Elastic deformations driven by non-uniform lubrication flows

Rubin, Shimon; Tulchinsky, Arie; Gat, Amir D.; Bercovici, Moran

doi:10.1017/jfm.2016.830

Cited by 19 publications

(18 citation statements)

References 29 publications

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“…The results predicted by the present theory agree favourably with the previous experimental studies [21,26]. While previous theoretical analyses [28,29,40,48] have successfully addressed this type of FSI for thinner plate-like top walls with t/w 1, the present theory is the first to quantify the hydrodynamic resistance in shallow compliant microchannels with thick top walls such that (t/w) 2 1.…”

Section: Resultssupporting

confidence: 87%

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

Wang

Christov

2019

Proc. R. Soc. A.

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Long, shallow microchannels embedded in thick, soft materials are widely used in microfluidic devices for lab-on-a-chip applications. However, the bulging effect caused by fluid–structure interactions between the internal viscous flow and the soft walls has not been completely understood. Previous models either contain a fitting parameter or are specialized to channels with plate-like walls. This work is a theoretical study of the steady-state response of a compliant microchannel with a thick wall. Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotropic solids, we obtain perturbative solutions for the flow and deformation. Specifically, only the channel's top wall deformation is considered, and the ratio between its thickness t and width w is assumed to be ( t / w ) 2 ≫1. We show that the deformation at each stream-wise cross section can be considered independently, and that the top wall can be regarded as a simply supported rectangle subject to uniform pressure at its bottom. The stress and displacement fields are found using Fourier series, based on which the channel shape and the hydrodynamic resistance are calculated, yielding a new flow rate–pressure drop relation without fitting parameters. Our results agree favourably with, and thus rationalize, previous experiments.

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Section: Resultssupporting

confidence: 87%

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

Wang

Christov

2019

Proc. R. Soc. A.

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“…Thus, pure bending models (e.g. such as the one considered by Rubin et al (2017) in previous work from our group) are insufficient for describing the behavior of realistic systems. Furthermore, accurate prediction of the deformation field requires accounting for the influence of the finite boundaries of the sheet.…”

Section: Introductionmentioning

confidence: 99%

Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

et al. 2019

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The interaction of a thin viscous film with an elastic sheet results in coupling of pressure and deformation, which can be utilized as an actuation mechanism for surface deformations in a wide range of applications, including microfluidics, optics, and soft robotics. Implementation of such configurations inherently takes place over finite domains and often requires some pre-stretching of the sheet. Under the assumptions of strong prestretching and small deformations of the lubricated elastic sheet, we use the linearized Reynolds and Föppl-von Kármán equations to derive closed-form analytical solutions describing the deformation in a finite domain due to external forces, accounting for both bending and tension effects. We provide a closed-form solution for the case of a square-shaped actuation region and present the effect of pre-stretching on the dynamics of the deformation. We further present the dependence of the deformation magnitude and timescale on the spatial wavenumber, as well as the transition between stretchingand bending-dominant regimes. We also demonstrate the effect of spatial discretization of the forcing (representing practical actuation elements) on the achievable resolution of the deformation. Extending the problem to an axisymmetric domain, we investigate the effects arising from nonlinearity of the Reynolds and Föppl-von Kármán equations and present the deformation behavior as it becomes comparable to the initial film thickness and dependent on the induced tension. These results set the theoretical foundation for implementation of microfluidic soft actuators based on elastohydrodynanmics.

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“…Beyond the direct application to supraglacial drainage, there has been renewed interest in the fluid mechanics associated with spreading below an elastic sheet, driven by applications in different settings including hydraulic fracturing (Wang & Detournay 2018), magmatic intrusions (Thorey & Michaut 2016), soft robotics (Rubin et al 2017) and control of viscous-fingering instabilities (Pihler-Puzovic et al 2014). It is well known that the spread of a shallow fluid layer beneath a bending elastic beam depends sensitively on the conditions at its front or nose (Lister et al 2013;Hewitt et al 2015b;Peng et al 2015).…”

Section: Introductionmentioning

confidence: 99%

The influence of a poroelastic till on rapid subglacial flooding and cavity formation

2018

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We develop a model of the rapid propagation of water at the contact between elastic glacial ice and a poroelastic subglacial till, motivated by observations of the rapid drainage of supraglacial lakes in Greenland. By treating the ice as an elastic bending beam, the fluid dynamics of contact with the subglacial hydrological network, which is modelled as a saturated poroelastic till, can be examined in detail. The model describes the formation and dynamics of an axisymmetric subglacial cavity, and the spread of pore pressure, in response to injection of fluid. A combination of numerical simulation and asymptotic analysis is used to describe these dynamics for both a rigid and a deformable porous till, and for both laminar and turbulent fluid flow. For constant injection rates and laminar flow, the cavity is isostatic and its spread is controlled by bending of the ice and suction of pore water in the vicinity of the ice–till contact. For a deformable till, this control can be modified: generically, a flexural wave that is initially trapped in advance of the contact point relaxes over time by diffusion of pore pressure ahead of the cavity. While the dynamics are found to be relatively insensitive to the properties of the subglacial till during injection with a constant flux, significant dependence on the till properties is manifest during the subsequent spread of a constant volume. A simple hybrid turbulent–laminar model is presented to account for fast injection rates of water: in this case, self-similar turbulent propagation can initially control the spread of the cavity, but there is a transition to laminar control in the vicinity of the ice–till contact point as the flow slows. Finally, the model results are compared with recent geophysical observations of the rapid drainage of supraglacial lakes in Greenland; the comparison provides qualitative agreement and raises suggestions for future quantitative comparison.

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Elastic deformations driven by non-uniform lubrication flows

Cited by 19 publications

References 29 publications

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

The influence of a poroelastic till on rapid subglacial flooding and cavity formation

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