Session T06: Drops: Heat Transfer, Evaporation and Buoyancy Effects (8:00am - 8:45am CST)

Fully Wickless Vapor Chamber - Thermal Diode

In this study, a vapor chamber (VC) - thermal diode (TD) apparatus, with wickless and wettability-patterned components is fabricated and tested. This device is the first truly-wickless system of its kind, and could be implemented as a heat transfer module in a cooling system for electronics. Our approach takes advantage of the water's phase-changing property, within a closed loop composed of two wickless wettability-patterned components (evaporator and condenser). The two plates have different wettability patterns, each specially designed to transform a rectangular copper plate to a functional component of a VC. The working medium evaporates from the hot central point of the evaporator and condenses on the cooled condenser. The wettability pattern of the condenser allows spatially controlled dropwise and filmwise condensation and offers an optimal way to move the condensate through wedge tracks utilizing capillary forces, while the evaporator's pattern enables the accumulation and the transport of the returning condensate liquid to the central portion where evaporation is strongest. If the condenser experiences a higher temperature than the evaporator, the wettability patterns no longer function harmoniously with each other. Thus, the device acts as a TD, preventing the heat flow in the opposite of the preferred direction.   

An Asymptotic Analysis on the Universality of the Coffee-Ring Effect

We study the evolution of the coffee ring generated by the transport of a dilute solute to the pinned contact line of a thin, evaporating droplet. The contact line is assumed to be smooth and simple, but otherwise arbitrary. We employ a novel integrated mass formulation to facilitate a systematic matched asymptotic analysis of the small-Capillary number, large-solute Péclet number limit. The analysis is presented both for evaporation limited by the vapour-diffusion and for a simple one-sided, non-equilibrium evaporative model in which the evaporative flux is essentially constant. The universal aspects of the asymptotic predictions for the evolution of the concentration profile in the bulk and coffee ring are discussed in detail and illustrated for circular and elliptical contact sets. Our results offer mechanistic insight into the effect of contact-line curvature on the coffee-ring dynamics from deposition up to jamming of the solute.   

Active Volatile Drops on Liquid Baths

We demonstrate the self-propulsion of a volatile drop on the surface of a liquid bath. Our system allows for direct probing of both the surface and the liquid bulk. Experimental characterization of both the temperature field on the drop surface and of hydrodynamic flows allows us to rationalize the system behavior. Evaporative heat pumping is converted into directed motion driven by thermocapillary stresses, which emerge on the drop surface as a result of a symmetry breaking of the drop temperature field. The dependence of the drop speed on the activity source, i.e. the evaporation flux, is derived with scaling arguments and captures the experimental data. Since the evaporation flux is limited by heat transfer in the bath, we also show that the system activity can be tuned by varying the bath viscosity. While the drop motion is two-dimensional, rationalizing the three-dimensional hydrodynamic flows in our system can provide insights into the mechanism of drop self-propulsion and interactions in unbounded environments.   

On explosive boiling of a Leidenfrost multicomponent drop

A self-induced explosion of the droplet can produce a multitude of smaller secondary droplets which promotes fuel atomization. Here, we study a unique explosive gasification process of a tri-component droplet consisting of water, ethanol, and oil (“ouzo”), by high-speed monitoring the entire gasification event taking place in the well-controlled, levitated Leidenfrost droplet state over a superheated plate. It is observed that the preferential evaporation of the most volatile component, ethanol, triggers nucleation of the oil microdroplets in the remaining drop, which consequently becomes an opaque oil micro-emulsion. The oil micro-droplets subsequently coalesce to a large one that, in turn, wraps around the remnant water. Because of the encapsulating oil layer, the droplet can no longer produce enough vapor for its levitation, and thus falls and contacts the superheated surface. The direct thermal contact leads to vapor bubble formation inside the drop and consequently drop explosion in the final stage. Our comprehensive understanding of the entire boiling process of multicomponent drops provides the premise for designs in combustion applications and other industrial settings.   

Evaporation of binary-mixture liquid droplets: how to make flattened micro-drops

Spreading and evaporation of drops is ubiquitous in nature and technology, from rain drops on a window to inkjet printing. During their entire evolution, these droplets are often assumed to retain a spherical cap shape to minimize their interfacial energy. Here, we show that in the case of binary mixture liquid droplets, surprisingly, the drop profiles can substantially deviate from the spherical cap shape, and even become completely flattened much like a micron-thick pancake. We explain these observations based on the differential evaporation of the two liquid components in the mixture that leads to a gradient in surface tension along the drop interface, driving a solutal Marangoni flow towards the edge of the droplet. We demonstrate that when this solutal Marangoni flow dominates over the opposing capillary flow, flattened drops form.   

