Fluid-filled Elastic Tube Research Articles

Reflection and transmission due to inhomogeneity from an incident wave in a fluid-filled elastic tube

The present paper studies the reflection and transmission of nonlinear waves in an inhomogeneous fluid-filled elastic tube due to an incident wave using the reductive perturbation method. It is found that the numbers and amplitudes of both reflected and transmitted envelope solitary waves due to inhomogeneity depend on the inhomogeneity of the radius, Young’s modulus, thickness, and density of the vessel wall, among other factors. The dependence of the reflection and transmission due to the incident wave on these system parameters is given in the present paper. The results show that the number of the reflected envelope solitary waves is only one or zero, while the number of the transmitted envelope solitary waves may be more than one. The reflection and transmission of an incident nonlinear wave due to inhomogeneity in a fluid-filled elastic tube have potential applications for blood waves in an arteries for both humans and animals.

Analysis of modulational instability of waves in the fluid-filled elastic tube

In this paper, we investigate the modulational instability of waves within a fluid-filled elastic tube considering the fluid viscosity. Through the reductive perturbation method, we derived a modified Nonlinear Schrödinger Equation (NLSE) with damping term for the system. Based on the modified NLSE, we found that modulational instability exists in this system though the fluid viscosity is considered. Both the instability and the stability region are given. Furthermore, the growth rate of the instability is obtained. The dependence of the growth rate on the system parameters such as perturbation wave length, the background wave length, the viscosity of the fluid and the elasticity of the tube is given in the present paper. It indicates that the fluid viscosity refrain the modulational instability. The results may be used to predict the production of the rogue wave in this system, as well as to the other similar system.

A Spectral Method Algorithm for Modeling the Dispersion of Non-Axisymmetric Modes in Fluid-Filled Elastic Tubes

In order to design a low-noise water-filled pipeline system, it is necessary to obtain knowledge of the dispersion characteristics of axial propagation modes in different water-filled elastic tubes. In this work, an algorithm is developed based on the spectral method, which has previously been used to solve the dispersion of axisymmetric modes in cylindrical structures but has not yet been applied to non-axisymmetric modes. The algorithm can obtain the dispersion characteristics, modal displacement, and stress distribution of axial propagation modes in a fluid-filled elastic multi-layer tube. The algorithm behaves well both at low and ultrasonic frequencies, and it is suitable for any tube dimensions, wall thickness and layers. The results of a water-filled PMMA tube obtained using the spectral method algorithm were verified using a COMSOL simulation, while the dispersion curves of the same tube from the literature were found to be missing some low-order modes. In addition, the dispersion curves of a water-filled three-layer tube are given. The spectral method algorithm has the advantages of fast calculation speed, less computational resources consumed, accurate results, and no modal omission.

On the longitudinal wave pumping in fluid-filled compliant tubes

This study investigates the physics of the longitudinal stretching-based wave pumping mechanism, a novel extension of the traditional impedance pump. In its simplest form, an impedance pump consists of a fluid-filled elastic tube connected to rigid tubes with a wave generator. These valveless pumps operate based on the principles of wave propagation in a fluid-filled compliant tube. Cardiovascular magnetic resonance imaging of the human circulatory system has shown substantial stretching of the aorta (the largest compliant artery of the body carrying blood) during the heart contraction and recoil of the aorta during the relaxation. Inspired by this dynamic mechanism, a comprehensive analysis of a longitudinal impedance pump is conducted in this study where waves are generated by stretching of the elastic wall and its recoil. We developed a fully coupled fluid–structure interaction computational model consisting of a straight fluid-filled elastic tube with longitudinal stretch at one end and a fixed reflection site at the other end. The pump's behavior is quantified as a function of stretching frequency and tube wall characteristics. Our results indicate that stretch-related wave propagation and reflection can induce frequency-dependent pumping. Findings suggest a non-linear pattern for the mean flow–frequency relationship. Based on the analysis of the propagated waveforms, the underlying physical mechanism in the longitudinal impedance pump is discussed. It is shown that both the direction and magnitude of the net flow strongly depend on the wave characteristics. These findings provide a fundamental understanding of stretch-related wave pumping and can inform the future design of such pumps.

