Stability and the transition to turbulence in the flow through conduits with compliant walls

Kumaran, V.

doi:10.1017/jfm.2021.602

Cited by 14 publications

(9 citation statements)

References 137 publications

(507 reference statements)

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“…Interfacial instability may provide another class of flows for testing fluid-gel interfacial BCs. There is a rich literature on elastohydrodynamic instability of compliant solid walls under the impact of flow [28][29][30]. More recently, linear instability over a poroelastic wall has been examined [31].…”

Section: Discussionmentioning

confidence: 99%

Comparison of four boundary conditions for the fluid-hydrogel interface

Zhang²,

Young

et al. 2022

Phys. Rev. Fluids

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In adopting a poroelastic model for a hydrogel, one views its constituent fluid and solid phases as interpenetrating continua, thereby erasing the "pore-scale" geometry. This gives rise to the need for additional boundary conditions (BCs) at the interface between a hydrogel and a clear fluid to supplement the momentum equations for the fluid and solid phases in the hydrogel. Using a thermodynamic argument on energy dissipation, we propose three sets of boundary conditions for the gel-fluid interface that link the normal and tangential velocity jumps across the interface to the normal and tangential stresses on either side of the interface. Using several flow problems-one-dimensional compression, two-layer Couette and Poiseuille shear flows, and deformation of a gel particle by a planar extension flow-as tests, we compare the predictions of these three BCs with that of a previously proposed BC. Some differences are stark and reveal flaws in certain BCs. Others are subtler and will require quantitative experimental data for validation. Based on these results, we recommend one set of BCs over the other three for computing the flow and deformation of hydrogels in contact with a clear fluid. In addition, we suggest benchmark experiments to validate the BCs and our recommendation.

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Section: Discussionmentioning

confidence: 99%

Comparison of four boundary conditions for the fluid-hydrogel interface

Zhang²,

Young

et al. 2022

Phys. Rev. Fluids

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“…Different formulations of the linear stability analysis can also lead to completely different conclusions (Patne and Shankar, 2019). The most recent advances and perspectives following this line of research are thoroughly reviewed by Kumaran (2021).…”

Section: Re = Rementioning

confidence: 99%

Reduced modeling and global instability of finite-Reynolds-number flow in compliant rectangular channels

Wang¹,

Christov²

2022

Preprint

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Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that the wall's elastic compliance can be exploited towards new modalities of microscale mixing. While previous studies mainly focused on the local instability induced by the fluid-structure interactions (FSIs) in the system, we derive a new one-dimensional (1D) model to study the FSI's effect on the global instability. The proposed 1D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analyzed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a reduced 1D wall deformation equation. Although a quantitative comparison to previous experiments is quite difficult, the behaviors of the proposed derived model show qualitatively agreement with the experimental observations, and capture several key effects. Specifically, we find the critical conditions under which the inflated base state of the 1D FSI model is linearly unstable to infinitesimal perturbations. The critical Reynolds numbers predicted are in agreement with experimental observations. The unstable modes are highly oscillatory, with frequencies close to the natural frequency of the wall, suggesting that the observed instabilities are resonance phenomena. Furthermore, during the start-up from an undeformed initial state, self-sustained oscillations can be triggered due to FSIs. Our proposed modeling framework can be applied to other microfluidic systems with similar geometric scale separation, even under different operation conditions.

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“…The theory of viscous flow interacting with compliant walls has come a long way from Gray's (1936) initial observations of the outstanding performance of dolphin skins in delaying turbulence, to the recent review of Kumaran (2021) enlightening us on the various instability mechanisms. In the 1950s, Kramer conducted pioneering tests in water by towing a dolphin-shaped object covered with viscoelastic materials of varying compliance (Kramer 1957).…”

Section: Introductionmentioning

confidence: 99%

Linear instabilities of pulsatile plane channel flow between compliant walls

2022

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The linear dynamics of perturbations developing in an infinite channel with compliant walls is investigated for pulsatile flow conditions. Two-dimensional modal perturbations are considered for Womersley-type pulsating base flows and the wall motion is only allowed in the normal direction. It is found that the flow dynamics is mainly governed by four control parameters: the Reynolds number $Re$ , the reduced velocity $V_R$ , the Womersley number $Wo$ and the amplitude of the base-flow modulation $\tilde Q$ . Linear stability analyses are carried out within the framework of Floquet theory, implementing an efficient approach for removing spurious eigenmodes. The characteristics of flow-based (Tollmien–Schlichting) and wall-based (both travelling-wave flutter and divergence) modes are investigated over a large control-parameter space. It is shown that travelling-wave flutter (TWF) modes are predominantly influenced by the reduced velocity and that the Reynolds number has only a marginal effect. The critical reduced velocity (corresponding to onset of linear instability) is demonstrated to depend both on the Womersley number and modulation amplitude for a given set of wall parameters. Similarly to the steady flow case, the Tollmien–Schlichting (TS) mode is also found to be only weakly affected by the flexibility of the wall in pulsatile flow conditions. Finally, the classification given by Benjamin (J. Fluid Mech., vol. 16, 1963, pp. 436–450) is found to be too restrictive in the case of pulsatile base flows. In particular, a new type of mode is identified that shares characteristics of two distinct Floquet eigenmodes: TS and TWF modes. Due to coupling of the different Floquet harmonics, a phenomenon specific to time-periodic base flows, this two-wave mode exhibits a beating over the intracyclic dynamics.

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Stability and the transition to turbulence in the flow through conduits with compliant walls

Abstract: Abstract

Cited by 14 publications

References 137 publications

Comparison of four boundary conditions for the fluid-hydrogel interface

Comparison of four boundary conditions for the fluid-hydrogel interface

Reduced modeling and global instability of finite-Reynolds-number flow in compliant rectangular channels

Linear instabilities of pulsatile plane channel flow between compliant walls

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