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Start-up flow in shallow deformable microchannels

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dc.affiliation.dptoUC3M. Departamento de Ingeniería Térmica y de Fluidoses
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Mecánica de Fluidoses
dc.contributor.authorMartínez Calvo, Alejandro
dc.contributor.authorSevilla Santiago, Alejandro
dc.contributor.authorPeng, Gunnar G.
dc.contributor.authorStone, Howard A.
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2022-09-15T16:53:36Z
dc.date.available2022-09-15T16:53:36Z
dc.date.issued2020-02-25
dc.description.abstractMicrofluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a nonlinear function of the pressure drop due to the deformation of the upper soft wall. Here, we extend the steady theory of Christov et al. (J. Fluid Mech., vol. 841, 2018, pp. 267–286) by considering the start-up flow from rest, both in pressure-controlled and in flow-rate-controlled configurations. The characteristic scales and relevant parameters governing the transient flow are first identified, followed by the development of an unsteady lubrication theory assuming that the inertia of the fluid is negligible, and that the upper wall can be modelled as an elastic plate under pure bending satisfying the Kirchhoff–Love equation. The model is governed by two non-geometrical dimensionless numbers: a compliance parameter β, which compares the characteristic displacement of the upper wall with the undeformed channel height, and a parameter γ that compares the inertia of the solid with its flexural rigidity. In the limit of negligible solid inertia, γ → 0, a quasi-steady model is developed, whereby the fluid pressure satisfies a nonlinear diffusion equation, with β as the only parameter, which admits a self-similar solution under pressure-controlled conditions. This simplified lubrication description is validated with coupled three-dimensional numerical simulations of the Navier equations for the elastic solid and the Navier–Stokes equations for the fluid. The agreement is very good when the hypotheses behind the model are satisfied. Unexpectedly, we find fair agreement even in cases where the solid and liquid inertia cannot be neglected.en
dc.description.sponsorshipThe authors are grateful to J. Rivero-Rodríguez and B. Scheid for key numerical advice, to I. C. Christov for pointing out a mistake in figure 2 of an earlier version of the manuscript, and to R. Zaera for helpful discussions. A.M.-C. and A.S. thank the Spanish MINECO, Subdirección General de Gestión de Ayudas a la Investigación, for its support through projects DPI2014-59292-C3-1-P and DPI2015-71901-REDT, and the Spanish MCIU-Agencia Estatal de Investigación through project DPI2017-88201- C3-3-R. These research projects have been partly financed through FEDER European funds. A.M.-C. also acknowledges support from the Spanish MECD through the grant FPU16/02562 and to its associated programme Ayudas a la Movilidad 2018 during his stay at the Complex Fluids Group in Princeton. H.A.S. thanks the NSF for support via CMMI-1661672 and through Princeton University’s Material Research Science and Engineering Center DMR-1420541.en
dc.description.statusPublicadoes
dc.format.extent27
dc.identifier.bibliographicCitationJournal of Fluid Mechanics, (2020), v. 885, A25, pp.: 1-26.en
dc.identifier.doihttps://doi.org/10.1017/jfm.2019.994
dc.identifier.issn0022-1120
dc.identifier.publicationfirstpageA25-1en
dc.identifier.publicationlastpageA25-27en
dc.identifier.publicationtitleJournal of Fluid Mechanicsen
dc.identifier.publicationvolume885
dc.identifier.urihttps://hdl.handle.net/10016/35721
dc.identifier.uxxiAR/0000029648
dc.language.isoengen
dc.publisherCambridge University Pressen
dc.relation.projectIDGobierno de España. DPI2014-59292-C3-1-Pes
dc.relation.projectIDGobierno de España. DPI2017-88201-C3-3-Res
dc.relation.projectIDGobierno de España. DPI2015-71901-REDTes
dc.relation.projectIDGobierno de España. FPU16/02562es
dc.rights© Cambridge University Press 2019.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaIngeniería Mecánicaes
dc.subject.otherFluid-structure interactionen
dc.subject.otherLubrication theoryen
dc.subject.otherMicrofluidicsen
dc.titleStart-up flow in shallow deformable microchannelsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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