Collisional Solitons Described by Two-Sided Beta Time Fractional Korteweg-de Vries Equations in Fluid-Filled Elastic Tubes

This article deals with the basic features of collisional radial displacements in a prestressed thin elastic tube filled having inviscid fluid with the presence of nonlocal operator. By implementing the extended Poincare–Lighthill–Kuo method and a variational approach, the new two-sided beta time fractional Korteweg-de-Vries (BTF-KdV) equations are derived based on the concept of beta fractional derivative (BFD). Additionally, the BTF-KdV equations are suggested to observe the effect of related parameters on the local and nonlocal coherent head-on collision phenomena for the considered system. It is observed that the proposed equations along with their new solutions not only applicable with the presence of locality but also nonlocality to study the resonance wave phenomena in fluid-filled elastic tube. The outcomes reveal that the BFD and other physical parameters related to tube and fluid have a significant impact on the propagation of pressure wave structures.

Verification of fluid-structure interaction modelling for wave propagation in fluid-filled elastic tubes

This paper presents a verification study of wave propagation in fluid-filled elastic tubes using a coupled numerical simulation method by comparing the simulation results with analytical solutions. A three-dimensional fluid-structure interaction numerical model is built using Ansys software. Wave propagation is investigated by applying a pressure pulse at the inlet of a fluid-filled elastic tube. The speed of the pressure wave and the radial displacement of the tube are simulated and compared with theoretical values. Simulation results yield a high level of accuracy. Different structural elements are used to represent the tube, and their impact on the results is discussed. The effects of tube material, tube constraints and fluid properties are also investigated in this study.

Stability of the aneurysm-type solution in a membrane tube with localized wall thinning filled with a fluid with a non-constant velocity profile

We perform the stability analysis of bulging localized structures on the wall of a fluid-filled axisymmetric membrane elastic tube. The wall of the tube is assumed to be subjected to localized thinning. The problem has no translational invariance anymore, hence the stability of a bulging wave centered in the point of the localization of imperfection is usual, and not orbital stability up to a shift as in the case of translationally invariant governing equations. Motionless wave solutions of the governing equations having the form of a localized bulging are called throughout the paper aneurysm solutions. We assume that the fluid is subjected to the power law for viscous friction of a non-Newtonian fluid, and also that the viscosity of the fluid does not play a significant role and it can be neglected. The velocity profile remains not constant along the cross section of the tube (even in the absence of the viscosity) because no-slip boundary conditions are performed on the tube walls. Stability is established by demonstrating the non-existence of the unstable eigenvalues with a positive real part of the linearized problem. This is achieved by constructing the Evans function depending only on the spectral parameter, analytic in the right half of the complex plane Ω+ and which zeroes in Ω+ coincide with the unstable eigenvalues of the problem. The non-existence of zeroes of the Evans function is performed using the argument principle from the analysis of complex variable. Finally, we discuss the possibility of applying of the results of the present analysis to the aneurysm formation in damaged human vessels under the action of the internal pressure.

Nonlocal symmetries and new interaction waves of the variable-coefficient modified Korteweg–de Vries equation in fluid-filled elastic tubes

Nonlocal symmetries and new interaction waves of the variable-coefficient modified Korteweg–de Vries equation in fluid-filled elastic tubes

Wave propagation through a viscous fluid-filled elastic tube under initial pressure: theoretical and biophysical model.

The velocity of propagation of pulse waves through the arteries is one of the indicators of the health of the cardiovascular system. By measuring the pulse wave velocity, cardiologists estimate the elasticity of the blood vessel walls and the changes that occur with aging. When the Moens-Korteweg equation is used in analysis, it leads to an erroneous assessment. This paper presents the solution of Navier-Stokes equations for propagation of pulse waves through an elastic tube filled with viscous fluid under initial pressure. The equation for pulse wave velocity depending on viscosity, density and initial fluid pressure, density and elasticity of the wall and geometry of the tube is derived. The results of the equation were compared with experimental results measured using a biophysical model of the cardiovascular system.

