A phase field study of morphological instabilities in multilayer thin films

We studied the microstructural evolution of multiple layers of elastically stiff films embedded in an elastically soft matrix using a phase field model. The coherent and planar film/matrix interfaces are rendered unstable by the elastic stresses due to a lattice parameter mismatch between the film and matrix phases, resulting in the break-up of the films into particles. With an increasing volume fraction of the stiff phase, the elastic interactions between neighbouring layers lead to: (i) interlayer correlations from an early stage; (ii) a longer wavelength for the maximally growing wave; and therefore (iii) a delayed break-LIP. Further, they promote a crossover in the mode of instability from a predominantly anti-symmetric (in phase) one to a symmetric (out of phase) one. We have computed a stability diagram for the most probable mode of break-up in terms of elastic modulus Mismatch and Volume fraction. We rationalize our results in terms of the initial driving force for destabilization, and corroborate our conclusions using simulations in elastically anisotropic systems.

Instabilities and Waves in Thin Films of Living Fluids

We formulate the thin-film hydrodynamics of a suspension of polar self-driven particles and show that it is prone to several instabilities through the interplay of activity, polarity, and the existence of a free surface. Our approach extends, to self-propelling systems, the work of Ben Amar and Cummings [Phys. Fluids 13 1160 (2001)] on thin-film nematics. Based on our estimates the instabilities should be seen in bacterial suspensions and the lamellipodium, and are potentially relevant to the morphology of biofilms. We suggest several experimental tests of our theory.

Instabilities of a compressible stratified fluid in horizontal sheared motion

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible atmosphere in the presence of a lower boundary are studied. A jump in the Brunt–Väisälä frequency is introduced and the level at which this jump occurs is assumed to be different from the shear zone, to simulate sharp temperature discontinuities in the atmosphere. The results are compared with those of Pellacani, Tebaldi, and Tosi and Lindzen and Rosenthal. In the present configuration, new unstable modes with larger growth rates are found. The wavelengths of the most unstable gravity waves for the parameters pertaining to observed cases of clear air turbulence agree quite closely with the experimental values. Physics of Fluids is copyrighted by The American Institute of Physics

Competing A-site and B-site driven ferroelectric instabilities in the (1-x)PbTiO3-(x)BiAlO3 system

The system (1-x)PbTiO3-(x)BiAlO3 has been investigated with regard to its solid solubility, crystal structure, microstructure, and ferroelectric transition. The unit cell volume and the tetragonality exhibit anomalous behavior near x=0.10. The Curie point (T-C) of PbTiO3 was however found to be nearly unchanged. The study seems to suggest that the decrease in the stability of the ferroelectric state due to dilution of the Ti-sublattice by smaller sized Al+3 ions is compensated by the increase in the ferroelectric stability by the Bi+3 ions.

Instabilities induced by variation of Brunt-Vaisala frequency in compressible stratified shear flows

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible fluid in the presence of a lower rigid boundary are studied. A jump in the Brunt-Vaisala frequency at a level different from the shear zone is introduced and the variation of the Brunt-Vaisala frequency with respect to the vertical coordinate in the middle layer of the three-layered model is considered. An analytic solution in each of the layers is obtained, and the dispersion relation is solved numerically for parameters relevant to the model. The effect of shear in the lowermost layer of the three-layered model for a Boussinesq fluid is discussed. The results are compared with the earlier studies of Lindzen and Rosenthal, and Sachdev and Satya Narayanan. In the present model, new unstable modes with larger growth rates are obtained and the most unstable gravity wave modes are found to agree closely with the observed ones at various heights. Physics of Fluids is copyrighted by The American Institute of Physics.