Interface-resolved evaporating droplets in homogeneous shear turbulence

We perform interface-resolved simulations of evaporating droplets in homogeneous shear turbulence (HST) using a recently developed volume of fluid method for phase-changing flows. First, we present a simple yet efficient variant of the Adams-Bashforth time integration method able to tackle in a robust manner numerical simulations in the HST configuration, both in single and multiphase conditions. Next, we consider an array of five isolated droplets, whose initial size is bigger than the Kolmogorov scale, immersed in a statistically steady-state field characterized by $Re_{\lambda}\approx 75$ and the dimensionless shear number $\mathcal{S}^*\approx 2.8$ and we allow them to exchange mass, momentum and energy across the interface. The simulations are conducted by varying two dimensionless parameters: the shear-based Weber number $We_{\mathcal{S}}$ and the ratio between the initial gas temperature and the saturation temperature $T_{g,0}/T_{sat}$. Results will be presented in a two-parameter space diagram and the effects of turbulence on the Sherwood and Nusselt numbers analyzed for the single droplets. Finally, by relaxing the assumption of uniform and constant gas density, the impact on the evaporation rate of weakly-compressible effects is assessed.   

Relative Trajectories of Falling, Evaporating Drops

Binary interactions are determined for spherical drops due to gravity, with exact methods for calculating the hydrodynamic forces at finite Stokes number and low Reynolds number. Mass is lost by the drops through isothermal evaporation controlled by diffusion, and bispherical coordinates are used to solve for the vapor concentration between the two liquid spheres. At small Reynolds number, the surrounding fluid inertia is negligible, and the hydrodynamic forces are linear functions of the translational velocities of the drops. However, at nonzero Stokes numbers, drop inertia must be taken into account, and the hydrodynamic forces do not balance the applied forces. For drops in close approach, lubrication forces and attractive molecular forces are considered. Comparison with trajectories for two drops of constant mass permits study of the evaporative effect, while comparison of trajectory results with those for two interacting drops, each evaporating at the isolated drop rate, allows analysis of the significance of the presence of the second drop. An important application is to raindrop growth. For water droplets in the atmosphere, at drop radii between 10 and 30 $\mu$m, drop inertia is substantial while the Reynolds based on the surrounding air is still small.   

Durable icephobic oleogel coating for effective anti-icing and de-icing

Icing and frosting cause many problems for communication and power lines, wind turbines, and solar panels. Accordingly, several anti-icing and de-icing technologies have been developed, but these energy-intensive technologies induce a lot of economic loss. It is therefore necessary to develop an effective and sustainable icephobic surface without the use of external energy. In this study, a new icephobic surface impregnated with a lubricant was developed. The ice adhesion strength was measured to evaluate the icephobic property of the surface. The ice adhesion of the proposed surface was measured as 0.39 kPa, much smaller than that of conventional icephobic surfaces. In particular, the measured strength is much smaller than 20 kPa. Thus, the adhered ice can be removed by natural wind or gravity without the supply of any external energy. The low ice adhesion strength was well maintained for 10 icing/de-icing cycles, which indicates high sustainability of the proposed oleogel coating. The present results demonstrate the realization of a highly effective and durable icephobic surface. The proposed oleogel coating would be utilized for various other engineering applications, including anti-biofouling, water-repellence and self-cleaning.   

Scaling laws for the timescales of quantities seen by evaporating droplets

We study statistical properties of the gas flow seen by dispersed evaporating droplets in homogeneous, isotropic, stationary turbulence. An accurate description of properties seen by particles is essential in any numerical method relying on the point-particle assumption. In this contribution we focus on their fluctuation timescales.\\ The timescale of velocity components seen by inertial particles was studied in the past\footnote{Jung, \emph{Physical Review E} 77, 016307 (2008)} and displays the interesting N-shaped dependency on the particle Stokes number. For evaporating particles, a description of the gas temperature and species mass fractions seen by droplets is required in addition to the velocity to correctly predict the evaporation rate. No such investigation of seen scalar timescale is available in the literature.\\ The relevant statistics are computed from Direct Numerical Simulation data for different flow conditions\footnote{Weiss \textit{et. al}, \emph{Physics of Fluids} 30, 083304 (2018)}. We present physically motivated models and scaling laws for the timescales of scalars seen by inertial particles. The influence of preferential sampling is discussed as well.   

Stability of evaporating sessile drops comprising binary mixtures

The evaporation and spreading dynamics of a binary mixture sessile drop are complex~due to the interplay~of thermal and~solutal~Marangoni stresses~alongside~the hydrodynamic transport,~evaporation, mass diffusion, capillary stress and surface tension of the drop. We~investigate the stability of volatile~bicomponent~sessile~drops~with high wettability~comprising ethanol-water deposited onto heated substrates.~We obtain the transient base state using~a one-sided~model under lubrication approximation before~freezing the base state~and introducing small disturbances to~perform a quasi-steady-state linear stability analysis.~The base state equations are derived assuming an ideal miscible mixture and the surface tension linearly depends on temperature and concentration. The stress singularity at the contact line is avoided by including a precursor film. We end up with an eigenvalue problem where the stability of the flow is determined from the real part of the eigenvalues. The stability equations for the binary system are solved to reveal the most dangerous unstable nodes. Our stability analysis shows that any evaporating sessile drop comprising a binary mixture is highly unstable and the results qualitatively agree with behaviour seen in experiments for ethanol-water.   

