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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. 

Confined flows of particles can lead to clogging, and therefore failure, of various fluidic systems across many applications. As a result, design guidelines need to be developed to ensure that clogging is prevented or at least delayed. In this Letter, we investigate the influence of the angle of reduction in the cross section of the channel on the bridging of semidilute and dense non-Brownian suspensions of spherical particles. We observe a decrease of the clogging probability with the reduction of the constriction angle. This effect is more pronounced for dense suspensions close to the maximum packing fraction where particles are in contact in contrast to semidilute suspensions. We rationalize this difference in terms of arch selection. We describe the role of the constriction angle and the flow profile, providing insights into the distinct behavior of semidilute and dense suspensions. 

Hypothesis: The dip coating of suspensions made of monodisperse non-Brownian spherical particles dispersed in a Newtonian fluid leads to different coating regimes depending on the ratio of the particle diameter to the thickness of the film entrained on the substrate. In particular, dilute particles dispersed in the liquid are entrained only above a threshold value of film thickness. In the case of anisotropic particles, in particular fibers, the smallest characteristic dimension will control the entrainment of the particle. Furthermore, it is possible to control the orientation of the anisotropic particles depending on the substrate geometry. In the thick film regime, the Landau-Levich-Derjaguin model remains valid if one account for the change in viscosity. Experiment: To test the hypotheses, we performed dip-coating experiments with dilute suspensions of non-Brownian fibers with different length-to-diameter aspect ratios. We characterize the number of fibers entrained on the surface of the substrate as a function of the withdrawal velocity, allowing us to estimate a threshold capillary number below which all the particles remain in the liquid bath. Besides, we measure the angular distribution of the entrained fibers for two different substrate geometries: flat plates and cylindrical rods. We then measure the film thickness for more concentrated fiber suspensions. Findings: The entrainment of the fibers on a flat plate and a cylindrical rod is primarily controlled by the smaller characteristic length of the fibers: their diameter. At first order, the entrainment threshold scales similarly to that of spherical particles. The length of the fibers only appears to have a minor influence on the entrainment threshold. No preferential alignment is observed for non-Brownian fibers on a flat plate, except for very thin films, whereas the fibers tend to align themselves along the axis of a cylindrical rod for a large enough ratio of the fiber length to the radius of the cylindrical rod. The Landau-Levich-Derjaguin law is recovered for more concentrated suspension by introducing an effective capillary number accounting for the change in viscosity. 

The displacement of a suspension of particles by an immiscible fluid in a capillary tube or in porous media is a canonical configuration that finds application in a large number of natural and industrial applications, including water purification, dispersion of colloids and microplastics, coating and functionalization of tubings. The influence of particles dispersed in the fluid on the interfacial dynamics and on the properties of the liquid film left behind remain poorly understood. Here, we study the deposition of a coating film on the walls of a capillary tube induced by the translation of a suspension plug pushed by air. We identify the different deposition regimes as a function of the translation speed of the plug, the particle size, and the volume fraction of the suspension. The thickness of the coating film is characterized, and we show that similarly to dip coating, three coating regimes are observed, liquid only, heterogeneous, and thick films. We also show that, at first order, the thickness of films thicker than the particle diameter can be predicted using the effective viscosity of the suspension. Nevertheless, we also report that for large particles and concentrated suspensions, a shear-induced migration mechanism leads to local variations in volume fraction and modifies the deposited film thickness and composition. 

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. 

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.