In this letter, we describe the capillary sorting of particles by size based on dip coating. A substrate withdrawn from a liquid bath entrains a coating whose thickness depends on the withdrawal speed and the liquid properties. If the coating material contains particles, they will only be entrained when the viscous force pulling them with the substrate overcomes the opposing capillary force at the deformable meniscus. This force threshold occurs at different liquid thicknesses for particles of different sizes. Here, we show that this difference can be used to separate small particles from a mixed suspension through capillary filtration. In a bidisperse suspension, we observe three distinct filtration regimes. At low capillary numbers, Ca, no particles are entrained in the liquid coating. At high Ca, all particle sizes are entrained. For a range of capillary numbers between these two extremes, only the smallest particles are entrained while the larger ones remain in the reservoir. We explain how this technique can be applied to polydisperse suspension. We also provide an estimate of the range of capillary number to separate particles of given sizes. The combination of this technique with the scalability and robustness of dip coating makes it a promising candidate for high-throughput separation or purification of industrial and biomedical suspensions.
The displacement of a suspension of particles by an immiscible fluid in a capillary tube or in a 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 o…
An object withdrawn from a liquid bath is coated with a thin layer of liquid. Along with the liquid, impurities such as particles present in the bath can be transferred to the withdrawn substrate. Entrained particles locally modify the thickness of the film, hence altering the quality and properties of the coating. In this study, we show that it is possible to entrain the liquid alone and avoid contamination of the substrate, at sufficiently low withdrawal velocity in diluted suspensions. Using a model system consisting of a plate exiting a liquid bath, we observe that particles can remain tra…
Withdrawing a plate from a suspension leads to the entrainment of a coating layer of fluid and particles on the solid surface. In this article, we study the Landau-Levich problem in the case of a suspension of non-Brownian particles at moderate volume fraction $10\% < ϕ< 41\%$. We observe different regimes depending on the withdrawal velocity $U$, the volume fraction of the suspension $ϕ$, and the diameter of the particles $2\,a$. Our results exhibit three coating regimes. (i) At small enough capillary number $Ca$, no particles are entrained, and only a liquid film coats the plate. (ii) At lar…
In order to characterize very weak adhesive surfaces, we have developed a quantitative test inspired by the Johnson, Kendall, and Roberts adhesion test for soft adhesives, which relies on the formation and then the rupture of a capillary bridge between the surface to be tested and a liquid bath. Both the shape and the kinetics of breakage of the capillary bridge for various coatings put into contact with liquids of various viscosities and surface tensions have been studied. Several pull off regimes can be distinguished. For low pull off velocities, a quasi-static regime is observed, well descr…
The theoretical and numerical models for gravity driven coating flow on upper cylinder and sphere are formulated. Using a perturbation method, the governing equations which depend on one Bond number $Bo$ are derived for a liquid film flow down the outside of a horizontal cylinder and a sphere. They can be simplified to one-dimensional form due to the symmetries. The general structure of the two-dimensional and axisymmetric capillary waves under high $Bo$ condition is focused on. An asymptotic theory is used to solve for the free-surface profiles in the outer and inner region, respectively. Eve…
Drying of colloidal droplets on solid, rigid substrates is associated with a capillary pressure developing within the droplet. In due course of time, the capillary pressure builds up due to droplet evaporation resulting in the formation of a colloidal thin film that is prone to crack formation. In this study, we show that introducing a minimal amount of nematic liquid crystal (NLC) can completely suppress the crack formation. The mechanism behind the curbing of the crack formation may be attributed to the capillary stress-absorbing cushion provided by the elastic arrangements of the liquid cry…
Hypothesis: Lateral accumulation and film defects during drying of hard particle coatings is a common problem, typically solved using polymeric additives and surface active ingredients, which require further processing of the dried film. Capillary suspensions with their tunable physical properties, devoid of polymers, offer new pathways in producing uniform and defect free particulate coatings. Experiments: We investigated the effect of small amounts of secondary liquid on the coating's drying behavior. Stress build-up and weight loss in a temperature and humidity controlled drying chamber wer…
This work describes a mechanical approach for manipulating the capillary length and spreading of liquid coatings on flexible substrates with high gravity. Experimental verification in the literature has focused on cases under standard gravity on earth, and to the authors' knowledge, this work is the first to explore its relevance to spreading puddles under high gravity. By using centrifugation with a high-density liquid base underneath a coated substrate, it is possible to apply acceleration normal to a substrate to decrease the capillary length and increase the rate of spreading. Due to the n…
Droplet formation of suspensions is present in many industrial and technological processes such as coating and food engineering. Whilst the finite time singularity of the minimum neck diameter in capillary break-up of simple liquids can be described by well known self-similarity solutions, the pinching of non-Brownian suspension depends in a complex way on the particle dynamics in the thinning thread. Here we focus on the very dilute regime where the filament contains only isolated beads to identify the physical mechanisms leading to the pronounced acceleration of the filament thinning observe…