Solidification of a rivulet : Temperature fields

We study experimentally the solidification of a water rivulet flowing down an inclined plane cooled to subzero temperatures. The system reaches ultimately a stationary state where the water continues to flows on top of the solidified structure. The ice exhibits a surprising linear geometry, with distance from the injection point. Thermal convection from the constant water supply plays a role in the establishment of the static ice shape. The resolution of the thermal problem enables to recover the geometry of the ice structure. The comparison between theoretical resolution of the thermal problem and the measurements taken from an infrared camera, shows very good agreements, validating the thermal boundary layer model.   

Bubble growth during ``magic carpet breakup`` of a drop on a heated substrate

Drop impact onto a hot substrate results in a multitude of different outcomes, depending on the substrate temperature and the impact parameters. In our previous study (R. Hatakenaka et al., \textit{Int. J. Heat Mass Transf.}, 2019), a new outcome named magic carpet breakup was identified under reduced ambient pressure (1 - 10 kPa) for water drops impinging onto a superheated smooth substrate with moderate impact velocity (0.46 m/s). Droplets are repelled from the hot surface so violently, that they spread out to a flattened shape in an explosive manner. Here we observe the existence of a growing vapor bubble underneath the drop. Its growth between the drop and the substrate is directly observed via high-speed total internal reflection (TIR) imaging. The bubble emerges at the center of impact point, grows, and finally coalesces with some additional smaller bubbles. Similar observation has been already reported by Yu et al. (\textit{Soft Matter}, 2019), however no quantitative data was presented. We will evaluate the bubble growth rate via image analysis and discuss an applicability of a classical bubble growth model to this problem.   

Bicomponent Droplets Spontaneously Explode upon Impact on Superheated Substrate

The impact of a liquid droplet on a superheated substrate often exhibits the Leidenfrost phenomenon, where the droplet floats on a thin layer of its own vapor without contacting the underlying substrate. While droplets of pure liquids maintain their shape integrity during and after impact at Weber numbers $<50$, binary droplets (containing liquids of different volatilities) may undergo a vigorous disruption (‘explosive boiling’) in a narrow operating regime of the substrate temperature and liquid composition matrix. We have characterized the explosive boiling of ethanol-in-water droplets of different compositions over a range of the substrate temperature and Weber number in an attempt to explain the responsible physical mechanism. A scaling analysis reveals the possibility of a collapsing vapor layer underneath the droplet, thereby enforcing short-lived liquid-solid contact, which was evidenced by interferometric imaging of the bottom surface of the impacting drops during explosive events. Upon contact, local superheating of the liquid at the bottom layer of the droplet initiates flash boiling of the more volatile component (ethanol), which manifests itself as a violent disintegration of the liquid volume.   

Dependence of evaporation of sessile drops on the deformation of soft substrates

The global outbreak of COVID-19 has sparked recent interest on how sprayed/exhaled human droplets (potentially hosting the virus) dry on masks, clothes, and human skin, which can contribute to prevention and mitigation of infectious diseases. To date, the evaporation and lifetime of liquid droplets on flat rigid surfaces has been extensively studied and is well understood. However, flexible substrates such as textiles or human skin, which can deform due to capillary forces remains unexplored. Our experimental results show that the evaporation rate of water droplets on thin square membranes which deform due to capillary forces does not obey the conventional accepted diffusion model and being propostional to the perimeter predicting the evaporation rate is proportional to the length of contact line. The evaporation rate of drops in the present experiments is found to decrease linearly with the ratio of membrane side length to critical elastocapillary length once the membrane deformation is triggered. A possible interpretation of this result is that substrate deformation effectively alters the free surface area available for evaporation questioning the validity of the quasi-stationary mass diffusion transfer and the enhanced evaporation near the three phase contact line on deformable substrates. Solving theoretically the intricate physical aspects of the evaporation of droplets on significantly deformed substrates calls for this investigation.   

Freely Suspended Drops Rising in Miscible Environments

Our work focuses on an experimental investigation of droplets freely rising through a miscible, more viscous liquid. We report observations of droplets of water rising through glycerol and corn syrup. The drops continually grow more oblate and, as they mix with the ambient liquid, their volume increases and their velocity decreases, eventually following power laws at long times. We present scaling relations that explain the observed phenomena.   

