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

被引:3
作者
Wang, Xiaojia [1 ]
Christov, Ivan C. [1 ]
机构
[1] Purdue Univ, Sch Mech Engn, W Lafayette, IN 47907 USA
基金
美国国家科学基金会;
关键词
microfluidics; SELF-EXCITED OSCILLATIONS; COLLAPSIBLE-CHANNEL; DYNAMICAL INSTABILITY; DRIVEN OSCILLATIONS; STABILITY; PRESSURE; TRANSITION; INTEGRATION; PARTICLES; FLUID;
D O I
10.1017/jfm.2022.802
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
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 one-dimensional (1-D) model to study the FSI's effect on the global instability. The proposed 1-D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analysed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a novel reduced 1-D wall deformation equation. Although a quantitative comparison with previous experiments is difficult, the behaviours of the proposed 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 1-D 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 by FSI. Our modelling framework can be applied to other microfluidic systems with similar geometric scale separation under different operating conditions.
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页数:36
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共 71 条
  • [1] Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation
    Anand, Vishal
    Muchandimath, Sanjan C.
    Christov, Ivan C.
    [J]. JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2020, 87 (05):
  • [2] Boyd J. P., 2001, Chebyshev and Fourier Spectral Methods, V2
  • [3] Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits
    Christov, Ivan C.
    [J]. JOURNAL OF PHYSICS-CONDENSED MATTER, 2022, 34 (06)
  • [4] Flow rate-pressure drop relation for deformable shallow microfluidic channels
    Christov, Ivan C.
    Cognet, Vincent
    Shidhore, Tanmay C.
    Stone, Howard A.
    [J]. JOURNAL OF FLUID MECHANICS, 2018, 841 : 267 - 286
  • [5] Optics-Free, Non-Contact Measurements of Fluids, Bubbles, and Particles in Microchannels Using Metallic Nano-Islands on Graphene
    Dhong, Charles
    Edmunds, Samuel J.
    Ramirez, Julian
    Kayser, Laure V.
    Chen, Fang
    Jokerst, Jesse V.
    Lipomi, Darren J.
    [J]. NANO LETTERS, 2018, 18 (08) : 5306 - 5311
  • [6] Continuous inertial focusing, ordering, and separation of particles in microchannels
    Di Carlo, Dino
    Irimia, Daniel
    Tompkins, Ronald G.
    Toner, Mehmet
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2007, 104 (48) : 18892 - 18897
  • [7] A review of Winkler's foundation and its profound influence on adhesion and soft matter applications
    Dillard, David A.
    Mukherjee, Bikramjit
    Karnal, Preetika
    Batra, Romesh C.
    Frechette, Joelle
    [J]. SOFT MATTER, 2018, 14 (19) : 3669 - 3683
  • [8] Dynamics of viscous liquid within a closed elastic cylinder subject to external forces with application to soft robotics
    Elbaz, S. B.
    Gat, A. D.
    [J]. JOURNAL OF FLUID MECHANICS, 2014, 758 : 221 - 237
  • [9] Compliant coatings for drag reduction
    Gad-el-Hak, M
    [J]. PROGRESS IN AEROSPACE SCIENCES, 2002, 38 (01) : 77 - 99
  • [10] Stability of fluid flow through deformable neo-Hookean tubes
    Gaurav
    Shankar, V.
    [J]. JOURNAL OF FLUID MECHANICS, 2009, 627 : 291 - 322