Session D34: Drops IV: Particle-Laden Drops

Impact of particle laden drops onto surfaces of various wettability

Understanding characteristics of the impact of complex drops (liquid and solid particles) onto substrates is important for many applications, e.g. for additive manufacturing. Complex drops (diameter $\approx$ 3.8 mm) were produced using polyethylene microspheres dispersed in deionized water. Drop impact was investigated on substrates with different wettability (contact angles $<$5$^{\circ}$ and 95$^{\circ}$) using high-speed cameras and image processing methods. By varying speed of the drops (1.7 to 3.7 m/s), diameter of the particles (200 and 500 $\mu$m) and particles volume fraction (0 to 35${\%}$), the influence of these variables on the impact dynamics of the drop and the distribution of particles after the impact was studied. For hydrophilic substrate, drops with 200 $\mu$m particles are arranged in a ring after the impact. For hydrophobic substrate, drops can split into several drops depending on drop velocity, size and volume fraction of particles. Also, the dynamics of drop spreading was elucidated.   

Yield stress fluid droplet impact on coated surfaces

Yield stress fluids, including gels and pastes, are effectively fluid at high stress and solid at low stress. In liquid-solid impacts, these fluids can stick and accumulate where they impact, motivating several applications of these rheologically-complex materials. Here we use high-speed imaging to experimentally study liquid-solid impact of yield stress fluids on dry and precoated surfaces. With a precoating of the same material, we can observe large, long-lifetime ejection sheets with redirected momentum that extend away from the impact location. Under critical splash conditions, sheet breakup occurs and ejected droplets can be nonspherical and threadlike due to the inability of capillary stresses to deform material above a certain lengthscale. By varying the droplet size, impact velocity, surface coating thickness, and rheological material properties, we develop appropriate dimensionless parameters, quantify splash characteristics including height and radial extent of deposition, and present a regime map of impact behaviors.   

Monolayer Splat

We investigate experimentally and numerically the evolution of dense suspension drops that collide against a smooth solid surface and flatten into a rapidly expanding monolayer. Further expansion of the monolayer creates a lace-like pattern of particle clusters separated by particle-free regions. Agreement between the measured expansion rates, and those calculated using a force balance on the outermost particle, demonstrates that the splat expands as fast as the edge particle moves. We also present a model describing how the inhomogeneous particle distribution within the splat grows from slight initial fluctuations. Two-dimensional simulations using this model yield average instability growth rates and saturation values in quantitative agreement with measurements. This shows the spatial inhomogeneity can be captured by balancing forces acting on individual particles as well.   

Splashing onset in dense suspension droplets

We investigate the splashing onset of droplets of dense suspensions upon the impact onto a solid substrate. Unlike in the splashing of pure liquid droplets, the ejecta of dense suspensions are individual solid particles. We show that a global hydrodynamic balance is unable to predict the splashing onset and propose to replace it by an energy balance at the level of the particles in the suspension. The key ingredient for this balance is to take into account collisions between the particles at the outer edge of the droplet. We experimentally verify that the resulting, particle-based Weber number gives a reliable, particle size and density dependent splash onset criterion. We further show that the same argument also explains why, in bimodal systems, smaller particles are more likely to escape than larger ones. Finally, we show that increasing the viscosity of the suspending liquid effectively decreases the efficiency of the collisions between particles and, consequently, increases the splash onset velocity.   

Dense suspension splash

Upon impact onto a solid surface at several meters-per-second, a dense suspension plug splashes when liquid-coated particles are ejected from the plug bulk. We use discrete-particle simulations to examine the momentum transfers responsible for splash formation. We find that a simulation using a densely packed plug containing dry, noncohesive, inelastic grains reproduces the unexpected experimental finding that mixing larger particles into a suspension of small particles creates a bigger splash [1]. We also find that with increasing impact speed, the measured momentum distribution of ejected particles tends toward the result from the dry-grains-only simulation. These results support the idea that the splash from a low-viscosity solvent suspension is created by inertia-dominated collisions between particles. In this regime, viscous drag from the interstitial fluid is negligible. In future work, we will examine splash formation in simulations where particles approaching contact do experience viscous drag.\\[4pt] [1] Peters et al, Phys.~Rev.~Lett. {\bf 111}, 028301 (2013).   

