Caging and fluid deformations in dense bidisperse suspensions

We investigate the link between the geometric environment of particles, the local deformations of the solvent, and the bulk effective viscosity in non-Brownian suspensions. First, we discuss the caging of particles by their neighbors,and especially the caging of small particles by large ones in bidisperse suspensions.We develop a model that attributes an effective volume to particles depending on their environment, and yields the local deformations and effective viscosity. We compare this model to data from the literature, as well as to our own experiments with suspensions of non-Brownian polystyrene beads. Using dissolved polymers and their coil-stretch transition as strain probes, we measure the local deformation of the liquid and the effect of caging thereon. We obtain a linear relationship between the amplified local strain rate and the particle volume fraction, in which the critical volume fraction $\phi_\mathrm{c}$ appears as an effective volume of the particles; this relationship is found valid up into the dense regime.Comment: 6 pages, 3 figure

Impact et solidification de gouttes d'eau

Whenever a water drop impacts a cold surface – whose surface temperature is lower than 0°C – it freezes as it spreads. The solidification slows the drop's spreading down, eases its fragmentation into droplets, leads to the liquid's retraction and gives the frozen drop a certain shape. The nature of the cold surface is crucial in the freezing process. Starting from the Stefan problem, we developed a model for the solidification dynamics, which takes into account the thermal diffusion within the substrate. This model yields a better appreciation of the influence of the substrate's thermal properties – its temperature and thermal effusivity – over the liquid's rate of freezing. It enables us to quantitatively predict the dynamics of solidification, and therefore to study the freezing of a drop during its impact. As regards the drop's spreading, we demonstrated that the effect of freezing could be assimilated to that of viscosity, as it slows the flow down. We showed that the fragmentation of a drop at low temperature was due to an increase in the density of air. Once spread, the drop is trapped by the ice, which hinders its retraction. We established a link between the shape of the spread drop and the duration of its trapping. Finally, we showed that the competition between the retraction of liquid water on ice and its freezing led to the different patterns observed.Lorsqu’une goutte d’eau tombe sur une surface froide – dont la température est inférieure à 0◦C – elle se met à geler en même temps qu’elle s’étale. La solidification ralentit l’étalement de la goutte, facilite sa fragmentation en gouttelettes, entraîne la rétraction de la goutte, et donne une certaine forme à la goutte gelée. La nature de la surface froide est déterminante dans le processus de solidification. Sur la base du problème de Stefan, nous avons développé un modèle de dynamique de solidification, prenant en compte la diffusion thermique dans le substrat. Ce modèle apporte une meilleure compréhension de l’influence des propriétés thermiques du substrat – sa température, son effusivité thermique – sur la vitesse de solidification d’un liquide. Il nous permet de prédire quantitativement la dynamique de solidification, et ainsi d’étudier la congélation d’une goutte pendant son impact. En ce qui concerne l’étalement de la goutte, nous avons montré que l’effet de la solidification pouvait être assimilée à celui de la viscosité, en ce qu’il ralentit l’écoulement. Nous avons montré que la fragmentation de la goutte à basse température est dû à l’augmentation de la densité de l’air. Une fois étalée, la goutte est piégée par la glace, qui l’empêche de se rétracter. Nous avons établi un lien entre la forme de la goutte étalée et la durée nécessaire à sa libération. Enfin, nous avons montré que la compétition entre la rétraction de l’eau liquide sur la glace et sa congélation était à l’origine des différents motifs observés

Impact et solidification de gouttes d'eau

Whenever a water drop impacts a cold surface – whose surface temperature is lower than 0°C – it freezes as it spreads. The solidification slows the drop's spreading down, eases its fragmentation into droplets, leads to the liquid's retraction and gives the frozen drop a certain shape. The nature of the cold surface is crucial in the freezing process. Starting from the Stefan problem, we developed a model for the solidification dynamics, which takes into account the thermal diffusion within the substrate. This model yields a better appreciation of the influence of the substrate's thermal properties – its temperature and thermal effusivity – over the liquid's rate of freezing. It enables us to quantitatively predict the dynamics of solidification, and therefore to study the freezing of a drop during its impact. As regards the drop's spreading, we demonstrated that the effect of freezing could be assimilated to that of viscosity, as it slows the flow down. We showed that the fragmentation of a drop at low temperature was due to an increase in the density of air. Once spread, the drop is trapped by the ice, which hinders its retraction. We established a link between the shape of the spread drop and the duration of its trapping. Finally, we showed that the competition between the retraction of liquid water on ice and its freezing led to the different patterns observed

The onset of heterogeneity in the pinch-off of suspension drops.

SignificanceThe pinch-off of a liquid drop extruded from a nozzle is a canonical situation that involves a series of self-similar regimes ending in a finite-time singularity. This configuration allows for exploring capillary flows over a large range of scales. In the case of suspension drops, the presence of particles breaks the self-similarity by introducing a length scale that can be much larger than the particle diameter. This length scale is a signature of the heterogeneities and delimitates a regime, in which a continuum approach of a suspension can be used from a regime where the discrete nature of the particles is involved

Droplet detachment and pinch-off of bidisperse particulate suspensions.

When a droplet is generated, the ligament connecting the drop to the nozzle thins down and eventually pinches off. Adding solid particles to the liquid phase leads to a more complex dynamic, notably by increasing the shear viscosity. Moreover, it introduces an additional length scale to the system, the diameter of the particles, which eventually becomes comparable to the diameter of the ligament. In this paper, we experimentally investigate the thinning and pinch-off of drops of suspensions with two different sizes of particles. We characterize the thinning for different particle size ratios and different proportions of small particles. Long before the pinch-off, the thinning rate is that of an equivalent liquid whose viscosity is that of the suspension. Later, when the ligament thickness approaches the size of the large particles, the thinning accelerates and leads to an early pinch-off. We explain how the bidisperse particle size distribution lowers the viscosity by making the packing more efficient, which speeds up the thinning. This result can be used to predict the dynamics of droplet formation with bidisperse suspensions

Solidification dynamic of an impacted drop

17 pages, 6 figuresInternational audienceThis paper is dedicated to the solidification of a water drop impacting a cold solid surface. In a first part, we establish a 1D solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamic of a liquid on a cold substrate, taking into account the thermal properties of this substrate. This model is then experimentally validated through a 1D solidification setup, using different liquids and substrates. In a second part, we show that during the actual drop spreading, a thin layer of ice develops between the water and the substrate, and pins the contact line at its edge when the drop reaches its maximal diameter. The liquid film then remains still on its ice and keeps freezing. This configuration lasts until the contact line eventually depins and the liquid film retracts on the ice. We measure and interpret this crucial time of freezing during which the main ice layer is built. Finally, we compare our 1D model prediction to the thickness of this ice pancake and we find a very good agreement. This allows us to provide a general expression for the frozen drop main thickness, using the drop impact and liquid parameters