Session P18: Drops: Levitation, Particle Laden, Sessile and Static Surface Interactions

Droplet Bridging into Porous Media

If the top of a sessile droplet is brought into contact with an opposing solid surface, the droplet can transfer depending on the relative speeds and wettabilities of the surfaces. What if the surface receiving the liquid was porous? We use side-view high-speed imaging to capture the transfer of liquid from a solid substrate to an opposing porous surface. The parameters that were varied include donor wettability, the porosity and pore size of the receiving surface, and the droplet’s volume, surface tension, and viscosity. Generally, the transfer process is split into two major regimes, wetting and wicking. The wetting regime is split into two more regimes, the donor-independent and donor-dependent regimes. The donor-independent regime follows the dynamics of droplet coalescence, starting in the inertially-limited viscous regime and diverging into capillary-inertial or viscocapillary regimes depending on the liquid. The donor-dependent regime is limited by the flow in the receding contact line’s viscous wedge. The wicking regime is governed by Darcy’s Law, completing the transfer of the droplet.   

Effect of Bond number on the longitudinal and lateral oscillation of drops supported by flat surfaces

Accurate prediction of the natural frequency for the oscillation of a liquid drop supported by a planar substrate is important to many drop applications. Similar to the oscillation of a free drop, the oscillation mode for a drop supported by a planar surface can be characterized by spherical harmonics, with n and m representing the longitudinal and azimuthal wavenumbers. Different from free drops, the two n=1 modes corresponding to the centroid translation in the directions normal (n=1,m=0) and tangential (n=1,m=1) to the surface trigger shape oscillations for supported drops. These two modes typically dominate the oscillations and the natural oscillation frequencies, normalized by the capillary frequency, are functions of the equilibrium contact angle, the Bond number (Bo), the contact line mobility, and the surface orientation. Parametric numerical and experimental studies have been performed to establish a comprehensive understanding of oscillation dynamics. In particular, for drops pinned on a vertical surface, an inviscid model has been developed to predict the oscillation frequency for wide ranges of Bo and contact angles. The model reveals the scaling relation between the normalized frequency and Bo. For a given equilibrium contact angle, the lateral oscillation frequency decreases quadratically with Bo.    

Wettability and infiltration of molten CMAS droplet on thermal barrier coatings

Sand particles ingested into a gas-turbine engine, melt in the combustor and often cause severe structural damage to components in the hot-section especially by depositing and eventually penetrating the thermal barrier coating on the engine components. To investigate the wetting and infiltration dynamics of molten CMAS droplets on the surface of thermal barrier coatings, a Lagrangian approach based on many-body dissipative particle dynamics (mDPD) is employed to simulate the mesoscopic dynamics of highly viscous molten CMAS droplets at a typical operating temperature of 1275 degrees Celsius. The physical system is carefully parameterized to best simulate the multiphase dynamics of molten CMAS droplets with diameters in the range of 10-100 micrometers. The use of an arbitrary boundary condition method in mDPD allows for arbitrary geometries to replicate experimental surfaces of thermal barrier coatings on the gas-turbine components. The apparent contact angles of sessile drops from experiments are used to calibrate the contact angle of a sessile droplet in mDPD by varying the liquid-solid interfacial tension. We simulate the infiltration dynamics of molten CMAS droplets on regularly patterned surfaces with specifically designed surface roughness to quantify the effects of surface heterogeneity on high viscous wetting and infiltration dynamics.   

Coalescence of sessile droplets on hydrophobic surfaces under magnetic fields

Digital microfluidics deals with the behavior of sessile droplets on an open surface and is advantageous over emulsion microfluidics due to the absence of confinement, which in turn enables droplets to act as independent virtual reactors that are often utilized in point-of-care diagnostics applications. Here, we employ a phase field method-based solver to investigate the dynamic behavior between a pair of sessile droplets on hydrophobic surfaces under the presence of a permanent magnetic field. The results suggest that a non-uniform magnetic field is capable of forcing a pair of droplets towards each other, which eventually leads to a jumping off phenomenon of the merged droplet after coalescence on a superhydrophobic surface (i.e., θ_c = 150°). Also, interestingly, there exists a critical magnetic Bond number Bo_cr, beyond which the droplets do not experience any coalescence phenomenon. Moreover, the merging event between droplets appears different on less superhydrophobic surfaces (θ_c ≤ 120°). Additionally, the viscosity of droplets plays a critical role in determining the upward flight of droplets, where the merged droplet experiences increased vertical migration at higher viscosity ratios.   

