Exact results for curvature-driven coarsening in two dimensions

We consider the statistics of the areas enclosed by domain boundaries ("hulls") during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than A has, for large time t, the scaling form Nh(A,t)=2c/(A+lambdat), demonstrating the validity of dynamical scaling in this system, where c=1/8pisquare root 3 is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of A/lambdat. Identical forms are obtained for coarsening from a critical initial state, but with c replaced by c/2.     

Macroion-induced compositional instability of binary fluid membranes

Macroion adsorption on a mixed, fluid, lipid membrane containing oppositely charged lipids induces local changes in lipid composition at the interaction zones, and gradients at their boundaries. Including these effects in the free energy of the macroion-dressed membrane we derive its spinodal equation, and show that nonideal lipid mixing can lead to (lipid-mediated) attraction between macroions and lateral phase separation in the composite membrane. The critical nonideality for this transition is substantially smaller than that of the bare lipid membrane, decreasing with macroion size and charge. That is, the lipid membrane is destabilized by macroion adsorption.     

Hydrodynamic instability in ohmic regimes with imperfect electric membranes

The transition to overlimiting currents directly from prelimiting regimes bypassing the limitingcurrent stage is considered for imperfect electric membranes. The hydrodynamic instability of the onedimensional equilibrium state, which is a result of the balance between diffusion and electromigration, is investigated. The influence of volume and surface effects on instability and the transition to overlimiting currents is estimated under variation of the membrane selectivity. It is found that the dominating mechanism of instability is destabilization of the residual space charge. The fact of the replacement of monotonic instability by vibratory instability with a vibration frequency of about 50?300 Hz has been discovered.     

Coarsening and pearling instabilities in silver nanofractal aggregates

We investigate the morphological changes of 3D supported fractal aggregates generated through the deposition of silver clusters on graphite. The fractal relaxation, activated after their formation by perturbing them either by thermal annealing or by using a surfactant, as oxide molecules, carried by silver clusters in a subsequent deposition, shows evidence of two distinct fragmentation patterns. The post coarsening, driven by thermal heating, gives a broad asymmetrical distribution of fragments in agreement with a random process, whereas the entire silver fractal pearling fragmentation is driven by chemical adjunction of the surfactant.     

Rosensweig instability of ferrogel thin films or membranes

We derive the dispersion relation of surface waves for magnetic gel membranes or thin films at the interface between two fluids in the presence of an external magnetic field normal to the free surface. Above a critical field strength surface waves become linearly unstable with respect to a stationary pattern of surface protuberances. This linear stability criterion generalizes that of the Rosensweig instability for ferrofluid and ferrogel free surfaces to take into account bending elasticity and intrinsic elastic and magnetic surface properties of the film or membrane, additionally. The latter is of interest for uniaxial ferrogel film or membranes, which show a locked-in permanent magnetization.     

Model reduction for parametric instability analysis in shells conveying fluid

Flexible pipes conveying fluid are often subjected to parametric excitation due to time-periodic flow fluctuations. Such systems are known to exhibit complex instability phenomena such as divergence and coupled-mode flutter. Investigators have typically used weighted residual techniques, to reduce the continuous system model into a discrete model, based on approximation functions with global support, for carrying out stability analysis. While this approach is useful for straight pipes, modelling based on FEM is needed for the study of complicated piping systems, where the approximation functions used are local in support. However, the size of the problem is now significantly larger and for computationally efficient stability analysis, model reduction is necessary. In this paper, model reduction techniques are developed for the analysis of parametric instability in flexible pipes conveying fluids under a mean pressure. It is shown that only those linear transformations which leave the original eigenvalues of the linear time invariant system unchanged are admissible. The numerical technique developed by Friedmann and Hammond (Int. J. Numer. Methods Eng. Efficient 11 (1997) 1117) is used for the stability analysis. One of the key research issues is to establish criteria for deciding the basis vectors essential for an accurate stability analysis. This paper examines this issue in detail and proposes new guidelines for their selection.     

Undulation instability of lipid membranes under an electric field

The influence of an external electric field on a poorly conductive membrane such as a lipid bilayer is studied theoretically. The unbalanced electric stress created by an ionic current across a non-perfectly flat membrane gives rise to a destabilizing surface energy enhancing undulations. The deformation of a membrane attached to a frame is derived and the electrohydrodynamic instability of a free floating membrane is studied. We find a most unstable mode of undulation, of wavelength in the microm range, connected to the crossover between membrane and solvent dominated dissipations.     

Hydrodynamics,electroosmosis, and electrokinetic instability in imperfect electric membranes

For the first time within the framework of the Nernst?Planck?Poisson?Stokes set, the behavior of an electrolytic solution in imperfect electric membranes is investigated numerically. The distributions of the electric potential, fluid velocities, charge density, and other values in the zones of the depleted and enriched solution and a porous membrane for all current modes are obtained: prelimit, limit, and superlimit. The dependence of selectivity of a membrane on the density of its space charge is obtained. The boundaries of superlimit modes, when the one-dimensional solution loses stability, are found and replaced by the twodimensional solution with the formation of microvortices in both the desalination and enriched-solution zones. The basic types of current arising at supercritical currents are investigated.     

Stokes instability in inhomogeneous membranes: application to lipoprotein suction of cholesterol-enriched domains

We examine the time-dependent distortion of a nearly circular viscous domain in an infinite viscous sheet when suction occurs. Suction, the driving force of the instability, can occur everywhere in the two phases separated by an interface. The model assumes a two-dimensional Stokes flow; the selection of the wavelength at short times is determined by a variational procedure. Contrary to the viscous fingering instability, undulations of the boundary may be observed for enough pumping, whatever the sign of the viscosity contrast between the two fluids involved. We apply our model to the suction by lipoproteins of cholesterol-enriched domains in giant unilamellar vesicles. Comparison of the number of undulations given by the model and by the experiments gives reasonable values of physical quantities such as the viscosities of the domains.     

Attractive instability of oppositely charged membranes induced by charge density fluctuations

We predict the conditions under which two oppositely charged membranes show a dynamic, attractive instability. Two layers with unequal charges of opposite sign can repel or be stable when in close proximity. However, dynamic charge density fluctuations can induce an attractive instability and thus facilitate fusion. We predict the dominant instability modes and time scales and show how these are controlled by the relative charge and membrane viscosities. These dynamic instabilities may be the precursors of membrane fusion in systems where artificial vesicles are engulfed by biological cells of opposite charge.     

Simple proof for Yang-Mills instability

The stability problem for the classical Yang-Mills field produced by a static, spherically symmetric external source is shown to be equivalent with the stability question of a massless Klein-Gordon particle moving in a Coulomb potential. The latter problem is explicitly solvable. Instability is found if the coupling strength exceeds a certain critical value.     

Criterion for extensional necking instability in polymeric fluids

We study the linear instability with respect to necking of a filament of polymeric fluid undergoing uniaxial extension. Contrary to the widely discussed Considère criterion, we find the onset of instability to relate closely to the onset of downward curvature in the time (and so strain) evolution of the zz component of the molecular strain, for extension along the z axis. In establishing this result numerically across five of the most widely used models of polymer rheology, and by analytical calculation, we argue it to apply generically. Particularly emphasized is the importance of polymer chain stretching in partially mitigating necking. We comment finally on the relationship between necking and the shape of the underlying steady state constitutive curve for homogeneous extension.