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The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling...
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The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.
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The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft,...
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The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung's (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain-energy density function. The fluid is described through a Navier-Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response.
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We are interested in the three-dimensional coupling between a compressible viscous fluid and an elastic structure immersed inside the fluid. They are contained in a fixed bounded set. The fluid motion is modeled by the compressibl...
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We are interested in the three-dimensional coupling between a compressible viscous fluid and an elastic structure immersed inside the fluid. They are contained in a fixed bounded set. The fluid motion is modeled by the compressible Navier-Stokes equations and the structure motion is described by the linearized elasticity equation. We establish the local in time existence and the uniqueness of regular solutions for this model. We emphasize that the equations do not contain extra regularizing term. The result is proved by first introducing a linearized problem and by proving that it admits a unique regular solution. The regularity is obtained thanks to successive estimates on the unknowns and their derivatives in time and thanks to elliptic estimates. At last, a fixed-point theorem allows to prove the existence and uniqueness of regular solution of the nonlinear problem.
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Flexible filaments moving in viscous fluids are ubiquitous in the natural microscopic world.For example,the swimming of bacteria and spermatozoa as well as important physiological functions at organ level,such as the cilia-induced...
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Flexible filaments moving in viscous fluids are ubiquitous in the natural microscopic world.For example,the swimming of bacteria and spermatozoa as well as important physiological functions at organ level,such as the cilia-induced motion of mucus in the lungs,or individual cell level,such as actin filaments or microtubules,all employ flexible filaments moving in viscous fluids.As a result of fluid-structure interactions,a variety of nonlinear phenomena may arise in the dynamics of such moving flexible filaments.In this paper we derive the mathematical tools required to study filament-driven propulsion in the asymptotic limit of stiff filaments.Motion in the rigid limit leads to hydrodynamic loads which deform the filament and impact the filament propulsion.We first derive the general mathematical formulation and then apply it to the case of a helical filament,a situation relevant for the swimming of flagellated bacteria and for the transport of artificial,magnetically actuated motors.We find that,as a result of flexibility,the helical filament is either stretched or compressed (conforming previous studies) and additionally its axis also bends,a result which we interpret physically.We then explore and interpret the dependence of the perturbed propulsion speed due to the deformation on the relevant dimensionless dynamic and geometric parameters.
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Quantifying the effects of pore-filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating ...
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Quantifying the effects of pore-filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28 degrees C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid-octadecane-saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so-called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.
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The role of fluid elasticity in the formation of fibers from polymer solution by electrospinning is investigated.Model solutions with different degrees of elasticity were prepared by blending small amounts of high molecular weight...
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The role of fluid elasticity in the formation of fibers from polymer solution by electrospinning is investigated.Model solutions with different degrees of elasticity were prepared by blending small amounts of high molecular weight polyethylene oxide (PEO) with concentrated aqueous solutions of low molecular weight polyethylene glycol (PEG).The elastic properties of these solutions,such as extensional viscosity and the longest relaxation time,were measured using the capillary breakup extensional rheometer (CaBER).The formation of beads-on-string and uniform fiber morphologies during electrospinning was observed for a series of solutions having the same polymer concentration,surface tension,zero shear viscosity,and conductivity but different degrees of elasticity.A high degree of elasticity is observed to arrest the breakup of the jet into droplets by the Rayleigh instability and in some cases to suppress the instability altogether.We examine the susceptibility of the jet to the Rayleigh instability in two ways.First,a Deborah number,defined as the ratio of the fluid relaxation time to the instability growth time,is shown to correlate with the arrest of droplet breakup,giving rise to electrospinning rather than electrospraying.Second,a critical value of elastic stress in the jet,expressed as a function of jet radius and capillary number,is shown to indicate complete suppression of the Rayleigh instability and the transition from 'beads-on-string' to uniform fiber morphology.
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In this study, the effects of polymer flexibility and entanglement on elastic instability were investigated by observing sodium hyaluronate (Hyaluronic Acid Sodium salt, Na-HA) solution in planar abrupt contraction-expansion micro...
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In this study, the effects of polymer flexibility and entanglement on elastic instability were investigated by observing sodium hyaluronate (Hyaluronic Acid Sodium salt, Na-HA) solution in planar abrupt contraction-expansion microchannels. The rigidity of Na-HA in a solution is affected by ion concentration in the solution. Therefore, we prepared Na-HA water solution and Na-HA PBS solution with concentrations from 0.15 wt% to 0.45 wt%. The rheological properties were measured and analyzed to detect the Na-HA overlap and entanglement concentrations. The flow regimes of the Na-HA solutions in several planar abrupt contraction-expansion channels were characterized in terms of rheological properties, polymer flexibility and polymer entanglement.
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An experimental study is performed to investigate the impact of fluid elasticity on miscible viscous fingering. Rectilinear flow experiments are performed by displacing aqueous Boger fluids (constant-viscosity elastic fluids) with...
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An experimental study is performed to investigate the impact of fluid elasticity on miscible viscous fingering. Rectilinear flow experiments are performed by displacing aqueous Boger fluids (constant-viscosity elastic fluids) with water. The observations are compared to those in Newtonian fluids (glycerol solutions) of the same viscosity. Elasticity is observed to reduce the width of fingers, leading to formation of thinner and longer fingers in fully developed flow. The shielding effect is reduced due to fluid elasticity resulting in growth of multiple fingers as compared to a single thick dominant finger observed for Newtonian fluids. The dominant wave number for the onset of instabilities is observed to be higher in more elastic fluids i.e. the interface breaks down into greater number of fingers in the more elastic fluid. Data is presented to show that fluid elasticity retards the growth of fingers. Elastic effects are observed to reduce the thin film of the displaced fluid on the walls of the Hele-Shaw cells.
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We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an...
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We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an implicit function argument. In so doing we have to revisit some classical work in the astrophysical literature concerning linear stability of perfect fluid stars. The results presented here extend previous work by the authors, which was restricted to the astrophysically insignificant situation of configurations near one of vanishing stress. In particular, 'mountains on neutron stars', which are made possible by the presence of an elastic crust in neutron stars, can be treated using the techniques developed here.
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In this work, we studied the derivation of the Korteweg-deVries equation in a prestressed elastic tube filled with an inviscid fluid. In the analysis, considering the physiological conditions of the arteries, the tube is assumed t...
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In this work, we studied the derivation of the Korteweg-deVries equation in a prestressed elastic tube filled with an inviscid fluid. In the analysis, considering the physiological conditions of the arteries, the tube is assumed to be subjected to a uniform inner pressure P_o and a constant axial stretch ratio λ_z. In the course of blood flow in arteries, it is assumed that a finite time dependent displacement field is superimposed on this static field but, due to axial tethering, the effect of axial displacement is neglected. The governing nonlinear equation for he radial motion of the tube under the effect of fluid pressure is obtained. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the longwave approximation is investigated. Treating the blood as an incompressible inviscid fluid, two cases are investigated separately. In the first case, a set of approximate fluid equations is used; namely, the field variables are assumed to be independent of the radial coordinate. Further, the momentum equation of the fluid in the radial direction is neglected. In the second case, the exact equations of an incompressible fluid are employed. It is shown that in both cases the governing equations reduce to the Korteweg-deVries equation but with different propagation speeds. Intensifying the effect of nonlinearity in the perturbation process, the modified forms of these evolution equations are also obtained. The result is numerically discussed for some elastic materials, existing in the current literature.
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