Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

A Compliant Mechanism Kit with Flexible Beams and Connectors

We present the concept, prototypes, and an optimal design method for a compliant mechanism kit as a parallel to the kits available for rigid-body mechanisms. The kit consists of flexible beams and connectors that can be easily hand-assembled using snap fits. It enables users, using their creativity and mechanics intuition, to quickly realize a compliant mechanism. The mechanisms assembled in this manner accurately capture the essential behavior of the topology, shape, size and material aspects and thereby can lead the way for a real compliant mechanism for practical use. Also described in this paper are the design of the connector to which flexible beams can be added in eight different directions; and prototyping of the spring steel connectors as well as beams using wire-cut electro discharge machining. It is noted in this paper that the concept of the kit also resolves a discrepancy in the finite element (FE) modeling of beam-based compliant mechanisms. The discrepancy arises when two or more beams are joining at one point and thus leading to increased stiffness. After resolving this discrepancy, this work extends the topology optimization to automatically generate designs that can be assembled with the kit. Thus, the kit and the accompanying analysis and optimal synthesis procedures comprise a self-contained educational as well as a research and pragmatic toolset for compliant mechanisms. The paper also illustrates how human creativity finds new ways of using the kit beyond the original intended use and how it is useful even for a novice to design compliant mechanisms.

Generalized asymptotic expansions for the wavenumbers in infinite flexible in vacuo orthotropic cylindrical shells

Analytical expressions are found for the wavenumbers and resonance frequencies in flexible, orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders n. The Donnell-Mushtari shell theory is used to model the dynamics of the cylindrical shell. Initially, an in vacuo cylindrical isotropic shell is considered and expressions for all the wavenumbers (bending, near-field bending, longitudinal and torsional) are found. Subsequently, defining a suitable orthotropy parameter epsilon, the problem of wave propagation in an orthotropic shell is posed as a perturbation on the corresponding problem for an isotropic shell. Asymptotic expressions for the wavenumbers in the in vacuo orthotropic shell are then obtained by treating epsilon as an expansion parameter. In both cases (isotropy and orthotropy), a frequency-scaling parameter (eta) and Poisson's ratio (nu) are used to find elegant expansions in the different frequency regimes. The asymptotic expansions are compared with numerical solutions in each of the cases and the match is found to be good. The main contribution of this work lies in the extension of the existing literature by developing closed-form expressions for wavenumbers with arbitrary circumferential orders n in the case of both, isotropic and orthotropic shells. Finally, we present natural frequency expressions in finite shells (isotropic and orthotropic) for the axisymmetric mode and compare them with numerical and ANSYS results. Here also, the comparison is found to be good. (C) 2011 Elsevier Ltd. All rights reserved.

A compliant mechanism kit with flexible beams and connectors along with analysis and optimal synthesis procedures

We present a compliant mechanism kit as a parallel to the kits available for rigid-body mechanisms. The kit consists of flexible beams and connectors that can be easily hand-assembled using snap fits. The mechanisms assembled using the kit accurately capture the aspects of the topology, shape, and size of joint-free compliant mechanisms. Thus, the kit enables designers to conceive and design new, practicable, single-piece compliant mechanisms that do not require assembly. The concept of the kit also resolves a discrepancy in the finite element (FE) modeling of beam-based compliant mechanisms. The discrepancy arises when two or more beams are joined at one point and thus leading to increased stiffness. After resolving this discrepancy, this work extends the topology optimization to automatically generate designs that can be assembled with the kit for quick and easy validation instead of time-consuming prototyping. Thus, the kit and the accompanying analysis and optimal synthesis procedures comprise a self-contained educational as well as a research and practice toolset for compliant mechanisms. The paper also illustrates how human creativity finds new ways of using the kit beyond the original intended use and how it enables even a novice to design compliant mechanisms. (C) 2011 Elsevier Ltd. All rights reserved.

Barrier crossing by a flexible long chain molecule - The kink mechanism

The problem and related earlier work All the above problems involve the passage of a long chain molecule, through a region in space, where the free energy per segment is higher, thus effectively presenting a barrier for the motion of the molecule. This is what we refer to as the Kramers proble...

