Session T05: Drops: Interaction with Elastic Surfaces, Particles and Fibers (8:00am - 8:45am CST)

A Thin-Film Model for Droplet Spreading on Soft Solid Substrates

The spreading of droplets on soft solid substrates is relevant to applications such as tumor biophysics and controlled droplet condensation and evaporation. In this paper, we apply lubrication theory to advance fundamental understanding of the important limiting case of spreading of a planar droplet on a linear viscoelastic solid. The contact-line region is described by a disjoining-pressure/precursor film approach, and nonlinear evolution equations describing how the liquid-air and liquid-solid interfaces evolve in space and time are derived and solved numerically. Parametric studies are conducted to investigate the effects of solid thickness, viscosity, shear modulus, and wettability on droplet spreading. Softer substrates are found to speed up spreading for perfectly wetting droplets but slow down spreading for partially wetting droplets. For perfectly wetting droplets, faster spreading is a result of more liquid being pumped toward the contact line due to a larger liquid film thickness there arising from the repulsive component of the disjoining pressure. In contrast, slower spreading of partially wetting droplets is a result of less liquid being pumped toward the contact line due to a smaller liquid film thickness there arising from the attractive component of the disjoining pressure. The model predictions for partially wetting droplets are qualitatively consistent with experimental observations, and allow us to disentangle the effects of substrate deformability and wettability on droplet spreading. Due to its systematic formulation, our model can readily be extended to more complex situations involving multiple droplets, substrate inclination, and droplet phase changes.   

Dynamics of compound particles in a quadratic flow

Droplets with encapsulated particles suspended in a secondary fluid are often encountered in various scenarios like nucleated cells, hydrogels, microcapsules, etc. Such ternary structures are called compound particles, and they are typically generated in microfluidic platforms, where they are exposed to a background flow. It is known that the structural stability of these structures is sensitive to the type, and strength of the background flow. In this work, we theoretically investigate the translational, and deformation dynamics of a concentric compound particle in an imposed quadratic flow in the absence of inertia (Reynolds number $=0$), and assuming that the confining drop is nearly spherical (low capillary number, $Ca<<1$). Increase in the size of the particle, or the viscosity of the droplet fluid enhances the deformation of the confining interface, thus reducing the stability of a compound particle. Deformation of the confining interface is lesser in quadratic flow compared to a linear flow, indicating weaker hydrodynamic interactions in the quadratic flow. Besides, we analyze the dynamics of a compound particle in a pulsatile quadratic flow, which can be used to transport them in microfluidics without breaking up the confining interface.   

Bouncing Droplets on Elastic, Superhydrophobic Cantilever Beam

During the past several decades, liquid droplet impact on rigid substrates has been well studied and documented. However, not all substrates surrounding us are rigid, including leaves and insect wings, as a few common examples. In the present study, we have experimentally analysed the impact of a microliter water droplet on superhydrophobic cantilever beams in the range of~\textit{30\textless We\textless 76~}(\textit{We}: Weber number). Thin copper sheets were coated with a commercially available~\textit{NeverWet}~spray to make it superhydrophobic, and high-speed imaging was used for visualisation. The timescales of droplet and cantilever beams were varied by changing the droplet size and beam length, respectively. It was observed that the overall system dynamics (bouncing of the droplet and oscillations of the cantilever) is dependent on the interplay between the two timescales discussed above. An analogous spring-mass system has been used to account for this coupling and explain the experimental observations. These findings could be utilized to achieve desirable contact times, droplet rebound kinetic energy, the energy transfer to the cantilever beam, and the droplet spreading diameter. The conditions to achieve maximum and minimum of these parameters have been outlined and corroborated by the experimental evidence.~   

``Stick-slip'' or ``Stick-break?'': Stiffness Mediated Magnetowetting Dynamics of Sessile Droplets

We experimentally demonstrate the alteration in the magnetowetting dynamics of sessile ferrofluid (water-based) droplets, placed atop elastomeric surfaces of different stiffness, in a non-uniform magnetic field. Although the deformation and subsequent splitting dynamics of the ferrofluid droplets are analogous to the previous studies involving rigid substrates, the characteristics of the concerned events are greatly influenced by the stiffness of the substrates. For example, the experiments reveal that rigid substrates facilitate a sharp decrease in the contact radius of the droplet during its deformation. In contrast, the soft substrates favor substantial decrease in the dynamic contact angle, measured around the air-water-solid three-phase contact line (TPCL). Further, the TPCL experiences a shift from ``stick-slip'' to the ``stick-break'' regime, with a decrease in the stiffness of the underlying substrate. The energetic arguments indicate that the above transition is governed by the dynamics of the ``wetting-ridge'' formed around the TPCL. The stiffness also affects the size of the secondary droplets produced from the splitting. The study is expected to shed light on the interaction of soft mediums and ferrofluid droplets in a magnetic field.   

