captures non-parabolic gapwise velocity profiles and out-of-plane flow effects. We provide substantial numerical evidence showing that approximate equations can successfully model real microfluidic and inertialmicrofluidic device geometries. By reducing three-dimensional flows to 2-D models, our validated model will allow for accelerated device modelling and design. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 192858588
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PubTypeId: academicJournal
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  Data: Thin-gap approximations for microfluidic device design.
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  Data: <searchLink fieldCode="AR" term="%22Ding%2C+Lingyun%22">Ding, Lingyun</searchLink><relatesTo>1</relatesTo><i> dingly@g.ucla.edu</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Terry%22">Wang, Terry</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Roper%2C+Marcus%22">Roper, Marcus</searchLink><relatesTo>1,2</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 3/25/2026, Vol. 1031, p1-17. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Microfluidic+devices%22">Microfluidic devices</searchLink><br /><searchLink fieldCode="DE" term="%22Potential+flow%22">Potential flow</searchLink><br /><searchLink fieldCode="DE" term="%22Microfluidics%22">Microfluidics</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+polynomials%22">Orthogonal polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Flow+simulations%22">Flow simulations</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Over 125 years ago, Henry Selby Hele-Shaw realised that the depth-averaged flow in thingap geometries can be closely approximated by two-dimensional (2-D) potential flow, in a surprising marriage between the theories of viscous-dominated and inviscid flows. Hele-Shaw approximation allows visualisation of potential flows over 2-D aerofoils and also undergirds important discoveries in the dynamics of interfacial instabilities and convection, yet it has found little use in modelling flows in microfluidic devices, although these devices often have thin-gap geometries. Here, we derive a Hele-Shaw approximation for the flow in the kinds of thin-gap geometries created within microfluidic devices. Using the method of weighted residuals, we reinterpret the Hele-Shaw approximation as the leading term of an orthogonal polynomial expansion that can be systematically extended to higher-order corrections. The resulting leading-order equation coincides with the previously derived 2-D approximations, but our derivation is shorter and more direct. By extending the expansion beyond leading order, we obtain a new reduced model that captures non-parabolic gapwise velocity profiles and out-of-plane flow effects. We provide substantial numerical evidence showing that approximate equations can successfully model real microfluidic and inertialmicrofluidic device geometries. By reducing three-dimensional flows to 2-D models, our validated model will allow for accelerated device modelling and design. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1017/jfm.2026.11275
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      – Code: eng
        Text: English
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        PageCount: 17
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      – SubjectFull: Microfluidic devices
        Type: general
      – SubjectFull: Potential flow
        Type: general
      – SubjectFull: Microfluidics
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      – SubjectFull: Orthogonal polynomials
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      – SubjectFull: Numerical analysis
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      – SubjectFull: Flow simulations
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            NameFull: Wang, Terry
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            – D: 25
              M: 03
              Text: 3/25/2026
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              Y: 2026
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