An efficient technique of [formula omitted]–expansion method for modified KdV and Burgers equations with variable coefficients

The extended generalized G′G–expansion is well defined and an efficient technique, which is used to obtain the exact traveling wave solutions to the governing nonlinear equations with constant coefficients as well as variable coefficients. In this paper, the modified Korteweg–de Vries (mKdV) equation and Burgers equation with variable coefficients are investigated through the extended generalized G′G–expansion method, which are exceptional cases of the nonlinear evolution equations widely used in a two-layer fluid system, in fluid-filled elastic tubes, in an atmospheric and oceanic dynamical system, traffic flow, turbulence in fluid dynamics, dusty plasma, ion-acoustic waves in a plasma system. New families of exact closed-form solutions are obtained in hyperbolic, trigonometric, and rational function solutions with the available free constants. With the help of computerized symbolic computation work, the newly formed closed-form solutions are validated by back substituting them into the equations using the computational mathematical software. Furthermore, the graphical representations of all these obtained solutions are discussed and demonstrated by giving the suitable best values of arbitrary functions and constants via three-dimensional surface and density plots. The dynamics of the solution profiles demonstrate the annihilation of 3D kink-type soliton waves, shock waves, double solitons, and multi-soliton wave structures.

The propagation of several well-known nonlinear waves in fluid-filled elastic tube

By using the reductive perturbation method, the nonlinear Schrödinger equation in fluid-filled elastic tube is obtained. We study several different kinds of the nonlinear wave solutions for the nonlinear Schrödinger equation. It is noted that the kinds of the nonlinear waves are determined by a parameter of ab (a is the amplitude of the background plane wave, while b is a controllable parameter which depend on the initial condition, boundary condition and other external perturbations). As the decreases of parameter ab, the number of the waves frequency increases, while their amplitude decreases. It is also found that all the waves amplitude increases as the wave number k and the radius of elastic tube increases, however, they are independent of the fluid density, the thickness of elastic tube and the Young’s modulus of the elastic tube. The amplitudes are different among different kinds of waves. However, the wave velocities of different waves are the same under the same parameters. They decrease as the wave number k, fluid density and the radius of elastic tube increase, while they increase as the thickness of elastic tube and the Young’s modulus of elastic tube increase.

Pumping Patterns and Work Done During Peristalsis in Finite-Length Elastic Tubes.

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 three-dimensional (3D) immersed boundary (IB) simulations of peristaltic pumping in tube walls made of hyperelastic material. The major dynamics observed in the 3D simulations were also displayed by our one-dimensional (1D) model under laminar flow conditions. Using the 1D model, several pumping regimes were investigated and presented in the form of a regime map that summarizes the system's response for a range of physiological conditions. Finally, the amount of work done during a peristaltic event in this configuration was defined and quantified. The variation of elastic energy and work done during pumping was found to have a unique signature for each regime. An extension of the 1D model is applied to enhance patient data collected by the device and find the work done for a typical esophageal peristaltic wave. This detailed characterization of the system's behavior aids in better interpreting the clinical data obtained from dilation catheters. Additionally, the pumping capacity of the esophagus can be quantified for comparative studies between disease groups.

The domain of existence of solitary waves in fluid-filled thin elastic tubes

Under given prestress conditions, solitary waves in fluid-filled elastic tubes are confined to a rather narrow set of combinations of the background fluid velocity and the wave speed. This set, which we call the domain of existence, is bounded by several curves that represent various physical and mathematical restrictions. Remarkably, these restrictions can be cast as purely algebraic conditions to be imposed upon the governing system of differential equations. Paramount among the physical restrictions are the avoidance of wrinkles and the self-impenetrability of the wave profile. In particular, the existence of a critical wave speed of impending wrinkling, independent of the background fluid velocity, is established rigorously.

