Instabilities of soft elastic microtubes filled with viscous fluids: Pearls, wrinkles, and sausage strings

A linear stability analysis is presented to study the self-organized instabilities of a highly compliant elastic cylindrical shell filled with a viscous liquid and submerged in another viscous medium. The prototype closely mimics many components of micro-or nanofluidic devices and biological processes such as the budding of a string of pearls inside cells and sausage-string formation of blood vessels. The cylindrical shell is considered to be a soft linear elastic solid with small storage modulus. When the destabilizing capillary force derived from the cross-sectional curvature overcomes the stabilizing elastic and in-plane capillary forces, the microtube can spontaneously self-organize into one of several possible configurations; namely, pearling, in which the viscous fluid in the core of the elastic shell breaks up into droplets; sausage strings, in which the outer interface of the mircrotube deforms more than the inner interface; and wrinkles, in which both interfaces of the thin-walled mircrotube deform in phase with small amplitudes. This study identifies the conditions for the existence of these modes and demonstrates that the ratios of the interfacial tensions at the interfaces, the viscosities, and the thickness of the microtube play crucial roles in the mode selection and the relative amplitudes of deformations at the two interfaces. The analysis also shows asymptotically that an elastic fiber submerged in a viscous liquid is unstable for Y = gamma/(G(e)R) > 6 and an elastic microchannel filled with a viscous liquid should rupture to form spherical cavities (pearling) for Y > 2, where gamma, G(e), and R are the surface tension, elastic shear modulus, and radius, respectively, of the fiber or microchannel.

Static balancing of a four-bar linkage and its cognates

Motivated by the need to statically balance the inherent elastic forces in linkages, this paper presents three techniques to statically balance a four-bar linkage loaded by a zero-free-length spring attached between its coupler point and an anchor point on the ground. The number of auxiliary links and balancing springs required for the three techniques is less than or equal to that of the only technique currently in the literature. One of the three techniques does not require auxiliary links. In these techniques, the set of values for the spring constants and the ground-anchor point of the balancing springs can vary over a one-parameter family. Thrice as many balancing choices are available when the cognates are considered. The ensuing numerous options enable a user to choose the most practical solution. To facilitate the evaluation of the balancing choices for all the cognates, Roberts-Chebyshev cognate theorem is extended to statically balanced four-bar linkages. (C) 2011 Elsevier Ltd. All rights reserved.

Formulas for algorithmic computation of impedance matrix using general circuit constants

A set of formulas is derived from general circuit constants which facilitates formation of the impedance matrix of a power system by the bus-impedance method. The errors associated with the lumpedparameter representation of a transmission line are thereby eliminated. The formulas are valid for short lines also, if the relevant general circuit constants are employed. The mutual impedance between the added line and the existing system is not considered, but the approach suggested can well be extended to it.

Contact instabilities of anisotropic and inhomogeneous soft elastic films

Anisotropy plays important roles in various biological phenomena such as adhesion of geckos and grasshoppers enabled by the attachment pods having hierarchical structures like thin longitudinal setae connected with threads mimicked by anisotropic films. We study the contact instability of a transversely isotropic thin elastic film when it comes in contact proximity of another surface. In the present study we investigate the contact stability of a thin incompressible transversely isotropic film by performing linear stability analysis. Based on the linear stability analysis, we show that an approaching contactor renders the film unstable. The critical wavelength of the instability is a function of the total film thickness and the ratio of the Young's modulus in the longitudinal direction and the shear modulus in the plane containing the longitudinal axis. We also analyze the stability of a thin gradient film that is elastically inhomogeneous across its thickness. Compared to a homogeneous elastic film, it becomes unstable with a longer wavelength when the film becomes softer in going from the surface to the substrate.

A numerical approach to determine the sufficiency of given boundary data sets for uniquely estimating interior elastic properties

We consider an inverse elasticity problem in which forces and displacements are known on the boundary and the material property distribution inside the body is to be found. In other words, we need to estimate the distribution of constitutive properties using the finite boundary data sets. Uniqueness of the solution to this problem is proved in the literature only under certain assumptions for a given complete Dirichlet-to-Neumann map. Another complication in the numerical solution of this problem is that the number of boundary data sets needed to establish uniqueness is not known even under the restricted cases where uniqueness is proved theoretically. In this paper, we present a numerical technique that can assess the sufficiency of given boundary data sets by computing the rank of a sensitivity matrix that arises in the Gauss-Newton method used to solve the problem. Numerical experiments are presented to illustrate the method.