Pressure criteria for crack formation and air invasion in drying droplets of colloidal suspensions

The drying of sessile droplets of colloidal suspensions with particle volume fraction beyond 5% leads to the formation of fracture patterns. As water evaporates, a solidification front propagates from the edge of the droplet, leaving behind a thin close-packed particle deposit that eventually covers the entire wetted area. We show that a simple mass conservation model captures the dynamics of the deposit formation across a large range of drying timescales. As the solid deposit grows, water flows radially through it to compensate for the water loss due to evaporation over the solid's surface. Flow in this porous material induces a pressure gradient leading to a large negative pore pressure, which is balanced by capillary pressure. Eventually, radial cracks form in the deposit, and subsequently air invades. Using mass conservation and Darcy's law, we show that the pressure inside the deposit controls the onset of both crack formation and air invasion. We observe two distinct regimes of air invasion which can be rationalized using a single hydrodynamic model, which further provides a criterion for the crossover between the two regimes.   

An Experimental Study on the Dynamics of Binder Drops Impacting on a Powder Surface in Binder Jetting Additive Manufacturing

Binder jetting additive manufacturing (AM) technology has been widely used for manufacturing complex and advanced structures. The binder jetting method creates 3D structures by jetting binder drops onto a powder bed with subsequent curing. While this method can provide fast and efficient non-contact manufacturing with additional design and material flexibilities, it suffers from several drawbacks, such as coarse resolution and manufacturing inconsistency. These undesired effects are caused by the complex drop-powder interactions during the printing process. In this study, we will experimentally investigate the complex binder-powder interactions during drop impacting and curing processes. While a high-speed imaging system will be used to capture the transient details during the drop-powder interactions, a micro digital image projection (m-DIP) system will be used to quantitatively measure the instantaneous 3D surface morphologies of binder drops impacting on powder surfaces. The findings derived from this study will be of great value to improve the current binder jetting AM procedures and develop more efficient and robust AM techniques tailored for fabricating high-quality functional structures in various applications.   

Probing Colloidal Assembly on Non-Axisymmetric Droplet Surfaces via Electrospray

Nanoparticles adsorbed to the surface of a spherical, sessile drop will form an unstructured deposit upon evaporation. When the surface flow is suppressed, particle motion at the interface is random and disordered. To investigate the influence of evaporative flow and capillary interactions on interfacial particle assembly, we created non-spherical droplets using substrate patterning and delivered microparticles to the interface with electrospray atomization. The contact line of the droplet was fixed throughout evaporation, resulting in convection towards sharp corners where the contact angle was lower. Additionally, the non-spherical droplet shape created regions of higher deviatoric curvature where particles assembled via capillary effects. When the particle density on the interface was low, there was a strong convective flow, driving individual particles toward the corners. For higher particle densities, the convective flow was reduced, allowing the particles to assemble into large, ordered monolayers over the course of evaporation. Our findings suggest that the relative influence of evaporative-driven flow and particle interactions can be exploited to build particle monolayers with controllable patterns.   

Dislocation of suspensions: a model for the accelerated pinch-off of suspension drops

Controlling the detachment of a drop from a nozzle is crucial for many printing and additive manufacturing applications. The dynamics of non-Brownian suspensions can often be modeled as a homogeneous Newtonian liquid, whose macroscopic viscosity is increased by the particles. However, this continuous behavior only holds as long as the liquid neck, which binds the drop to the nozzle, is much wider than the particle size. Close to the pinch-off, the discrete nature of the particles comes into play.. Previous studies have shown that the pinch-off is thus accelerated, and is actually faster than that of a homogeneous liquid of equivalent viscosity. However, the mechanism behind this accelerated pinch-off remains unclear. We propose to describe it as the dislocation of the suspension, during which minimizing viscous dissipation causes particles to spread rather than to slide or to spin. Therefore, we consider an extensional flow of the particles rather than a shear flow. This approach leads to scaling laws describing the onset and the end of the dislocation, as well as the thinning dynamics, all of which match our experimental results. Our model also holds when considering polydisperse suspensions, provided that the viscosity and the average particle size of the suspension are known.   

