Equilibrium sedimentation profiles of charged colloidal suspensions

We investigate the sedimentation equilibrium of a charge stabilized colloidal suspension in the regime of low ionic strength. We analyze the asymptotic behaviour of the density profiles on the basis of a simple Poisson--Boltzmann theory and show that the effective mass we can deduce from the barometric law corresponds to the actual mass of the colloidal particles, contrary to previous studies.Comment: 13 pages, 4 figures, 1 tabl

New analytical progress in the theory of vesicles under linear flow

Vesicles are becoming a quite popular model for the study of red blood cells (RBCs). This is a free boundary problem which is rather difficult to handle theoretically. Quantitative computational approaches constitute also a challenge. In addition, with numerical studies, it is not easy to scan within a reasonable time the whole parameter space. Therefore, having quantitative analytical results is an essential advance that provides deeper understanding of observed features and can be used to accompany and possibly guide further numerical development. In this paper shape evolution equations for a vesicle in a shear flow are derived analytically with precision being cubic (which is quadratic in previous theories) with regard to the deformation of the vesicle relative to a spherical shape. The phase diagram distinguishing regions of parameters where different types of motion (tank-treading, tumbling and vacillating-breathing) are manifested is presented. This theory reveals unsuspected features: including higher order terms and harmonics (even if they are not directly excited by the shear flow) is necessary, whatever the shape is close to a sphere. Not only does this theory cure a quite large quantitative discrepancy between previous theories and recent experiments and numerical studies, but also it reveals a new phenomenon: the VB mode band in parameter space, which is believed to saturate after a moderate shear rate, exhibits a striking widening beyond a critical shear rate. The widening results from excitation of fourth order harmonic. The obtained phase diagram is in a remarkably good agreement with recent three dimensional numerical simulations based on the boundary integral formulation. Comparison of our results with experiments is systematically made.Comment: a tex file and 6 figure

3D Numerical simulations of vesicle and inextensible capsule dynamics

published in Journal of Computational PhysicsInternational audienceVesicles are locally-inextensible fluid membranes while inextensible capsules are in addition endowed with in-plane shear elasticity mimicking the cytoskeleton of red blood cells (RBCs). Boundary integral (BI) methods based on the Green's function techniques are used to describe their dynamics, that falls into the category of highly nonlinear and nonlocal dynamics. Numerical solutions raise several obstacles and challenges that strongly impact the results. Of particular complexity is (i) the membrane inextensibility, (ii) the mesh stability and (iii) numerical precisions for evaluation of the boundary integral equations. Despite intense research these questions are still a matter of debate. We regularize the single layer integral by subtraction of exact identities for the terms involving the normal and the tangential components of the force. In addition, the regularized kernel remains explicitly self-adjoint. The stability and precision of BI calculation is enhanced by taking advantage of additional quadrature nodes located in vertices of an auxiliary mesh, constructed by a standard refinement procedure from the main mesh. We extend the partition of unity technique to boundary integral calculation on triangular meshes: We split the calculation of the boundary integral between the original and the auxiliary mesh using a smooth weight function, which takes the distance between the source and the target as the argument and falls to zero beyond a certain cut-off distance. We provide an efficient lookup algorithm that allows us to discard most of the vertices of the auxiliary mesh lying beyond the cut-off distance from a given point without actually calculating the distances to them. The proposed algorithm offers the same treatment of near-singular integration regardless if the source and the target points belong to the same surface or not. Additional innovations are used to increase the stability and precision of the method: The bending forces are calculated by differential geometry expressions using local coordinates defined in vicinity of each vertex. The approximation of the surface in vicinity of a vertex is obtained by fitting with a second-degree polynomial of local coordinates. We solve for the Lagrange multiplier associated with membrane incompressibility using two penalization parameters per suspended entity: one for deviation of the global area from prescribed value and another for the sum of squares of local strains defined on each vertex. The proposed advancement is to vary the penalization parameters at each time step in such a way, that the global area of each membrane be conserved and the sum of squares of local strains be at minimum. This optimization is achieved by solving a linear system of rank three times the number of entities involved in the simulation. If no auxiliary mesh is used, the method reduces to steepest descent method thanks to the explicit self-adjointness of the regularized single-layer kernel in the boundary integral equation. Inextensible capsules, a model of RBC, are studied by storing the position in the reference configuration for each vertex. The elastic force is then calculated by direct variation of the elastic energy. Various nonequilibrium physical examples on vesicles and capsules will be presented and the convergence and precision tests highlighted. Overall, a good convergence is observed with numerical error inversely proportional to the number of vertices used for surface discretization, the highest order of convergence allowed by piece-wise linear interpolation of the surface

Dynamics and rheology of a dilute suspension of vesicles: higher order theory

Vesicles under shear flow exhibit various dynamics: tank-treading ($tt$), tumbling ($tb$) and vacillating-breathing ($vb$). A consistent higher order theory reveals a direct bifurcation from $tt$ to $tb$ if $C_a\equiv \tau \dot\gamma$ is small enough ($\tau$= vesicle relaxation time towards equilibrium shape, $\dot\gamma$=shear rate). At larger $C_a$ the $tb$ is preceded by the $vb$ mode. For $C_a\gg 1$ we recover the leading order original calculation, where the $vb$ mode coexists with $tb$. The consistent calculation reveals several quantitative discrepancies with recent works, and points to new features. We analyse rheology and find that the effective viscosity exhibits a minimum at $tt-tb$ and $tt-vb$ bifurcation points.Comment: 4 pages, 5 figure

Dynamics of Bio-Polymeric Brushes Growing from a Cellular Membrane: Tentative Modelling of the Actin Turnover within an Adhesion Unit; the Podosome