We study numerically the hydrodynamics of dip coating from a suspension and report a mechanism for colloidal assembly and pattern formation on smooth and uniform substrates. Below a critical withdrawal speed of the substrate, capillary forces required to deform the meniscus prevent colloidal particles from entering the coating film. Capillary forces are overcome by hydrodynamic drag only after a minimum number of particles organize in a close-packed formation within the meniscus. Once within the film, the formed assembly moves at nearly the withdrawal speed and rapidly separates from the next …
Dip-coating is a common technique used to cover a solid surface with a thin liquid film, the thickness of which was successfully predicted by the theory developed by Landau & Levich and Derjaguin in the 1940's. In this work, we present an extension of their theory to the case where the dipping bath contains two immiscible liquids, one lighter than the other, resulting in the entrainment of two thin films on the substrate. We report how the thicknesses of the coated films depend on the capillary number, on the ratios of the properties of the two liquids and on the relative thickness of the uppe…
Dip-coating consists in 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 the 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…
We employ a millimeter-scale piezoelectric acoustic actuator, which generates MHz-frequency surface acoustic waves (SAWs) in a solid substrate, to actively coat a drop of water by a macroscopic film of silicon oil as a paradigm for a small scale and low power coating system. We build upon previous studies on SAW induced dynamic wetting of a solid substrate, also known as the acoustowetting phenomena, to actively drive a model low surface-energy liquid -- silicon oil -- coat a model liquid object -- a sessile drop of water. The oil film spreads along the path of the propagating SAW and comes in…
The withdrawal of a liquid or the translation of a liquid slug in a capillary tube leads to the deposition of a thin film on the inner wall. When particles or contaminants are present in the liquid, they deposit and contaminate the tube if the liquid film is sufficiently thick. In this article, we experimentally investigate the condition under which particles are deposited during the air invasion in a capillary tube initially filled with a dilute suspension. We show that the entrainment of particles in the film is controlled by the ratio of the particle and the tube radii and the capillary num…
We assess experimentally the ability of a simple flow-based sorting device, recently proposed numerically by [Zhu et al., Soft Matter, 2014, 10, 7705-7711], to separate capsules according to their stiffness. The device consists of a single pillar with a half-cylinder cross-section which partially obstructs a flow channel so that initially centred, propagating capsules deform and circumvent the obstacle into an expanding channel (or diffuser). We perform experiments with millimetric capsules of fixed size which indicate that the deviation of the capsule in the diffuser varies monotonically with…
A solid, withdrawn from a liquid bath, entrains a thin liquid film. This simple process, first described by Landau, Levich and Derjaguin (LLD), is commonly observed in everyday life. It also plays a central role in liquid capture by animals, and is widely used for surface-coating purposes in industry. Motivated by the emerging interest in the mechanics of very soft materials, and in particular the resulting elastocapillary coupling, we develop a dip-coating model that accounts for the additional presence of a soft solid layer atop the rigid plate. The elastic response of this soft layer is des…
We study experimentally the motion and deformation of individual capsules transported by a constant volume-flux flow of low Reynolds number, through the T-junction of a channel with rectangular cross-section. We use millimetric ovalbumin-alginate capsules which we manufacture and characterise independently of the flow experiment. Centred capsules travel at constant velocity down the straight channel leading to the T-junction where they decelerate and expand in the spanwise direction before turning into one of the two identical daughter channels. There, non-inertial lift forces act to re-centre…
We report an experimental study of the drying-induced peeling of a bilayer, consisting of an elastomeric disk coated with a suspension of nanoparticles. We show that although capillary forces associated with the scale of the droplet can not compete with the adhesion of the elastomer on a surface, nevertheless large tensile stresses develop in the coating, which results in a moment bending the bilayer. We attribute this stress to the nano-menisci in the pores of the colloidal material and we propose a model that describes successfully the early stage curvature of the bilayer. Thus, we show that…
The University of Tokyo（东京大学）；Central University of Rajasthan（拉贾斯坦中央大学）；Université de Lille（里尔大学）；ESPCI Paris（巴黎高等物理化工国立工程学院）；Aoyama Gakuin University（青山学院大学）
Many microfluidics devices, coating processes or diphasic flows involve the motion of a liquid meniscus on a wet wall. This motion induces a specific viscous force, that exhibits a non-linear dependency in the meniscus velocity. We propose a review of the theoretical and experimental work made on this viscous force, for simple interfacial properties. The interface is indeed assumed either perfectly compressible (mobile interface) or perfectly incompressible (rigid interface). We show that, in the second case, the viscous force exerted by the wall on the meniscus is a combination of two power l…
In this work a Lattice Boltzmann Immersed Boundary method is used for predicting the dynamics of rigid and deformable adhesive micro carriers (1 um) navigating a capillary by the size of 10 um with 20% hematocrit. Red cells and particles are modeled as a collection of mass spring elements responding to a bending potential, an elastic potential and total enclosed area conservation constraint. Furthermore, particle surfaces are uniformly decorated with adhesive molecules (ligands) interacting with receptors disposed on the walls. Particle adhesion is modeled as a short range ligad receptor inter…
The fragmentation of liquid sheets produces a collection of droplets. The size distribution of the droplets has a considerable impact on the coating efficiency of sprays and the transport of contaminants. Although many processes commonly used particulate suspensions, the influence of the particles on the spreading dynamics of the sheet and its subsequent fragmentation has so far been considered negligible. In this paper, we consider experimentally a transient suspension sheet that expands radially. We characterize the influence of the particles on the dynamics of the liquid sheet and the fragm…
