Static and dynamic fluid-driven fracturing of adhered elastica

Ball, Thomasina V.; Neufeld, Jerome A.

doi:10.1103/physrevfluids.3.074101

Cited by 27 publications

(54 citation statements)

References 28 publications

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“…Similar multiphysics problems can also be motivated by biomedical and physiological applications, such as the reopening of strongly collapsed airways [18]. These problems are unsteady, thus one must obtain dynamic equations for the motion of the fluid front during expansion (or collapse) [50,51,52,53]. Therefore, the present analysis could be extended/become the foundation of further research on these problem as well.…”

Section: Resultsmentioning

confidence: 95%

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: Resultsmentioning

confidence: 95%

Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

Anand

Muchandimath

Christov

2020

Journal of Applied Mechanics

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“…The corresponding deformation h(r, t ) is assumed axisymmetric (with r the radial coordinate and t the time) and is measured using a laser line on the top surface of the membrane. As the outer boundary of the membrane is not maintained mechanically, we assume that stretching is negligible compared to bending as long as h d. Analysis of our results shows that our experiments are reasonably described with two models: the prewetting film (PF) model [8] and the vapor tip (VT) model [20]. As the behaviors predicted with these two approaches are quantitatively very close, we are not able to discriminate between them.…”

Section: Introductionmentioning

confidence: 81%

“…Several hypotheses are needed to derive the shape and the dynamics of the deformation of the membrane by an injected fluid. We use the notations of Lister et al [8] and of Ball et al [20].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…In the absence of a real initial prewetting film, the cutoff length could be justified by a better microscopic model of the contact line, and the main scalings could remain the same. Recently, a new set of experiments without any initial prewetting film have been performed and modeled by considering an interstice filled with vapor between the membrane and the fluid at the advancing front [20]. The gas pressure regularizes the divergence of the viscous stresses at the moving contact line [16,20,21].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a new set of experiments without any initial prewetting film have been performed and modeled by considering an interstice filled with vapor between the membrane and the fluid at the advancing front [20]. The gas pressure regularizes the divergence of the viscous stresses at the moving contact line [16,20,21]. This model predicts a lag distance between the front of elastic deformation and the contact line of the advancing fluid.…”

Section: Introductionmentioning

confidence: 99%

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Uplift of an elastic membrane by a viscous flow

et al. 2019

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The uplift of an initially flat elastic membrane by an upward viscous flow is investigated experimentally. The deformed shape of the membrane results from a balance between the flow pressure, the elastic response of the membrane, and the fluid weight. This last effect becomes non-negligible for a large enough deformed area. The usual theoretical approach supposes the presence of a prewetting film regularizing the viscous stresses according to Lister et al. [Phys. Rev. Lett. 111, 154501 (2013)]. Nevertheless, in our experiments without prewetting films, the measurements are correctly described with this theory in the elastic regime. Microscale roughness of membranes could introduce an equivalent characteristic scale in the problem. An alternative explanation could be provided by the appearance of a fluid lag filled with gas, for which a new theoretical framework has been recently proposed by Ball and Neufeld [Phys. Rev. Fluids 3, 074101 (2018)]. We compare the two approaches and find that both describe reasonably our experiments. However, consistency tests of both models show that the prewetting film model is more appropriate to describe our experimental data.

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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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Static and dynamic fluid-driven fracturing of adhered elastica

Cited by 27 publications

References 28 publications

Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

Uplift of an elastic membrane by a viscous flow

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

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