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.

Reversibility of crumpling on compressed thin sheets: reversibility of crumpling.

Compressing thin sheets usually yields the formation of singularities which focus curvature and stretching on points or lines. In particular, following the common experience of crumpled paper where a paper sheet is crushed in a paper ball, one might guess that elastic singularities should be the rule beyond some compression level. In contrast, we show here that, somewhat surprisingly, compressing a sheet between cylinders make singularities spontaneously disappear at large compression. This "stress defocusing" phenomenon is qualitatively explained from scale-invariance and further linked to a criterion based on a balance between stretching and curvature energies on defocused states. This criterion is made quantitative using the scalings relevant to sheet elasticity and compared to experiment. These results are synthesized in a phase diagram completed with plastic transitions and buckling saturation. They provide a renewed vision of elastic singularities as a thermodynamic condensed phase where stress is focused, in competition with a regular diluted phase where stress is defocused. The physical differences between phases is emphasized by determining experimentally the mechanical response when stress is focused or defocused and by recovering the corresponding scaling laws. In this phase diagram, different compression routes may be followed by constraining differently the two principal curvatures of a sheet. As evidenced here, this may provide an efficient way of compressing a sheet that avoids the occurrence of plastic damages by inducing a spontaneous regularization of geometry and stress.

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.