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Water usually contains dissolved gases, and because freezing is a purifying process these gases must be expelled for ice to form. Bubbles appear at the freezing front and are then trapped in ice, making pores. These pores come in a range of sizes from microns to millimeters and their shapes are peculiar; never spherical but elongated, and usually fore-aft asymmetric. We show that these remarkable shapes result of a delicate balance between freezing, capillarity, and mass diffusion. A nonlinear ordinary differential equation suffices to describe the bubbles, which features two nondimensional numbers representing the supersaturation and the freezing rate, and two additional parameters representing simultaneous freezing and nucleation treated as the initial condition. Our experiments provide us with a large variety of pictures of bubble shapes. We show that all of these bubbles have their rounded tip well described by an asymptotic regime of the differential equation and that most bubbles can have their full shape quantitatively matched by a full solution. This method enables the measurement of the freezing conditions of ice samples, and the design of freeze-cast porous materials. Furthermore, the equation exhibits a bifurcation that explains why some bubbles grow indefinitely and make long cylindrical “ice worms,” well known to glaciologists. 

At large scales, particulate suspensions flow like homogeneous viscous liquids, but at the particle scale, the role of the local heterogeneity brought by the particles cannot be neglected. The volume fraction also matters; in dense suspensions, particulate effects can be felt across distances much larger than the particle diameter. Therefore, whether a suspension should behave as a homogeneous or heterogeneous fluid is a matter of scale. Here, we consider the canonical situation of the pinch-off of suspension drops to study the behavior of suspensions at different scales. Initially, the filament of suspension thins down like a homogeneous liquid until reaching a critical thickness at which the thinning accelerates. Eventually, a region devoid of particles appears, and the breakup occurs similarly to a homogeneous viscous liquid. Although this problem have been studied for almost 20 y, the role of heterogeneity in the acceleration of the pinch-off is still not understood. We show that the onset of heterogeneity corresponds to the dislocation of the suspensions where local fluctuations in particle concentration increase. We derive scaling laws for the dynamics in the heterogeneous regime and develop a model to predict the coherence length at which the discrete nature of the particles appears, and we demonstrate that this length depends both on the particle size and on the volume fraction of the suspension. We extend this approach to polydisperse suspensions. Our work sheds light on the mesoscopic scale below which starts the heterogeneous regime and a continuum approach is not valid anymore. 

In this study, we investigate the transition between the Newtonian and the viscoelastic regimes during the pinch-off of droplets of dilute polymer solutions and discuss its link to the coil-stretch transition. The detachment of a drop from a nozzle is associated with the formation of a liquid neck that causes the divergence of the local stress in a vanishingly small region. If the liquid is a polymer solution, this increasing stress progressively unwinds the polymer chains, up to a point where the resulting increase in the viscosity slows down drastically the thinning. This threshold to a viscoelastic behavior corresponds to a macroscopic strain rate. In the present study, we characterize the variations of with respect to the polymer concentration and molar weight, to the solvent viscosity, and to the nozzle size, i.e. , the weight of the drop. We provide empirical scaling laws for these variations. We also analyze the thinning dynamics at the transition and show that it follows a self-similar dynamics controlled by the time scale  c −1 . This characteristic time is different and always shorter than the relaxation time of the polymer. 

Dip coating consists of withdrawing a substrate from a bath to coat it with a thin liquid layer. This process is well understood for homogeneous fluids, but heterogeneities, such as particles dispersed in liquid, lead to more complex situations. Indeed, particles introduce a new length scale, their size, in addition to the thickness of the coating film. Recent studies have shown that, at first order, the thickness of the coating film for monodisperse particles can be captured by an effective capillary number based on the viscosity of the suspension, providing that the film is thicker than the particle diameter. However, suspensions involved in most practical applications are polydisperse, characterized by a wide range of particle sizes, introducing additional length scales. In this study, we investigate the dip coating of suspensions having a bimodal size distribution of particles. We show that the effective viscosity approach is still valid in the regime where the coating film is thicker than the diameter of the largest particles, although bidisperse suspensions are less viscous than monodisperse suspensions of the same solid fraction. We also characterize the intermediate regime that consists of a heterogeneous coating layer and where the composition of the film is different from the composition of the bath. A model to predict the probability of entraining the particles in the liquid film depending on their sizes is proposed and captures our measurements. In this regime, corresponding to a specific range of withdrawal velocities, capillarity filters the large particles out of the film. 

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.