Asymptotic expansions for the coupled wavenumbers in an infinite orthotropic flexible fluid-filled cylindrical shell

Analytical expressions are found for the coupled wavenumbers in flexible, fluid-filled, circular cylindrical orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders. The Donnell-Mushtari shell theory is used to model the shell and the effect of the fluid is introduced through the fluid-loading parameter mu. The orthotropic problem is posed as a perturbation on the corresponding isotropic problem by defining a suitable orthotropy parameter epsilon, which is a measure of the degree of orthotropy. For the first study, an isotropic shell is considered (by setting epsilon = 0) and expansions are found for the coupled wavenumbers using a regular perturbation approach. In the second study, asymptotic expansions are found for the coupled wavenumbers in the limit of small orthotropy (epsilon << 1). For each study, isotropy and orthotropy, expansions are found for small and large values of the fluid-loading parameter mu. All the asymptotic solutions are compared with numerical solutions to the coupled dispersion relation and the match is seen to be good. The differences between the isotropic and orthotropic solutions are discussed. The main contribution of this work lies in extending the existing literature beyond in vacuo studies to the case of fluid-filled shells (isotropic and orthotropic).

Dynamics of a flexible splitter plate in the wake of a circular cylinder

Rigid splitter plates in the wake of bluff bodies are known to suppress the primary vortex shedding. In the present work, we experimentally study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate is free to continuously deform along its length due to the fluid forces acting on it; the flexural rigidity (EI) of the plate being an important parameter. Direct visualizations of the splitter plate motions, for very low values of flexural rigidity (EI), indicate periodic traveling wave type deformations of the splitter plate with maximum tip amplitudes of the order of I cylinder diameter. As the Reynolds number based on cylinder diameter is varied, two regimes of periodic splitter plate motions are found that are referred to as mode I and mode II, with a regime of aperiodic motions between them. The frequency of plate motions in both periodic modes is found to be close to the plane cylinder Strouhal number of about 0.2, while the average frequencies in the non-periodic regime are substantially lower. The measured normalized phase speed of the traveling wave for both periodic modes is also close to the convection speed of vortices in the plane cylinder wake. As the flexural rigidity of the plate (EI) is increased, the response of the plate was found to shift to the right when plotted with flow speed or Re. To better capture the effect of varying EI, we define and use a non-dimensional bending stiffness, K*, similar to the ones used in the flag flutter problem, K*=EI/(0.5 rho(UL3)-L-2), where U is the free-stream velocity and L is the splitter plate length. Amplitude data for different EI cases when plotted against this parameter appear to collapse on to a single curve for a given splitter plate length. Measurements of the splitter plate motions for varying splitter plate lengths indicate that plates that are substantially larger than the formation length of the plane cylinder wake have similar responses, while shorter plates show significant differences.

Self-assembled dipeptide nanotubes constituted by flexible beta-phenylalanine and conformationally constrained alpha,beta-dehydrophenylalanine residues as drug delivery system

Peptide based self assembled nanostructures have attracted growing interest in recent years due to their numerous potential applications particularly in biomedical sciences. Di-peptide Phe-Phe was shown previously to self-assemble into nanotube like structures. In this work, we studied the affect of peptide backbone length and conformational flexibility on the self assembly process by using two dipeptides based on the Phe-Phe backbone (beta Phe-Phe and beta Phe-Delta Phe): one containing a flexible beta Phe amino acid, and the other containing both a flexible bPhe as well as a backbone constraining Alpha Phe (alpha,beta-dehydrophenylalanine) amino acid. Electron microscopy and X-ray diffraction experiments revealed that these new di-peptides can self-assemble into nanotubes having different properties than the native Phe-Phe nanotubes. These nanotubes were stable over a broad range of temperatures and the introduction of non-natural amino acids provided them with stability against the action of nonspecific proteases. Moreover, these dipeptides showed no cytotoxicity towards HeLa and L929 cells, and were able to encapsulate small drug molecules. We further showed that anticancerous drug mitoxantrone was more efficient in killing HeLa and B6F10 cells when entrapped in nanotubes as compared to free mitoxantrone. Therefore, these beta-phenylalanine and alpha, beta-dehydrophenylalanine containing dipeptide nanotubes may be useful in the development of biocompatible and proteolytically stable drug delivery vehicles.

Morphology and electrostatics play active role in neuronal differentiation processes on flexible conducting substrates

This commentary discusses and summarizes the key highlights of our recently reported work entitled ``Neuronal Differentiation of Embryonic Stem Cell Derived Neuronal Progenitors Can Be Regulated by Stretchable Conducting Polymers.'' The prospect of controlling the mechanical-rigidity and the surface conductance properties offers a unique combination for tailoring the growth and differentiation of neuronal cells. We emphasize the utility of transparent elastomeric substrates with coatings of electrically conducting polymer to realize the desired substrate-characteristics for cellular development processes. Our study showed that neuronal differentiation from ES cells is highly influenced by the specific substrates on which they are growing. Thus, our results provide a better strategy for regulated neuronal differentiation by using such functional conducting surfaces.