Electrostatic control of the coffee stain effect

The ``coffee stain effect,'' as first explained by Deegan et al. 1997, has received a great deal of attention amongst modellers and experimentalists in recent years, perhaps due in part to its obvious casual familiarity. However, it maintains interest because of its intriguing reliance on an interplay of a trio of effects: contact line pinning, inhomogeneous mass flux, and resulting capillarity-driven flow. What is more, the effect, and especially its suppression or reversal, find applications in fields as diverse as sample recovery, mass spectroscopy and the printing of Organic LEDs. We examine the motion a nanoparticle-laden droplet deposited on a precursor film, incorporating the effects of capillarity, concentration-dependent rheology, together with a heated substrate and resultant mass flux and Marangoni effects. We allow the substrate to act as an electrode and incorporate a second electrode above the droplet. The potential difference together with a disparity in electrical properties between the two regions results in electrical (Maxwell) stresses at the interface. We show via lubrication theory and via direct numerical simulations that the ring effect typically observed may be suppressed or augmented via appropriate use of electric fields.   

Spontaneous formation of nanostructures inside inkjet-printed colloidal drops

Nanostructures formed in inkjet-printed colloidal drops are systematically examined with different substrates and ink formulations. Various deposition patterns from multi-ring, radial spoke, firework to spider web, foam and island structures are observed. With a high particle loading, deposition transitions from multi-ring near the drop edge to spider web and finally to foam and islands in the center of the drop with 20 nm sulfate-modified polystyrene particles. At the same particle loading, 200 nm particles self-assemble into radial spokes at the drop edge and islands in the center, due to reduced contact line pinning resulted from less particles. In drops with a low particle concentration, due to fingering instability of the contact line, 20 nm particles form radial spokes enclosed by a ring, while 200 nm particles assemble into firework-like structures without a ring. Moreover, at a high particle loading, ruptures are observed on the multi-ring structure formed by 20 nm carboxylic-modified particles, due to stronger capillary forces from the contact line. Furthermore, for a drop printed on a less hydrophilic substrate, the interparticle interactions enable a more uniform deposition rather than complex nanostructures.   

Building micro-soccer-balls with evaporating colloidal fakir drops

Drop evaporation can be used to self-assemble particles into three-dimensional microstructures on a scale where direct manipulation is impossible. We present a unique method to create highly-ordered colloidal microstructures in which we can control the amount of particles and their packing fraction. To this end, we evaporate colloidal dispersion drops from a special type of superhydrophobic microstructured surface, on which the drop remains in Cassie-Baxter state during the entire evaporative process. The remainders of the drop consist of a massive spherical cluster of the microspheres, with diameters ranging from a few tens up to several hundreds of microns. We present scaling arguments to show how the final particle packing fraction of these balls depends on the drop evaporation dynamics, particle size, and number of particles in the system.   

Influence of Relative Humidity on the Spreading Dynamics of a Drying Drop of Whole Blood

Newtonian and non-Newtonian fluids start spreading after coming into contact with a solid substrate till the anchoring of the triple line. Our experimental work aims to study the effect of the relative humidity on the spreading dynamics of drops of whole blood. Drops of blood of same volume (+/- 4.8 \%) are injected using a digital micropipette and gently deposited onto microscope ultraclean glass substrates. Experiments are conducted in a glove box at ambient temperature and a range of investigated relative humidities between 13.0\% and 80.0\%. The recorded images are post-processed using ImageJ in which the position of the contact line is measured every 20 ms. We show that the spreading dynamics is, in a first time, governed by relative humidity and later no more influence by relative humidity. Two spreading regimes are observed and analyzed compared to classical viscous drops. In previous work, we show that relative humidity influences the contact angle and the initial wetting radius. In the first regime, we find a spreading power law exponent that decreases for an increasing relative humidity. In the second regime, all the data collapse on each other and the evolution of the dimensionless radius no more depend on relative humidity.   

Opportunities for Fluid Dynamics Research in the Forensic Discipline of Bloodstain Pattern Analysis

This review [Forensic Science International, vol. 231, pp. 375-396, 2013] highlights research opportunities for fluid dynamics (FD) studies related to the forensic discipline of bloodstain pattern analysis (BPA). The need for better integrating FD and BPA is mentioned in a 2009 report by the US National Research Council, entitled ``Strengthening Forensic Science in the United States: A Path Forward''. BPA aims for practical answers to specific questions of the kind: ``How did a bloodletting incident happen?'' FD, on the other hand, aims to quantitatively describe the transport of fluids and the related causes, with general equations. BPA typically solves the indirect problem of inspecting stains in a crime scene to infer the most probable bloodletting incident that produced these patterns. FD typically defines the initial and boundary conditions of a fluid system and from there describe how the system evolves in time and space, most often in a deterministic manner. We review four topics in BPA with strong connections to FD: the generation of drops, their flight, their impact and the formation of stains. Future research on these topics would deliver new quantitative tools and methods for BPA, and present new multiphase flow problems for FD.