SCALE EFFECTS ON ULTRASONIC WAVE DISPERSION CHARACTERISTICS OF MONOLAYER GRAPHENE EMBEDDED IN AN ELASTIC MEDIUM

Ultrasonic wave propagation in a graphene sheet, which is embedded in an elastic medium, is studied using nonlocal elasticity theory incorporating small-scale effects. The graphene sheet is modeled as an one-atom thick isotropic plate and the elastic medium/substrate is modeled as distributed springs. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. After that, an ultrasonic type of wave propagation model is also derived. The explicit expressions for the cut-off frequencies are also obtained as functions of the nonlocal scaling parameter and the y-directional wavenumber. Local elasticity shows that the wave will propagate even at higher frequencies. But nonlocal elasticity predicts that the waves can propagate only up to certain frequencies (called escape frequencies), after which the wave velocity becomes zero. The results also show that the escape frequencies are purely a function of the nonlocal scaling parameter. The effect of the elastic medium is captured in the wave dispersion analysis and this analysis is explained with respect to both local and nonlocal elasticity. The simulations show that the elastic medium affects only the flexural wave mode in the graphene sheet. The presence of the elastic matrix increases the band gap of the flexural mode. The present results can provide useful guidance for the design of next-generation nanodevices in which graphene-based composites act as a major element.

Structure, tensile properties and cytotoxicity assessment of sebacic acid based biodegradable polyesters with ricinoleic acid

A new family of ricinoleic acid based polyesters was synthesized using catalyst free melt-condensation polymerization with sebacic acid, citric acid, mannitol and ricinoleic acid as precursors. The use of FT-IR and NMR characterisation techniques confirms the presence of ester linkages in the as-synthesized polymers. Depending on the precursor combination, their relative amount and the degree of curing, a broad range of elastic modulus (22-327 MPa) and tensile strength (0.7-12.7 MPa) can be obtained in the newly synthesized biopolymers. The polymers show rubbery behaviour at a physiological temperature (37 degrees C) and the contact angles of the synthesized polymers fall in the range of 42 degrees to 71 degrees, making them ideal substrates to study delivery of drugs through polymer scaffolds. The cytocompatibility assessment of the cured polymers confirmed good cell attachment and growth of smooth muscle cells (C2C12 myoblast cells). Importantly, oriented cell growth was observed after culturing myoblast cells for 3 days. The in vitro degradation in PBS indicates that the mild cured polymers follow a first order reaction kinetics and have degradation rate constants in the range of 0.009-0.038 h(-1), depending on the relative proportions of monomers. Overall, the results of our study indicate that the physical properties can be tailored by varying the composition of the monomers and curing conditions in the newly developed polyesters. Hence, they may be used as potential substrates for tissue engineering scaffolds and for localized drug delivery.

Conditions for the onset of elastic and material instabilities in hyperelastic materials

Several constitutive inequalities have been proposed in the literature to quantify the notion that ‘stress increases with strain’ in an elastic material. Due to some inherent shortcomings in them, which we discuss, we propose a new tensorial criterion for isotropic materials. We also present necessary conditions in terms of elasticity tensors for the onset of elastic instabilities.

Gap-Dependent Quasiparticle Dynamics and Coherent Acoustic Phonons in CaFe2As2 across Spin Density Wave Phase Transition

We report ultrafast quasiparticle (QP) dynamics and coherent acoustic phonons in undoped CaFe2As2 iron pnictide single crystals exhibiting spin-density wave (SDW) and concurrent structural phase transition at temperature T-SDW similar to 165K using femtosecond time-resolved pump-probe spectroscopy. The contributions in transient differential reflectivity arising from exponentially decaying QP relaxation and oscillatory coherent acoustic phonon mode show large variations in the vicinity of T-SDW. From the temperature-dependence of the QP recombination dynamics in the SDW phase, we evaluate a BCS-like temperature dependent charge gap with its zero-temperature value of similar to(1.6 perpendicular to 0.2)k(B)T(SDW), whereas, much above T-SDW, an electron-phonon coupling constant of similar to 0.13 has been estimated from the linear temperature-dependence of the QP relaxation time. The long-wavelength coherent acoustic phonons with typical time-period of similar to 100 ps have been analyzed in the light of propagating strain pulse model providing important results for the optical constants, sounds velocity and the elastic modulus of the crystal in the whole temperature range of 3 to 300 K.

Thermal vibration analysis of monolayer graphene embedded in elastic medium based on nonlocal continuum mechanics

This paper presents the thermal vibration analysis of single-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. The graphene is modeled based on continuum plate theory and axial stress caused by the thermal effects is also considered. Nonlocal governing equation of motion for this graphene sheet system is derived from the principle of virtual displacements. The closed form solution for thermal-vibration frequencies of a simply supported rectangular nanoplate has been obtained by using the Navier's method of solution. Numerical results obtained by the present theory are compared with available solutions in the literature and the molecular dynamics results. The influences of the small scale coefficient, the room or low temperature, the high temperature, the half wave number and the aspect ratio of nanoplate on the natural frequencies are considered and discussed in detail. The thermal vibration analysis of single- and double-layer graphene sheets are considered for the analysis. The mode shapes of the respective graphene system are also captured in this work. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the graphene.