Indentation of an elastic disk on a circular supporting ring.

Thin elastic two-dimensional systems under compressive stresses may relieve part of their stretching energy by developing out-of-plane undulations. We investigate experimentally and theoretically the indentation of an elastic disk supported by a circular ring and show that compressive stresses are relieved via two different routes: either developing buckles which are spread over the system or developing a d-cone where deformation is concentrated in a subregion of the system. We characterize the indentation threshold for wrinkles or d-cone existence as a function of aspect ratio.

Boundary-induced inhomogeneity of particle layers in the solidification of suspensions.

When a suspension freezes, a compacted particle layer builds up at the solidification front with noticeable implications on the freezing process. In a directional solidification experiment of monodisperse suspensions in thin samples, we evidence a link between the thickness of this layer and the sample depth. We attribute it to an inhomogeneity of particle density that is attested by the evidence of crystallization at the plates and of random close packing far from them. A mechanical model based on the resulting modifications of permeability enables us to relate the layer thickness to this inhomogeneity and to select the distribution of particle density that yields the best fit to our data. This distribution involves an influence length of sample plates of about 11 particle diameters. Altogether, these results clarify the implications of boundaries on suspension freezing. They may be useful to model polydisperse suspensions with large particles playing the role of smooth boundaries with respect to small ones.

Wall friction and Janssen effect in the solidification of suspensions.

We address the mechanical effect of rigid boundaries on freezing suspensions. For this we perform the directional solidification of monodispersed suspensions in thin samples and we document the thickness h of the dense particle layer that builds up at the solidification front. We evidence a change of regime in the evolution of h with the solidification velocity V with, at large velocity, an inverse proportionality and, at low velocity, a much weaker trend. By modelling the force balance in the critical state for particle trapping and the dissipation phenomena in the whole layer, we link the former evolution to viscous dissipation and the latter evolution to solid friction at the rigid sample plates. Solid friction is shown to induce an analog of the Janssen effect on the whole layer. We determine its dependence on the friction coefficient between particles and plates, on the Janssen's redirection coefficient in the particle layer, and on the sample depth. Fits of the resulting relationship to data confirm its relevance at all sample depths and provide quantitative determinations of the main parameters, especially the Janssen's characteristic length and the transition thickness h between the above regimes. Altogether, this study thus clarifies the mechanical implication of boundaries on freezing suspensions and, on a general viewpoint, provides a bridge between the issues of freezing suspensions and of granular materials.

Interaction of Multiple Particles with a Solidification Front: From Compacted Particle Layer to Particle Trapping.

The interaction of solidification fronts with objects such as particles, droplets, cells, or bubbles is a phenomenon with many natural and technological occurrences. For an object facing the front, it may yield various fates, from trapping to rejection, with large implications regarding the solidification pattern. However, whereas most situations involve multiple particles interacting with each other and the front, attention has focused almost exclusively on the interaction of a single, isolated object with the front. Here we address experimentally the interaction of multiple particles with a solidification front by performing solidification experiments of a monodisperse particle suspension in a Hele-Shaw cell with precise control of growth conditions and real-time visualization. We evidence the growth of a particle layer ahead of the front at a close-packing volume fraction, and we document its steady-state value at various solidification velocities. We then extend single-particle models to the situation of multiple particles by taking into account the additional force induced on an entering particle by viscous friction in the compacted particle layer. By a force balance model this provides an indirect measure of the repelling mean thermomolecular pressure over a particle entering the front. The presence of multiple particles is found to increase it following a reduction of the thickness of the thin liquid film that separates particles and front. We anticipate the findings reported here to provide a relevant basis to understand many complex solidification situations in geophysics, engineering, biology, or food engineering, where multiple objects interact with the front and control the resulting solidification patterns.

Mechanical characterization of cross-linked serum albumin microcapsules.

Controlling the deformation of microcapsules and capsules is essential in numerous biomedical applications. The mechanical properties of the membrane of microcapsules made of cross-linked human serum albumin (HSA) are revealed by two complementary experiments in the linear elastic regime. The first provides the surfacic shear elastic modulus Gs by the study of small deformations of a single capsule trapped in an elongational flow: Gs varies from 0.002 to 5 N m(-1). The second gives the volumic Young's modulus E of the membrane by shallow and local indentations of the membrane with an AFM probe: E varies from 20 kPa to 1 MPa. The surfacic and volumic elastic moduli increase with the size of the capsule up to three orders of magnitude and with the protein concentration of the membrane. The membrane thickness is evaluated from these two membrane mechanical characteristics and increases with the size and the initial HSA concentration from 2 to 20 µm.

Self-organized dendritic sidebranching in directional solidification: sidebranch coherence within uncorrelated bursts.

We experimentally study the level of organization of dendritic sidebranching in directional solidification. For this, we extract successive interface positions at a fixed distance from the dendrite tips and we perform various correlation analyses. The sidebranching signals appear composed of randomly distributed bursts in which sidebranching coherence is surprisingly large and robust. This is attested by the large autocorrelation found in single bursts and the large cross-correlation found in any couple of bursts, even belonging to different sides of a dendrite or to different dendrites. However, the phase coherence of sidebranching breaks down at the transition between bursts. This restricts the coherence of extended sidebranching signals to a mean burst length and prevents the occurrence of large scale cross-correlation between them. This balanced view on sidebranching coherence stresses the capability of self-organization of dendrites in material science and sheds light on the nature of sidebranching on curved growing forms.

Dynamics of vesicle unbinding under axisymmetric flow.

The competition between adhesion and external flow to unbind settled vesicles from substrates is investigated. An experimental setup is developed to apply a hydrodynamic pulling force in the range of a few piconewtons to a vesicle with retained axisymmetry. In the limit of a small excess of membrane area, vesicles are found to transit during unbinding from a process of fluid film thickening at constant contact area to a finite-time process of contact radius drop to zero with an exponent 1/2. Both characteristic times vary linearly with the inverse flow rate. On the contrary, deflated vesicles under a moderate pulling force exhibit a decrease of contact area at a constant film thickness before a film thickening.