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 monodispersed 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 induced by the sample plates. A mechanical model enables us to relate it to the layer thickness with a dependency on the sample depth 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 nine particle diameters. These results clarify the implications of boundaries on suspension freezing. They may be useful to model polydispersed suspensions since large particles could play the role of smooth boundaries with respect to small ones.Comment: 16 pages, 13 figure

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.Comment: 13 pages, 10 figures, submitted to Langmui

Phase dynamics in convective structures : from small scale instabilities to large-scale time-dependence

International audienc

Capillarité, anisotropie et formes de croissance

National audienc

The significant digit law : a paradigm of statistical scale symmetries

In many different topics, the most significant digits of data series display a non-uniform distribution which points to an equiprobability of logarithms. This surprising ubiquitous property, known as the significant digit law, is shown here to follow from two similar, albeit different, scale symmetries: the scale-invariance and the scale-ratio invariance. After having legitimized these symmetries in the present context, the corresponding symmetric distributions are determined by implementing a covariance criterion. The logarithmic distribution is identified as the only distribution satisfying both symmetries. Attraction of other distributions to this most symmetric distribution by dilation, stretching and merging is investigated and clarified. The natures of both the scale-invariance and the scale-ratio invariance are further analyzed by determining the structure of the sets composed by the corresponding symmetric distributions. Altogether, these results provide new insights into the meaning and the role of scale symmetries in statistics

Lecture : “Hydrodynamics and thermodynamics at small scale”

International audienc

Lecture « From amplitude equation to phase diffusion dynamics”

International audienc

Front propagation in stirred media

International audienceThis work experimentally investigates the propagation of chemical fronts in steady laminar cellular flows at large Péclet numbers and large Damköhler numbers. Its objective consists in using simple 2d flows for building a relevant model of front propagation that may be extrapolated to more complex configurations. Fronts are generated in an aqueous solution by an auto-catalytic oxydo-reduction reaction : the chlorite-iodide rection. They propagate in a thin channel in which a chain of counter-rotative parallel vortices is induced by electro-convection. The form, the dynamics and the mean velocity of fronts are determined in the whole Hele-Shaw regime of the flow. This provides the experimental ground for addressing the modeling of the evolution of the front mean velocity with the flow amplitude. Interestingly, both the front velocities and the front trajectories displayed experimentally are well recovered from a least-time criterion model, including their intrinsic dependence on the boundary layer width. Effective front propagation in a laminar steadily stirred medium is thus understood from an optimization principle similar to the Fermat principle of ray propagation in heterogeneous media

Pattern formation in the solidification of suspensions : the role of Self-Organized Criticality

International audienc