Does roughening of rock-fluid-rock interfaces emerge from a stress-induced instability?

Non-planar solid-fluid-solid interfaces under stress are very common in many industrial and natural materials. For example, in the Earth’s crust, many rough and wavy interfaces can be observed in rocks in a wide range of spatial scales, from undulate grain boundaries at the micrometer scale, to stylolite dissolution planes at the meter scale. It is proposed here that these initially flat solid-fluid-solid interfaces become rough by a morphological instability triggered by elastic stress. A model for the formation of these unstable patterns at all scales is thus presented. It is shown that such instability is inherently present due to the uniaxial stress that promotes them, owing to the gain in the total elastic energy: the intrinsic elastic energy plus the work of the external forces. This is shown explicitly by solving the elastic problem in a linear stability analysis, and proved more generally without having resort to the computation of the elastic field.     

Birth and morphological evolution of step bunches under electromigration

We analyze the dynamics of electromigration-induced step bunching in the absence of desorption. We show that, even when the instability occurs at long wavelength, hinting to a smooth morphology, the surface suddenly splits into bunches escorted with wide terraces, in agreement with several observations. As the size of the bunches increases, a nonstandard regime is exhibited, namely, the bunches do not match tangentially to the facet, as would the classical Pokrosvky-Talapov shape dictate. This Letter presents a complete scenario of evolution of bunches from their birth up to their ultimate stage.     

Impedance spectroscopy of chitosan/poly(vinyl alcohol) films

Journal of Solid State Electrochemistry - Polymer films were cast from aqueous solutions of chitosan (CS) and poly(vinyl alcohol) (PVA) in employing tetraethoxysilane (TEOS) as a crosslinking...     

An adaptive finite element method for the modeling of the equilibrium of red blood cells

This contribution is concerned with the numerical modeling of an isolated red blood cell (RBC), and more generally of phospholipid membranes. We propose an adaptive Eulerian finite element approximation, based on the level set method, of a shape optimization problem arising in the study of RBCs. We simulate the equilibrium shapes that minimize the elastic bending energy under prescribed constraints of fixed volume and surface area. An anisotropic mesh adaptation technique is used in the vicinity of the cell membrane to enhance the robustness of the method. Efficient time and spatial discretizations are considered and implemented. We address in detail the main features of the proposed method, and finally we report several numerical experiments in the two‐dimensional and the three‐dimensional axisymmetric cases. The effectiveness of the numerical method is further demonstrated through numerical comparisons with semi‐analytical solutions provided by a reduced order model. Copyright © 2015 John Wiley & Sons, Ltd.     

Large-amplitude behavior of the Grinfeld instability: a variational approach

In previous work, we have performed amplitude expansions of the continuum equations for the Grinfeld instability and carried them to high orders. Nevertheless, the approach turned out to be restricted to relatively small amplitudes. In this article, we use a variational approach in terms of multi-cycloid curves instead. Besides its higher precision at given order, the method has the advantages of giving a transparent physical meaning to the appearance of cusp singularities and of not being restricted to interfaces representable as single-valued functions. Using a single cycloid as ansatz function, the entire calculation can be performed analytically, which gives a good qualitative overview of the system. Taking into account several but few cycloid modes, we obtain remarkably good quantitative agreement with previous numerical calculations. With a few more modes taken into consideration, we improve on the accuracy of those calculations. Our approach extends them to situations involving gravity effects. Results on the shape of steady-state solutions are presented at both large stresses and amplitudes. In addition, their stability is investigated.Received: 3 September 2003, Published online: 24 October 2003PACS: 47.20.Hw Morphological instability; phase changes - 05.70.Ln Nonequilibrium and irreversible thermodynamics - 46.25.-y Static elasticity - 81.10.Aj Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation     

Vesicles in haptotaxis with hydrodynamical dissipation

We analyze the problem of vesicle migration in haptotaxis (a motion directed by an adhesion gradient), though most of the reasoning applies to chemotaxis as well as to a variety of driving forces. A brief account has been published on this topic [#!Cantat99a!#]. We present an extensive analysis of this problem and provide a basic discussion of most of the relevant processes of migration. The problem allows for an arbitrary shape evolution which is compatible with the full hydrodynamical flow in the Stokes limit. The problem is solved within the boundary integral formulation based on the Oseen tensor. For the sake of simplicity we confine ourselves to 2D flows in the numerical analysis. There are basically two regimes (i) the tense regime where the vesicle behaves as a “droplet” with an effective contact angle. In that case the migration velocity is given by the Stokes law. (ii) The flask regime where the vesicle has a significant (on the scale of the vesicle size) contact curvature. In that case we obtain a new migration law which substantially differs from the Stokes law. We develop general arguments in order to extract analytical laws of migration. These are in good agreement with the full numerical analysis. Finally we mention several important future issues and open questions. Received 24 June 2002 and Received in final form 4 February 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: isabelle.cantat@univ-rennes1.fr     

Elastic interaction of point defects on biological membranes

The interaction between inclusions mediated by biological membranes undulations is analyzed. The interaction law is interpreted in terms of symmetries associated with inclusions. We show, in particular, that for a C3 and C3v symmetries the interaction law falls as 1/r3. We show that for completely isotropic inclusions, the dominant interaction vanishes to all orders, and the first contribution stems from the induced interaction which behaves as 1/r4. The same law holds for any other symmetry which is higher than C4. We introduce a straightforward method to compute these interactions. We point out important differences with results in the literature and explain the discrepancies.     

An advected-field method for deformable entities under flow

We study dynamics of a deformable entity (such as a vesicles under hydrodynamical constraints). We show how the problem can be solved by means of Green's functions associated with the Stokes equations. A gauge-field invariant formulation makes the study of dynamics efficient. However, this procedure has its short-coming. For example, if the fluids are not Newtonian, then no Green's function is available in general. We introduce a new approach, the advected field one, which opens a new avenue of applications. For example, non-Newtonian entities can be handled without additional deal. In addition problems like budding, droplet break-up in suspensions, can naturally be treated without additional complication. We exemplify the method on vesicles filled by a fluid having a viscosity contrast with the external fluid, and submitted to a shear flow. We show that beyond a viscosity contrast (the internal fluid being more viscous), the vesicle undergoes a tumbling bifurcation, which has a saddle-node nature. This bifurcation is known for blood cells. Indeed red cells either align in a shear flow or tumble according to whether haematocrit concentration is high or low. Received 19 December 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: chaouqi.misbah@ujf-grenoble.fr