Convection-dominated dissolution for single and multiple immersed sessile droplets

We numerically investigate both single and multiple droplet dissolution with droplets consisting of less dense liquid dissolving in a denser host liquid. In this situation, buoyancy can lead to convection and thus plays an important role in the dissolution process. Here, we vary the Rayleigh number $Ra$ which characterizes the strength of buoyancy as compared to the viscous damping force. For single droplet dissolution, we observe the diffusively and convectively dominated regimes with distinct flow morphologies: when $Ra\geq 10$, a buoyant plume is clearly visible, which contrasts sharply with the pure diffusion case at low $Ra$. For multiple droplet dissolution, the well-known shielding effect comes into play at low $Ra$, so that the dissolution rate is slower as compared to the single droplet case. However, at high $Ra$, convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, which leads to non-trivial phenomena, contrasting the shielding effect.   

Self-propulsion of boiling droplets on thin oil films

Droplet self-propulsion strategies have been studied for applications in self-cleaning, anti-icing, and anti-fouling surfaces. To increase the velocity of a droplet on a surface, one would typically think to minimize contact between the droplet and the surface. Here we investigate the self-propulsion of boiling droplets that, despite their contact with a viscous film, attain velocities comparable to those of levitating Leidenfrost droplets on ratchets. The propulsion of the droplet originates from the asymmetric release of vapor from beneath the boiling droplet. The effect of surface texture, viscosity, temperature, and droplet size are explored. We develop a scaling model that predicts, with good agreement, the droplet velocities by balancing the viscous dissipation in the oil film with the momentum created by vapor ejection beneath the boiling droplet.   

Not Participating

Ultrasonic actuation of the liquid-vapor interface between co-flowing layers of vapor and slow-moving sub-cooled liquid which exploits the difference in acoustic impedance to form a multi-scale train of droplets ejected into the vapor flow is investigated experimentally. The increased interfacial surface area of the ejected droplets results in increased heat transfer between the vapor and the liquid and a significant increase in vapor condensation rate. A two-stream liquid-vapor experimental setup was designed to assess the effects of the acoustic actuation on the formation and ejection of the subcooled liquid droplets and the enhanced condensation over a range of flow rates and liquid subcooling. The present measurements yield the increases in the sensible heat of the liquid stream and the increased rate of mass transfer from the vapor to liquid stream. Comparisons of temperature distributions in the absence and presence of actuation are used to assess the enhanced heat transfer between the vapor and liquid phase at both steady-state and transient conditions and indicate applications to tube heat exchangers.   

Durable Jumping Dropwise Condensation with Carbon Nanofiber Composites

Metals are usually desired in heterogenous condensation of water due to their thermal and mechanical properties. However, their hydrophilic surfaces facilitate the formation of high-thermal-resistance condensate film known as filmwise condensation (FWC). Although the formation of such films can be suppressed by a hydrophobic layer so that water leaves as discrete droplets, i.e. dropwise condensation (DWC), the thickness of these organic layers required for robustness introduces additional thermal resistance. This challenge becomes even more apparent on less robust superhydrophobic surfaces, on which jumping dropwise condensation (JDWC) occurs. We present a facile method of preparing a thin (\textasciitilde 2 um) superhydrophobic polytetrafluoroethylene (PTFE) --~carbon nanofiber (CNF) composite coating on copper, able to sustain JDWC for 10 h under flow condensation at 111 C steam flowing at 3 m/s, and an additional 50 h of DWC before FWC is observed. The estimated mean shear stress on the coating is \textgreater 57 mPa, equivalent to a load of 94{\%} of the coating's own mass. The robustness of the coating is provided by the CNFs, which simultaneously improve the composite thermal conductivity. We achieve a heat transfer coefficient improvement of up to 900{\%} when compared to plain copper without modification.   

Thermohydronamics of Multiple Droplet Streams Impinging on Liquid Film

The thermohydrodynamics of multiple stream droplet trains impinging on a thin liquid film was investigated numerically and experimentally. Numerically, CFD simulations under uniform surface heating were performed by using the Coupled Level Set-Volume-of-Fluid (CLS-VOF) method. A structured 3D half-symmetric mesh with dynamic mesh adaption was used to capture the formation and propagation of the droplet-induced crown and secondary droplets with time-dependent spatial and temporal resolutions. A piezo-electric droplet generator was used to produce mono-dispersed droplets with controlled droplet properties, including droplet diameter, velocity, droplet Weber number and droplet stream spacing. High-speed imaging was used to capture droplet-induced hydrodynamics and the morphology of the droplet-induced liquid film. A reasonable agreement was obtained between numerical and experimental results based on several factors including impact crater properties and surface temperature profiles. In summary, numerical and experimental results reveal that Weber number, droplet horizontal impact spacing and the overall impingement pattern play a significant role on cooling process and hydrodynamics during multiple droplet train impingement on a liquid film.