Droplet motion on a vibrating vertical wire

Dynamics of a droplet along a wire has many engineering applications. For example, wire mesh has been used to collect droplets or dust particles as a method of air filtration. In this series of theory and experimentation, we investigate how vibration of a vertical wire affects droplet motion. To that end, we test the effects of vibration in directions both normal to and in line with a vertical wire. We observe three different behaviors by the droplet under vibration: stationary, sliding, or shedding. We summarize our observations in a phase diagram characterizing these behaviors in terms of the frequency and amplitude of wire vibration as well as droplet volume. In general, we found that vibration of the wire enhanced the chance of droplet sliding and increased falling speed down the wire in the sliding regime. Finally, we attempt to develop a theoretical model to explain this behavior based on variations in contact angle hysteresis of the droplet due to the vibration. By fluctuating the advancing and receding angle of the droplet, we believe that vibration causes a decrease in the overall capillary force of the droplet, thus causing it to fall or shed from the wire.   

Blowing away sticky particles

The context of our study is STELLAR, a European project. The project aims at reducing drag and fuel consumption during flight with novel wings whose aerodynamic properties are sensitive to contamination by insect debris. Can the airflow blow away these debris? To understand the physical mechanisms involved in this phenomenon, we designed a model experiment where a spherical bead is deposited inside a wind tunnel on an horizontal surface coated with a thin layer of a viscous liquid. What is the velocity of the bead as a function of its size and density, of the thickness and viscosity of the film and the velocity of the airflow? Is it possible to lift away the bead?   

Topography of Particle-laden Droplet Deposits on Soft Materials

A ``coffee ring'' is a particle deposit that can form when a particle-laden droplet evaporates, leaving particles near the droplet contact line. Observed in everyday life, such deposits appear in a wide range of liquid, particle, and substrate combinations. Previous studies focused on the fluidics of evaporating suspension droplets on rigid materials, where the ring formation was shown to occur for pinned contact lines and its possible suppression with surfactants, or other externally driven means were investigated. Here we investigate the effect of soft substrates and showed that we can control the topography of the deposit on demand by simply changing the environmental humidity, regulating the evaporative flux. We perform particle tracking of particle-laden droplets that dry on soft substrates at varied environmental conditions. We show with experimental observations and theoretical analysis that when droplets dry quickly, particles advect towards the receding contact line, which we relate to the viscous dissipation within the soft solid, retarding the contact line motion. Coffee ring formation in the presence of a receding contact line and its regulation by humidity bring a new perspective to the conditions of the manifestation of this frequent deposit topography.   

Wettability control of droplet durotaxis

Durotaxis refers to cell motion directed by stiffness gradients of an underlying substrate. Recent work has shown that droplets also move spontaneously along stiffness gradients through a process reminiscent of durotaxis. Wetting droplets, however, move toward softer substrates, an observation seemingly at odds with cell motion. Here, we extend our understanding of this phenomenon, and show that wettability of the substrate plays a critical role: while wetting droplets move in the direction of lower stiffness, nonwetting liquids reverse droplet durotaxis. Our numerical experiments also reveal that Laplace pressure can be used to determine the direction of motion of liquid slugs in confined environments. Our results suggest new ways of controlling droplet dynamics at small scales, which can open the door to enhanced bubble and droplet logic in microfluidic platforms.   

Self-Excited Motions of Volatile Drops on Swellable Sheets

When a volatile droplet, such as acetone, is deposited on a floating swellable PDMS sheet, it becomes asymmetric, lobed, and mobile. We describe and quantify this phenomenon that involves nonequilibrium swelling, evaporation and motion, working together to realize a self-excitable spatially extended oscillator. Solvent penetration causes the film to swell locally and eventually buckle, changing its shape and the drop responds by moving. Simultaneously, solvent evaporation from the swollen film causes it to regain its shape once the droplet has moved away. The process repeats and leads to complex pulsatile spinning and/or sliding motion. We provide a phase diagram that delineates the regimes where these self-excited motions exist, along with scaling laws for the frequency of droplet spinning. An even simpler realization of the effect is provided by a drop of acetone placed on a narrow quasi-1-dimensional sagging PDMS film clamped at both ends -- which spontaneously oscillates back and forth while causing the film to buckle and unbuckle. This allows us to build a minimal model for the excitable droplet system, which highlights the slow swelling of and evaporation of acetone from the film and the fast motion of the drop. Finally, we consider a few potential applications of this phenomena.