Podosomes are involved in the adhesion process of various cells to a solid substrate. They have been proven to consist of a dense actin core surrounded by an actin cloud. The podosomes, which nucleate when the cell comes in the vicinity of a substrate, contribute to link the membrane to the solid surface, but rather than frozen links, collective dynamical behaviors are experimentally observed. Depending on the differentiation stage, podosomes assemble and form clusters, rings or belts. Considering the dynamics of a polymeric brush, we design a simple model aiming at the description of a single podosome, the basic unit of these complex adhesion-structures and compare our theoretical conclusions to recent experimental results. Particularly, we explain, by solving the diffusion problem around the podosome, why the structure is likely to have a finite life-span

Activated drying in hydrophobic nanopores and the line tension of water

International audienceWe study the slow dynamics of water evaporation out of hydro-phobic cavities by using model porous silica materials grafted with octylsilanes. The cylindrical pores are monodisperse, with a radius in the range of 1–2 nm. Liquid water penetrates in the nanopores at high pressure and empties the pores when the pressure is lowered. The drying pressure exhibits a logarithmic growth as a function of the driving rate over more than three decades, showing the ther-mally activated nucleation of vapor bubbles. We find that the slow dynamics and the critical volume of the vapor nucleus are quantita-tively described by the classical theory of capillarity without adjust-able parameter. However, classical capillarity utterly overestimates the critical bubble energy. We discuss the possible influence of surface heterogeneities, long-range interactions, and high-curvature effects, and we show that a classical theory can describe vapor nucleation provided that a negative line tension is taken into account. The drying pressure then provides a determination of this line tension with much higher precision than currently available methods. We find consistent values of the order of −30 pN in a variety of hydrophobic materials. drying transition | hydrophobicity | kinetics | nanobubbles

Wetting controlled boiling at the nanoscale

Boiling is the out-of-equilibrium transition which occurs when a liquid is heated above its vaporization temperature. At the nanoscale, boiling may be triggered by irradiated nanoparticles immersed in water or nanocomposite surfaces and often results in micro-explosions. It is generally believed that nanoscale boiling occurs homogeneously when the local fluid temperature exceeds its spinodal temperature, around 573 K for water. Here, we employ molecular dynamics simulations to show that nanoscale boiling is an heterogenous phenomenon occuring when water temperature exceeds a wetting dependent onset temperature. This temperature can be 100 K below spinodal temperature if the solid surface is weakly wetting water. In addition, we show that boiling is a slow process controlled by the solid-liquid interfacial thermal conductance, which turns out to decrease significantly prior to phase change yielding long nucleation times. We illustrate the generality of this conclusion by considering both a spherical metallic nanoparticle immersed in water and a solid surface with nanoscale wetting heterogeneities. These results pave the way to control boiling using nanoscale patterned surfaces

Crack repulsion and attraction in Linear Elastic Fracture Mechanics

Predicting the direction of a crack submitted to mixed mode loading is key in a variety of domains ranging from earth science to structure safety. In the context of Linear Elastic Fracture Mechanics (LEFM), many bifurcation criteria have been proposed overtime: the Principle of Local Symmetry (PLS) [1], the Maximum Tangential Stress (MTS)[2], the Strain Energy Density (SED) criterion[3], ... The MTS and PLS are the most widely used and give extremely similar results [4]. Whether the theoretical framework of LEFM+PLS is sufficient to study propagation paths of interacting cracks is still under debate. The simplest case of crack interaction is sometimes referred in the literature as en-passant cracks pairs (EP-cracks): two initially straight, parallel and offset cracks which are submitted to far-field opening stress. It was observed experimentally many time that EP-cracks propagate straight ahead until their inner tips overlap, where they begin to attract one another. This behavior can be reproduced correctly assuming the PLS [5]. However, it has been observed that cracks may repel one another in some instances [6]. In this case, it seems that the PLS systematically underestimates the angle of repulsion [7]. We present a simple iterative method, based on FEM computation of the stress state at a given time and determination of the SIF after an infinitesimally small propagation step, to compute quickly and accurately the crack propagation direction in the context of LEFM and under the assumption of PLS. Applying it to the case of EP-cracks, we were able to determine under which conditions the trajectories were initially repulsive or attractive. We find surprising results, among which the fact that perfectly aligned cracks do not interact and that repulsion is a non-monotonous function of the inner tips' separation distances. This method is robust and fast enough to be iterated in order to compute full crack paths. We numerically reproduced the trajectories observed in the experiments presented in an earlier paper [6]. This study allowed us to provide further insights into quantifying the impact of boundary and initial conditions on the shape of crack paths, and into the limitations of applying the LEFM+PLS framework to the case of interacting cracks.   References: [1] B. Cotterell and J.R. Rice. Slightly curved or kinked cracks. International Journal of Fracture, 16(2):155?169, 1980. [2] F Erdogan and G C Sih. On the crack extension in plane loading and transverse shear. Journal Basic Engr., 85:519?527, 1963. [3] G.C. Sih. Some basic problems in fracture mechanics and new concepts. Engineering Fracture Mechanics, 5(2):365?377, 1973. [4] J.B. Leblond. Mécanique de la rupture fragile et ductile. Hermes Science publication, Editions Lavoisier, 2003. [5] Melissa L. Fender, Frédéric Lechenault, and Karen E. Daniels. Universal shapes formed by two interacting cracks. Physical Review Letters, 105(12):2?5, 2010. [6] Marie-Julie Dalbe, Juha Koivisto, Loïc Vanel, Amandine Miksic, Osvanny Ramos, Mikko Alava, and Stéphane Santucci. Repulsion and Attraction between a Pair of Cracks in a Plastic Sheet. Physical review letters, 114(20):205501, 2015