Transient gas flow in elastic microchannels

Elbaz, Shai; Jacob, Hila; Gat, Amir D.

doi:10.1017/jfm.2018.287

Cited by 15 publications

(12 citation statements)

References 45 publications

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“…Future work could include extending our results to rarefied (gas) flows at or below that micron scale, which brings up the issue of wall slip and compressibility [55]. It would also be of interest to determine the first correction due to friction at the lateral side walls, i.e., to relax the assumption δ 1.…”

Section: Resultsmentioning

confidence: 99%

Non-Newtonian fluid–structure interactions: Static response of a microchannel due to internal flow of a power-law fluid

Anand

David

Christov

2019

Journal of Non-Newtonian Fluid Mechanics

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We study fluid-structure interactions (FSIs) in a long and shallow microchannel, conveying a non-Newtonian fluid, at steady state. The microchannel has a linearly elastic and compliant top wall, while its three other walls are rigid. The fluid flowing inside the microchannel has a shear-dependent viscosity described by the power-law rheological model. We employ lubrication theory to solve for the flow problem inside the long and shallow microchannel. For the structural problem, we employ two plate theories, namely Kirchhoff-Love theory of thin plates and Reissner-Mindlin first-order shear deformation theory. The hydrodynamic pressure couples the flow and deformation problem by acting as a distributed load onto the soft top wall. Within our perturbative (lubrication theory) approach, we determine the relationship between flow rate and the pressure gradient, which is a nonlinear first-order ordinary differential equation for the pressure. From the solution of this differential equation, all other quantities of interest in non-Newtonian microchannel FSIs follow. Through illustrative examples, we show the effect of FSI coupling strength and the plate thickness on the pressure drop across the microchannel. Through direct numerical simulation of non-Newtonian microchannel FSIs using commercial computational engineering tools, we benchmark the prediction from our mathematical prediction for the flow rate-pressure drop relation and the structural deformation profile of the top wall. In doing so, we also establish the limits of applicability of our perturbative theory.

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Section: Resultsmentioning

confidence: 99%

Non-Newtonian fluid–structure interactions: Static response of a microchannel due to internal flow of a power-law fluid

Anand

David

Christov

2019

Journal of Non-Newtonian Fluid Mechanics

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“…For example, the material composing the tube may not be only elastic but also porous (i.e., poroelastic ) [95]. It may also be worthwhile to consider microflows of gases in elastic tubes, which necessitates accounting for compressibility of the fluid [96, 97] and, possibly, wall slip [98, 99]. Another potential avenue for future research stems from the fact that many soft biological tissues are hyperelastic .…”

Section: Discussionmentioning

confidence: 99%

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Anand

Christov

2020

Z Angew Math Mech

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A flow vessel with an elastic wall can deform significantly due to viscous fluid flow within it, even at vanishing Reynolds number (no fluid inertia). Deformation leads to an enhancement of throughput due to the change in cross‐sectional area. The latter gives rise to a non‐constant pressure gradient in the flow‐wise direction and, hence, to a nonlinear flow rate–pressure drop relation (unlike the Hagen–Poiseuille law for a rigid tube). Many biofluids are non‐Newtonian, and are well approximated by generalized Newtonian (say, power‐law) rheological models. Consequently, we analyze the problem of steady low Reynolds number flow of a generalized Newtonian fluid through a slender elastic tube by coupling fluid lubrication theory to a structural problem posed in terms of Donnell shell theory. A perturbative approach (in the slenderness parameter) yields analytical solutions for both the flow and the deformation. Using matched asymptotics, we obtain a uniformly valid solution for the tube's radial displacement, which features both a boundary layer and a corner layer caused by localized bending near the clamped ends. In doing so, we obtain a “generalized Hagen–Poiseuille law” for soft microtubes. We benchmark the mathematical predictions against three‐dimensional two‐way coupled direct numerical simulations (DNS) of flow and deformation performed using the commercial computational engineering platform by ANSYS. The simulations show good agreement and establish the range of validity of the theory. Finally, we discuss the implications of the theory on the problem of the flow‐induced deformation of a blood vessel, which is featured in some textbooks.

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“…Most soft robots are actuated pneumatically [40] Thus, understanding compressible flows interacting with compliant viscoelastic structures may provide insight into the design of pneumatically actuated biomimetic soft robots. So far, however, the FSI literature on viscoelastic (see, e.g., [36]) or elastic (see, e.g., [21,24,41,42]) tubes with transient (inertial) response has only considered incompressible flow, while the FSI literature on compressible (and variable density) flows has only dealt with linearly elastic structures [e.g. 24,43,44], except for some systems-level modeling of wave speeds for water hammer phenomena in viscoelastic tubes [45,46] at large Re.…”

Section: Introductionmentioning

confidence: 99%

“…So far, however, the FSI literature on viscoelastic (see, e.g., [36]) or elastic (see, e.g., [21,24,41,42]) tubes with transient (inertial) response has only considered incompressible flow, while the FSI literature on compressible (and variable density) flows has only dealt with linearly elastic structures [e.g. 24,43,44], except for some systems-level modeling of wave speeds for water hammer phenomena in viscoelastic tubes [45,46] at large Re. The present work fills a knowledge gap on low Re compressible flow in viscoelastic tubes with transient response.…”

Section: Introductionmentioning

confidence: 99%

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Transient compressible flow in a compliant viscoelastic tube

Anand,

Christov

2020

Preprint

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Motivated by problems arising in the pneumatic actuation of controllers (for MEMS, labs-on-a-chip or biomimetic soft robots) and the study of microrheology of both gases and soft solids, we analyze the transient fluid-structure interactions (FSIs) in a viscoelastic tube conveying compressible flow at low Reynolds number. We express the density of the fluid as a linear function of the pressure, and we use the lubrication approximation to further simplify the fluid dynamics problem. On the other hand, the structural mechanics is governed by a modified Donnell shell theory accounting for Kelvin-Voigttype linear viscoelastic mechanical response. The fluid and structural mechanics problems are coupled through the tube's radial deformation and the hydrodynamic pressure. For small compressibility numbers and weak coupling, the equations are solved analytically via a perturbation expansion. Three illustrative problems are analyzed. First, we obtain exact implicit solutions for the pressure under steady conditions, taking into account flow rarefaction. Second , we solve the transient problem of impulsive pressurization of the tube's inlet. Third, we analyze the transient response to an oscillatory inlet pressure. We show that an oscillatory inlet pressure leads to acoustic streaming in the tube, attributed to the nonlinear pressure gradient induced by the interplay of FSI and compressibility. Furthermore, we demonstrate an enhancement in the volumetric flow rate due to the coupling. The hydrodynamics pressure oscillations are shown to exhibit a low-pass frequency response (when averaging over the period of oscillations), while the frequency response of the tube itself is similar to that of a band-pass filter.

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Transient gas flow in elastic microchannels

Cited by 15 publications

References 45 publications

Non-Newtonian fluid–structure interactions: Static response of a microchannel due to internal flow of a power-law fluid

Non-Newtonian fluid–structure interactions: Static response of a microchannel due to internal flow of a power-law fluid

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Transient compressible flow in a compliant viscoelastic tube

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