The evaporation of a droplet in well, and effect of the spatial variation of the evaporative flux on the deposition from a sessile droplet

The evaporation of sessile droplets occurs in numerous physical contexts, with applications in nature, industry and biology, including nano-fabrication, chemical decontamination, and ink-jet printing. As a consequence of the wide variety of everyday applications, the evolution of and deposition from an evaporating droplet has been subject to extensive investigation in recent years, with particular interest in different evaporation modes, the prediction of lifetimes, and the ring-like deposit (the ``coffee-ring'') that often forms at the contact line of a pinned evaporating droplet. In this talk we describe some recent developments in the study of evaporating droplets. We first formulate and analyse a mathematical model for the evolution and lifetime of an evaporating droplet in a well of rather general shape and validate the model by comparing the theoretical predictions with experimental results for the special case of cylindrical wells. We then investigate the effect of the spatial variation in the evaporative flux on the deposition from an evaporating droplet, determining the flow velocity, concentration of particles within the droplet, and the evolution of the deposit for a one-parameter family of evaporative fluxes.   

Experimental study of colloidal particles confined in a 2D microfluidic droplet

Particles are sometimes added during droplet formation to replace surfactants as surface active agents and improve the stability of the dispersions [1,2]. Generally, it is assumed that these particles follow classic Brownian motion. However, if the particles are confined their behaviour can be modified [3], as observed numerically [4] for spherical and cylindrical particles inside a rigid spherical cavity. However, the dynamics of confined particles in droplets formed in microfluidic channels is still poorly understood.

In the present work, the displacement of particles inside a fixed aqueous droplet in oil was investigated using fluorescently tagged polystyrene particles illuminated by a continuous laser. With this set up it is possible to track both time and spatial evolution of the particles inside the droplet at different particle concentrations. Quasi 2D-droplets were generated in a flat glass microchannel and the images were taken with a high-resolution camera equipped with a microscope lens at a frequency of 4Hz. The trajectories of the particles were obtained to calculate both radial and tangential mean square displacement (MSD). The results showed that the MSD behaviour changes significantly with the particles concentration and the radial location in the drop.   

Numerical study of the interfacial fluctuation of a droplet levitating above a moving wall

We conducted a two-dimensional simulation of a droplet levitating above a wall moving at a constant velocity. The droplet is solved using the front-tracking method, and the moving wall is modeled with our discrete-forcing immersed boundary method. When the droplet approaches the moving wall with a relative velocity in the tangential direction, the droplet levitates due to the local pressure increase between the droplet and the moving wall. This pressure is in good agreement with the value of the pressure predicted by the lubrication theory. We report the effect of the geometry of the moving wall on the stability of the droplet. For the walls of larger curvature, the air-liquid interface of the droplet facing the moving wall was observed to ripple, which is also confirmed by our previous experimental studies. The simulation results for different Weber and Froud numbers are compared with the experimental results, and the dependence of each parameter on the unsteadiness of the droplet interface are discussed.   

Delayed Coalescence on Solids and Liquids

By employing vibration of a viscous oil bath, one can inhibit the coalescence of oil drops and support them on an air cushion indefinitely as was shown by Couder et al., 2005. Herein we demonstrate that non-coalescence can be extended to solids by using soft gels where impacting water drops do not coalesce immediately because of the elasticity of the gel. Similarly, presence of surfactants can delay coalescence arising from the enhanced surface elasticity as noted by Kellay et al., 2001. Furthermore, vibrating the substrate, either soft gels or the surfactant baths, can then lead to an infinite time of coalescence expanding the regime of levitation to low viscosity liquids and even solids.