Rouge waves in fluid-filled elastic tube

By the reductive perturbation method, we investigate the Rogue waves in a fluid-filled elastic tube. Based on a nonlinear Schrodinger equation obtained from a fluid-filled elastic tube, the rouge wave solution in the fluid-filled elastic tube is discussed. The characteristics of a single rouge waveare studied for this system. Then, the effects of the system parameters, such as the wave number k, the parameters <inline-formula><tex-math id="M">\begin{document}$\epsilon$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191308_M.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191308_M.png"/></alternatives></inline-formula>, the density of the fluid, the thickness of the elastic tube, the Yang's modulus of the elastic tube, and the radius of the elastic tube on the rouge wave are also investigated. Finally, the model is applied to the blood vessels of both animal and the human to ascertain the effects of the rouge wave in different arteries and vessels. The results of the present study may have potential applications in medical science.

Biophysical modeling of wave propagation phenomena: experimental determination of pulse wave velocity in viscous fluid-filled elastic tubes in a gravitation field.

Biophysical understanding of arterial hemodynamics plays an important role in proper medical diagnosis and investigation of cardiovascular disease pathogens. One of the major cardiovascular parameters is pulse wave velocity (PWV), which depends on the mechanical properties of the arterial wall. The PWV contains information on the condition of the cardiovascular system as well as its physiological age. In humans and most animals, blood flow through the blood vessels is affected by several internal and external forces. The most influencing external force on blood flow is gravity. In the upright position of the body, blood moves from heart to head, opposite to gravity, and from the heart to the legs, in direction of the gravitational force. To investigate how gravity affects PWV, we have developed a biophysical model of cardiovascular system that simulates blood flow in the upright position of the body. The paper presents the results of measurement of PWV in an elastic tube filled with fluids of different viscosities in the gravitational field.

The Effect of a Residual Stress on Wave Propagation in a Fluid-Filled Thick Elastic Tube

The propagation of harmonic waves in an elastic tubes filled fluid is presented in this study. The tube material is considered to be incompressible, homogeneous, isotropic, initially axially stretched, inflated and thick elastic like human arteries. The viscous fluid is assumed to be incompressible and Newtonian. The differential equations of both materials are obtained in cylindrical coordinates. The analytical solutions of the equations of motion for the fluid, numerical solutions of the equations of motion for the tube have been found. The residual circumferential strain in the unloaded state of artery causes opening angle. The dispersion relation is presented as a function of the axial stretch, opening angle, internal pressure and material parameters. The effects of these parameters are shown and discussed on graphics.

Nonlinear time fractional Korteweg-de Vries equations for the interaction of wave phenomena in fluid-filled elastic tubes

This work investigates the wave-wave interactions by considering two-sided time fractional Korteweg-de Vries equations (TFKdVEs). The generalized $\exp(-\Phi(\xi))$ -expansion method (GEEM) along with Khalil's fractional derivatives is employed to divulge several types of scattered wave solutions of TFKdVEs. It is found that the fractional parameters significantly modified the interaction of nonlinear wave dynamics. The results obtained may be useful for clarifications of the interaction between two waves not only in non-conservative fluid-filled elastic tubes but also in shallow water and plasma physics.

Dynamical stability of running solitary waves in fluid-filled elastic membrane tubes

We examine the problem of stability of solitary waves, propagating in a fluid-filled membrane tube. We consider waves with speeds starting from those given by the linear dispersion relation (it is known that there may exist four families of solitary waves having such speeds), i. e. the waves of a finite amplitude bifurcating from the quiescent state of the system. It is shown that if a solitary wave speed is bounded away from zero the solitary wave itself is orbitally stable, when the fluid initially stationary (the mean flow is absent).

Analytical treatment of the couple stress fluid-filled thin elastic tubes

In this paper, we present the symmetries and self-adjointness of the problem about the couple stress fluid-filled thin elastic tubes. Some soliton solutions of the specified problem are constructed with the aid of Lie group symmetry method.

On the propagation of transient waves in a viscoelastic Bessel medium

In this paper we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave-front. To do so, we take profit of a revisited version of the so called Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the long time behavior of the response function of the material. This result is obtained by means of the Tauberian theorems for the Laplace transform. Finally, we relate the obtained results to a peculiar model for fluid-filled elastic tubes.