Magnetic Field Induced Instabilities In Localized Two-Dimensional Electron Systems

The results of extensive transport studies in localized regime of mesoscopic two-dimensional electron systems (2DES) with varying disorder are presented. A quick overview of previously achieved result is given. The main focus is on the observation of density dependent instabilities manifested by strong resistance oscillations induced by high perpendicular magnetic fields B-perpendicular to. While the amplitude of the oscillations is strongly enhanced with increasing B-perpendicular to, their position in electron density remains unaffected. The temperature dependence of resistivity shows a transition from an activated behaviour at high temperature to a saturated behaviour at low T. In the positions of resistance minima, the T dependence can even become metal-like (d rho/dT > 0). The activation energies obtained from the high T behaviour exhibit a formation of plateaux in connection with the resistance oscillations when analyzed as a function of electron density. We suggest the interplay between a strongly interacting electron phase and the background disorder as a possible explanation for our observation.

Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration of the m =1 counter-rotating instability in a `hot' nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using the Wentzel-Kramers-Brillouin approximation. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian discm must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.

Effect of viscosity stratification on secondary and nonmodal instabilities

The effect of viscosity stratification on the different mechanism of transition to turbulence is not well understood. In this paper, a viscosity variation normal to the flow in a channel is investigated. The primary and secondary instability are computed, and the transient growth is analysed. It is found that viscosity stratification can have different effects in each case.

Criteria for prediction of flow instabilities and microstructural manifestations during warm working of AISI 304L stainless steel

The deformation characteristics of 304L stainless steel in compression in the temperature range 20–700°C and strain rate range 0·001–100 s−1 have been studied with the aim of characterising the .flow instabilities occurring in the microstructure. At higher temperatures and strain rates the stainless steel exhibits flow localisation, whereas at temperatures below 500°C and strain rates lower than 0·1 s−1 the flow instabilities are due to dynamic strain aging. Strain induced martensite formation is responsible for the flow instabilities at room temperature and low strain rates (0·01 s−1). In view of the occurrence of these instabilities, cold working is preferable to warm working to achieve dimensional tolerance and reproducible properties in the product. Among the different criteria tested to explain the occurrence of instabilities, the continuum criterion, developed on the basis of the principles of maximum rate of entropy production and separability of the dissipation function, predicts accurately all the above instability features.

Flow Instabilities and fracture in Ti-6Al-4V deformed in compression at 298 K to 673 K

Uniaxial compression tests were conducted on Ti-6Al-4V specimens in the strain-rate range df 0.001 to 1 s(-1) and temperature range of 298 to 673 K. The stress-strain curves exhibited a peak flow stress followed by flow softening. Up to 523 K, the specimens cracked catastrophically after the flow softening started. Adiabatic shear banding was observed in this regime. The fracture surface exhibited both mode I and II fracture features. The state of stress existing in a compression test specimen when bulging occurs is responsible for this fracture. The instabilities observed in the present tests are classified as ''geometric'' in nature and are state-of-stress dependant, unlike the ''intrinsic'' instabilities, which are dependant on the dynamic constitutive behavior of the material.

Influence of initial texture on the microstructural instabilities during compression of commercial ?-Titanium at 25 °C to 400 °C

Cylindrical specimens of textured commercial pure alpha-titanium plate, cut with the cylinder axis along the rolling direction for one set of experiments and in the long transverse direction for the other set, were compressed at strain rates in the range of 0.001 to 100 s-1 and temperatures in the range of 25-degrees-C to 400-degrees-C. At strain rates greater-than-or-equal-to 1 s-1, both sets of specimens exhibited adiabatic shear bands, but the intensity of shear bands was found to be higher in the rolling direction specimens than in the long transverse direction specimens. At strain rates -0.1 s-1, the material deformed in a microstructurally inhomogeneous fashion. For the rolling direction specimens, cracking was observed at 100-degrees-C and at strain rates -0.1 s-1. This is attributed to dynamic strain aging. Such cracking was not observed in the long transverse specimens. The differences in the intensity of adiabatic shear bands and that of dynamic strain aging between the two sets of test specimens are attributed to the strong crystallographic texture present in these plates.

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.

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.

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.