Static response of deformable microchannels: a comparative modelling study

Shidhore, Tanmay C.; Christov, Ivan

doi:10.1088/1361-648x/aaa226

Cited by 27 publications

(90 citation statements)

References 51 publications

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“…(32). Based on applying the hydrodynamic bulge test idea to simulation data from the present study, as well as previous simulations [35] and experiments [23] without pre-stress, is λ = 5, is λ = 2, and △ is λ = 1. All other quantities are as given in Table 1.…”

Section: Characterization Of Materials Properties and Range Of Validitmentioning

confidence: 61%

“…The simulations are twoway coupled to ensure full fidelity. Many of the details of such simulations have been presented in previous publications [22,28,35,42]. Nevertheless, to ensure that this work is selfcontained, a short summary is provided next.…”

Section: Resultsmentioning

confidence: 99%

“…Here, G := E/[2(1 + ν)] is the shear modulus, and κ is Timoshenko's "shear correction factor" [31], which is commonly introduced to account for nonuniform distribution of the transverse shear strain across the thickness [32,33,34]. Following Zhang [34], and as in previous works [28,35], we take κ = 1 to ensure consistency of three-dimensional (3D) linear elasticity and RM plate theory in the limit of t/w → 0. Equations (1a) and (1b) completely describe the in-plane displacement field, which is independent of the transverse deflection and/or rotations.…”

Section: Differential Equations For the Displacementmentioning

confidence: 99%

“…Similarly, Fluent solves the steady 3D incompressible Navier-Stokes equation on a deforming domain without any a priori approximations. Previously, we carried out mesh refinement studies [35], and we explored choices of algorithms for mesh smoothing [28], in similar FSI problems. We carry over the lessons learned to the present study to obtain the right blend of numerical accuracy and computational effort.…”

Section: Computational Approachmentioning

confidence: 99%

“…Zhang [34] proved mathematically that the equations of linear elasticity and those of the RM plate theory, both in the limit of t/w → 0, agree only when κ = 1. Therefore, as in our previous works [28,35], we take κ = 1 when generating our results below. However, we keep the variable κ throughout our equations for consistency with the applied mechanics literature.…”

Section: A3 Constitutive Equationsmentioning

confidence: 99%

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Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

Anand

Muchandimath

Christov

2020

Journal of Applied Mechanics

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Characterizing the elastic properties of soft materials through bulge testing relies on accurate measurement of deformation, which is experimentally challenging. To avoid measuring deformation, we propose a hydrodynamic bulge test for characterizing the material properties of thick, pre-stressed elastic sheets via their fluid-structure interaction with a steady viscous fluid flow. Specifically, the hydrodynamic bulge test relies on a pressure drop measurement across a rectangular microchannel with a deformable top wall. We develop a mathematical model using first-order shear-deformation theory of plates with stretching, and the lubrication approximation for Newtonian fluid flow. Specifically, a relationship is derived between the imposed flow rate and the total pressure drop. Then, this relationship is inverted numerically to yield estimates of the Young's modulus (given the Poisson ratio), if the pressure drop is measured (given the steady flow rate). Direct numerical simulations of two-way-coupled fluid-structure interaction are carried out in ANSYS to determine the cross-sectional membrane deformation and the hydrodynamic pressure distribution. Taking the simulations as "ground truth," a hydrodynamic bulge test is performed using the simulation data to ascertain the accuracy and validity of the proposed methodology for estimating material properties. An error propagation analysis is performed via Monte Carlo simulation to characterize the susceptibility of the hydrodynamic bulge test estimates to noise. We find that, while a hydrodynamic bulge test is less accurate in characterizing material properties, it is less susceptible to noise, than a hydrostatic bulge test, in the input (measured) variable.

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Section: Characterization Of Materials Properties and Range Of Validitmentioning

confidence: 61%

Section: Resultsmentioning

confidence: 99%

Section: Differential Equations For the Displacementmentioning

confidence: 99%

Section: Computational Approachmentioning

confidence: 99%

Section: A3 Constitutive Equationsmentioning

confidence: 99%

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Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

Anand

Muchandimath

Christov

2020

Journal of Applied Mechanics

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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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Geometric Theory of Flexible and Expandable Tubes Conveying Fluid: Equations, Solutions and Shock Waves

Gay–Balmaz¹,

Putkaradze²

2018

J Nonlinear Sci

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We present a theory for the three-dimensional evolution of tubes with expandable walls conveying fluid. Our theory can accommodate arbitrary deformations of the tube, arbitrary elasticity of the walls, and both compressible and incompressible flows inside the tube. We also present the theory of propagation of shock waves in such tubes and derive the conservation laws and Rankine-Hugoniot conditions in arbitrary spatial configuration of the tubes, and compute several examples of particular solutions. The theory is derived from a variational treatment of Cosserat rod theory extended to incorporate expandable walls and moving flow inside the tube. The results presented here are useful for biological flows and industrial applications involving high speed motion of gas in flexible tubes.

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Static response of deformable microchannels: a comparative modelling study

Cited by 27 publications

References 51 publications

Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

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

Geometric Theory of Flexible and Expandable Tubes Conveying Fluid: Equations, Solutions and Shock Waves

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