Organic passivation layer on flexible Surlyn substrate for encapsulating organic photovoltaics

Barrier materials are required for encapsulating organic devices. A simple methodology based on organic passivation layer on a flexible substrate has been developed in this work. Stearyl stearate ( SS) was directly coated over the flexible Surlyn film. The barrier films with SS passivation layer exhibited much lower water vapor transmission rates compared to the neat Surlyn films. Moreover, the effect of the process of deposition of organic passivation layer on the resultant water vapor properties of the barrier films was evaluated. The accelerated lifetime studies conducted on encapsulated organic photovoltaics showed that the passivation layer improved the device performance by several fold compared to the non-passivated barrier films. (C) 2014 AIP Publishing LLC.

A hybrid finite element formulation for flexible multibody dynamics

This work deals with the transient analysis of flexible multibody systems within a hybrid finite element framework. Hybrid finite elements are based on a two-field variational formulation in which the displacements and stresses are interpolated separately yielding very good coarse mesh accuracy. Most of the literature on flexible multibody systems uses beam-theory-based formulations. In contrast, the use of hybrid finite elements uses continuum-based elements, thus avoiding the problems associated with rotational degrees of freedom. In particular, any given three-dimensional constitutive relations can be directly used within the framework of this formulation. Since the coarse mesh accuracy as compared to a conventional displacement-based formulation is very high, the scheme is cost effective as well. A general formulation is developed for the constrained motion of a given point on a line manifold, using a total Lagrangian method. The multipoint constraint equations are implemented using Lagrange multipliers. Various kinds of joints such as cylindrical, prismatic, and screw joints are implemented within this general framework. Hinge joints such as spherical, universal, and revolute joints are obtained simply by using shared nodes between the bodies. In addition to joints, the formulation and implementation details for a DC motor actuator and for prescribed relative rotation are also presented. Several example problems illustrate the efficacy of the developed formulation.

Efficient simulation and rendering of realistic motion of one-dimensional flexible objects

In gross motion of flexible one-dimensional (1D) objects such as cables, ropes, chains, ribbons and hair, the assumption of constant length is realistic and reasonable. The motion of the object also appears more natural if the motion or disturbance given at one end attenuates along the length of the object. In an earlier work, variational calculus was used to derive natural and length-preserving transformation of planar and spatial curves and implemented for flexible 1D objects discretized with a large number of straight segments. This paper proposes a novel idea to reduce computational effort and enable real-time and realistic simulation of the motion of flexible 1D objects. The key idea is to represent the flexible 1D object as a spline and move the underlying control polygon with much smaller number of segments. To preserve the length of the curve to within a prescribed tolerance as the control polygon is moved, the control polygon is adaptively modified by subdivision and merging. New theoretical results relating the length of the curve and the angle between the adjacent segments of the control polygon are derived for quadratic and cubic splines. Depending on the prescribed tolerance on length error, the theoretical results are used to obtain threshold angles for subdivision and merging. Simulation results for arbitrarily chosen planar and spatial curves whose one end is subjected to generic input motions are provided to illustrate the approach. (C) 2016 Elsevier Ltd. All rights reserved.

Choice of Flexible Production Technologies Under Strategic Delegation

This work analyzes a managerial delegation model in which firms can choose between a flexible production technology which allows them to produce two different products and a dedicated production technology which limits production to only one product. We analyze whether the incentives to adopt the flexible technology are smaller or greater in a managerial delegation model than under strict profit maximization. We obtain that the asymmetric equilibrium in which only one firm adopts the flexible technology can be sustained under strategic delegation but not under strict profit maximization when products are substitutes. We extend the analysis to consider welfare implications.

FTT-MA: A Flexible Time-Triggered Middleware Architecture for Time Sensitive, Resource-Aware AmI Systems

There is an increasing number of Ambient Intelligence (AmI) systems that are time-sensitive and resource-aware. From healthcare to building and even home/office automation, it is now common to find systems combining interactive and sensing multimedia traffic with relatively simple sensors and actuators (door locks, presence detectors, RFIDs, HVAC, information panels, etc.). Many of these are today known as Cyber-Physical Systems (CPS). Quite frequently, these systems must be capable of (1) prioritizing different traffic flows (process data, alarms, non-critical data, etc.), (2) synchronizing actions in several distributed devices and, to certain degree, (3) easing resource management (e.g., detecting faulty nodes, managing battery levels, handling overloads, etc.). This work presents FTT-MA, a high-level middleware architecture aimed at easing the design, deployment and operation of such AmI systems. FTT-MA ensures that both functional and non-functional aspects of the applications are met even during reconfiguration stages. The paper also proposes a methodology, together with a design tool, to create this kind of systems. Finally, a sample case study is presented that illustrates the use of the middleware and the methodology proposed in the paper.