In this paper, we present an analytical calculation of the rotational mobility functions of a particle rotating on the centerline of an elastic cylindrical tube whose membrane exhibits resistance towards shearing and bending. We find that the correction to the particle rotational mobility about the cylinder axis depends solely on membrane shearing properties while both shearing and bending manifest themselves for the rotational mobility about an axis perpendicular to the cylinder axis. In the quasi-steady limit of vanishing frequency, the particle rotational mobility nearby a no-slip rigid cylinder is recovered only if the membrane possesses a non-vanishing resistance towards shearing. We further show that for the asymmetric rotation along the cylinder radial axis, a coupling between shearing and bending exists. Our analytical predictions are compared and validated with corresponding boundary integral simulations where a very good agreement is obtained.
We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting case…
Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow model with two pressure-area constitutive relations. These expressions for elastic tubes are the equivalent of Poiseuille and Poiseuille-type expressions for rigid tubes which were previously derived for the flow of Newtonian and non-Newtonian fluids under various flow conditions. Formulae and procedures for identifying the pressure field and tube geometric pro…
The elasto-inertial effects on particle focusing in a square-tube flow were investigated experimentally and numerically. Microscale experiments using spherical particles in dilute polymer solutions demonstrated that the particles are focused on the midline and/or the diagonal in a downstream cross-section, depending on the polymer concentration. Numerical computations based on the FENE-P model for the viscoelastic flow reproduced these focusing patterns. It was revealed that the transitions among the patterns are accounted for by the elastic forces due to the first normal stress difference and…
We examine transient axial creeping flow in the annular gap between a rigid cylinder and a concentric elastic tube. The gap is initially filled with a thin fluid layer. The study focuses on viscous-elastic time-scales for which the rate of solid deformation is of the same order-of-magnitude as the velocity of the fluid. We employ an elastic shell model and the lubrication approximation to obtain a forced nonlinear diffusion equation governing the viscous-elastic interaction. In the case of an advancing liquid front into a configuration with a negligible film layer (compared with the radial def…
We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius of the tube may change along its length. The discussed problem is connected to the blood flow in large human arteries and especially to nonlinear wave propagation due to the pulsations of the heart. The long-wave approximation for modeling of waves in blood is applied. The obtained model Korteweg-deVries equation possessing a variable coefficient is reduced to a nonlinear dynamical system of 3 first order differential equations. The low probability of arising of a solitary wave is shown. Periodic w…
Elastic channels are an important component of many soft matter systems, in which hydrodynamic interactions with confining membranes determine the behavior of particles in flow. In this work, we derive analytical expressions for the Green's functions associated to a point-force (Stokeslet) directed parallel or perpendicular to the axis of an elastic cylindrical channel exhibiting resistance against shear and bending. We then compute the leading order self- and pair mobility functions of particles on the cylinder axis, finding that the mobilities are primarily determined by membrane shear and t…
Balloon dilation catheters are often used to quantify the physiological state of peristaltic activity in tubular organs and comment on their ability to propel fluid which is important for healthy human function. To fully understand this system's behavior, we analyzed the effect of a solitary peristaltic wave on a fluid-filled elastic tube with closed ends. A reduced order model that predicts the resulting tube wall deformations, flow velocities and pressure variations is presented. This simplified model is compared with detailed fluid-structure 3D immersed boundary simulations of peristaltic p…
The present work aims to study the phenomenon of shock wave focusing and the effect of viscosity in it. The focusing is achieved with a shock tube and a converging section attached to it. The converging section transforms the planar shock into a spherical shock and focuses it into a confined area. A shock of an initial strength Ms=2.94 has been chosen for the present studies. A detailed numerical study of the focusing region shows the formation of a mushroom-shaped structure behind the reflected shock and vortex formation. This was visualised through numerical shadowgraph images and by tracing…
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 proble…
On the basis of the linear hydrodynamic equations, we present an analytical theory for the low-Reynolds-number motion of a solid particle moving inside a larger spherical elastic cavity which can be seen as a model system for a fluid vesicle. In the particular situation where the particle is concentric with the cavity, we use the stream function technique to find exact analytical solutions of the fluid motion equations on both sides of the elastic cavity. In this particular situation, we find that the solution of the hydrodynamic equations is solely determined by membrane shear properties and …
The importance of fluid-elastic forces in tube bundle vibrations can hardly be over-emphasized, in view of their damaging potential. In the last decades, advanced models for representing fluid-elastic coupling have therefore been developed by the community of the domain. Those models are nowadays embedded in the methodologies that are used on a regular basis by both steam generators providers and operators, in order to prevent the risk of a tube failure with adequate safety margins. From an R&D point of view however, the need still remains for more advanced models of fluid-elastic coupling, in…
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 mod…
Simulation results for head-on collisions of equal-sized spherical polymer nanodroplets using molecular dynamics are presented. Elastic behavior of an initial compressed phase for the colliding droplets is analyzed. Deformations and contact radii of the nanodroplets are compared with the Hertzian model of elastic solid balls. It is found that at least the initial phase of collision can be explained by this continuum model, except at the very moment of the beginning of collision.
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 incorpora…
We perform a stability analysis for a fluid-structure interaction problem in which a spherical elastic shell or membrane is immersed in a 3D viscous, incompressible fluid. The shell is an idealised structure having zero thickness, and has the same fluid lying both inside and outside. The problem is formulated mathematically using the immersed boundary framework in which Dirac delta functions are employed to capture the two-way interaction between fluid and immersed structure. The elastic structure is driven parametrically via a time-periodic modulation of the elastic membrane stiffness. We per…
We study single-phase and particulate turbulent channel flows, bounded by two incompressible hyper-elastic walls. Different wall elasticities are considered with and without a 10% volume fraction of finite-size rigid spherical particles, while elastic walls are modelled as a neo-Hookean material. We report a significant drag increase and an enhancement of the turbulence activity with growing wall elasticity for both single-phase and particulate cases in comparison with the single-phase flow over rigid walls. A drag reduction and a turbulence attenuation is obtained for the particulate cases wi…
Motivated by the reopening mechanics of strongly collapsed airways, we study the steady propagation of an air finger through a collapsed oil-filled channel with a single compliant wall. In a previous study using fully-compliant elastic tubes, a `pointed' air finger was found to propagate at high speed and low pressure, which may enable rapid reopening of highly collapsed airways with minimal tissue damage (Heap & Juel 2008). In this paper, we identify the selection mechanism of that pointed finger, which remained unexplained, by conducting an experimental study in a rigid rectangular Hele-Shaw…
The propagation of acoustic waves in a poro-elastic medium of infinite extension containing spherical cavities randomly distributed is investigated. The scattering coefficients are computed in the low frequency limit using the sealed pore boundary conditions. Also in this limit, using explicit Waterman-Truell (WT) formulas and a generalization of the Linton-Martin (LM) formula to poro-elastic medium, expressions of the wave numbers of the coherent waves are proposed. Expressions of the effective mass densities and moduli are derived from the WT formulas. The effective properties of the coheren…
The interaction of a shock wave with a spherical density inhomogeneity leads to the development of a vortex ring through the impulsive deposition of baroclinic vorticity. The present fluid dynamics videos display this phenomenon and were experimentally investigated at the Wisconsin Shock Tube Laboratory's (WiSTL) 9.2 m, downward firing shock tube. The tube has a square internal cross-section (0.25 m x 0.25 m) with multiple fused silica windows for optical access. The spherical soap bubble is generated by means of a pneumatically retracted injector and released into free-fall 200 ms prior to in…
We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements …
