Understanding the dynamics of liquid films that make up bubbles is of practical and fundamental importance. Practically, this understanding is crucial for tuning bubble stability, while fundamentally, thin films are an excellent platform to study 2D flows. Here we study the spatiotemporal film thickness dynamics of bubbles subjected to evaporation driven Marangoni flows. Initially, we demonstrate how bubble stability can be dramatically tuned with the help of evaporation driven flows. Subsequently, we reveal that the spatial symmetry of thickness profiles evolves non-monotonically with the volatile species concentration, with profiles being axisymmetric at the two extremes in concentration. At $50\%$ concentration, spatial symmetry breaks down and thickness fluctuations are chaotic everywhere in space, with the fluctuation statistics becoming spatially invariant and ergodic. For these cases, the power spectrum of thickness fluctuations follow the Kolmogorov $-5/3$ scaling - a first such demonstration for forcing by evaporation. These results along with the reported setup provide an excellent framework to further investigate 2D chaotic flows.
The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wave number and time. The method is applied to transient Rayleigh-Benard-Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and pur…
The transport and aggregation of particles in suspensions is an important process in many physicochemical and industrial processes. In this work, we study the transport of particles in an evaporating binary droplet. Surprisingly, the accumulation of particles occurs not only at the contact line (due to the coffee-stain effect) or at the solid substrate (due to sedimentation), but also at a particular radial position near the liquid-air interface, forming a "ring", which we term as the Marangoni ring. The formation of this ring is primarily attributed to the solutal Marangoni flow triggered by …
The evaporation from a micropillar evaporator is a problem governed by various interfacial phenomena such as the capillarity-induced liquid flow, thin-film evaporation intensifying near the contact lines, and thermocapillarity-induced Marangoni flow. However, past research has not been able to assess the effect of Marangoni flow due to the missing coupling between cell- and device-level modeling. In this work, we develop a comprehensive model for the evaporation from a micropillar evaporator by coupling the liquid flow with the energy transfer in both liquid and solid domains at both cell- and…
Interfacial stability is important for many processes involving heat and mass transfer across two immiscible phases. When this transfer takes place in the form of evaporation of a binary solution with one component being more volatile than the other, gradients in surface tension can arise. These gradients can ultimately destabilise the liquid-gas interface. In the present work, we study the evaporation of an ethanol-water solution, for which ethanol has a larger volatility. The solution is contained in a horizontal Hele-Shaw cell which is open from one end to allow for evaporation into air. A …
Marangoni instabilities in binary mixtures are different from those in pure liquids. In contrast to a large amount of experimental work on Marangoni convection in pure liquids, such experiments in binary mixtures are not available in the literature, to our knowledge. Using binary mixtures of sodium chloride/water, we have systematically investigated the pattern formation for a set of substrate temperatures and solute concentrations in an open system. The flow patterns evolve with time, driven by surface-tension fluctuations due to evaporation and the Soret effect, while the air-liquid interfac…
Temporal and spatio-temporal (turbulence) distributed chaos in Bénard-Marangoni and Rayleigh-Bénard convection have been studied using results of laboratory experiments and direct numerical simulations in the terms of effective chaotic diffusivity (viscosity) and action. It is shown that for the both cases decaying part of the power spectra has stretched exponential form - for temporal spectrum $E(f) \propto \exp-(f/f_β)^{1/2}$ and for spatial spectrum $E(k) \propto \exp-(k/k_β)^{2/3}$, where the $f_β$ and $k_β$ represent low-frequency (large-scale) coherent oscillations.
The interface between a pure liquid and its vapor is usually close to saturation temperature, hence strongly hindering any thermocapillary flow. In contrast, when the gas phase contains an inert gas such as air, surface-tension-driven convection is easily observed. We here reconcile these two facts by studying the corresponding crossover experimentally, as a function of a new dimensionless number quantifying the degree of damping of interfacial temperature fluctuations. Critical conditions are in convincing agreement with a simple nonlocal one-sided model, in quite a range of evaporation rates…
The Marangoni contraction of sessile droplets occurs when a binary mixture of volatile liquids is placed on a high-energy surface. Although the surface is wetted completely by the mixture and its components, a quasi-stationary non-vanishing contact angle is observed. This seeming contradiction is caused by Marangoni flows that are driven by evaporative depletion of the volatile component near the edge of the droplet. Here we show that the composition of such droplets is governed by Taylor dispersion, a consequence of diffusion and strong internal shear flow. We demonstrate that Taylor dispersi…
Phase segregation triggered by selective evaporation can emerge in multicomponent systems, leading to complex physiochemical hydrodynamics. Recently, Li et al. (Phys. Rev. Lett., vol. 120, 2018, 224501) and Kim & Stone (J. Fluid Mech., vol. 850, 2018, pp. 769-783) reported a segregative behavior (i.e., demixing) in an evaporating binary droplet. In this work, by means of experiments and theoretical analysis, we investigate the flow dynamics after the occurrence of the phase segregation. As example, we take the 1,2-hexanediol-water binary droplet system. First, we experimentally reveal the over…
It is usually expected that surface tension driven flow dominates at small scales. Evaporation from the meniscus of ethanol/methanol confined in a capillary induces Marangoni convection at the meniscus which has been investigated by previous researchers. However, Marangoni convection is unexpectedly absent at an evaporating water meniscus confined inside a small micro-channel which is reported in this work. The velocity near the water meniscus is studied using confocal micro-PIV. The water meniscus is formed at the end of a micro-channel filled with water keeping the meniscus exposed to atmosp…
This work presents fluid dynamics videos obtained via numerical (CFD) calculations using ComSol (finite elements method) software, showing the evaporation of HFE7100 (3M company refrigerant) into a nitrogen gas flow along the liquid interface. The overall temperature evolution and liquid motion, which is caused by surface-tension (Marangoni) and buoyancy (Rayleigh) instability mechanisms, are shown as well. Flow behavior in the liquid caused by the aforementioned instability mechanisms can be nicely seen. Finally, these observations are made for three liquid thicknesses in order to appreciate …
For a small sessile or pendant droplet it is generally assumed that gravity does not play any role once the Bond number is small. This is even assumed for evaporating binary sessile or pendant droplets, in which convective flows can be driven due to selective evaporation of one component and the resulting concentration and thus surface tension differences at the air-liquid interface. However, recent studies have shown that in such droplets gravity indeed can play a role and that natural convection can be the dominant driving mechanism for the flow inside evaporating binary droplets (Edwards et…
The drying of a drop of human blood exhibits coupled physical mechanisms, such as Marangoni flow, evaporation and wettability. The final stage of a whole blood drop evaporation reveals regular patterns with a good reproducibility for a healthy person. Other experiments on anaemic and hyperlipidemic people were performed, and different patterns were revealed. The flow motion inside the blood drop is observed and analyzed with the use of a digital camera: the influence of the red blood cells (RBCs) motion is revealed at the drop periphery as well as its consequences on the final stage of drying.…
We present a realization of a fast interfacial Marangoni microswimmer by a half-spherical alginate capsule at the air-water interface, which diffusively releases water-soluble spreading molecules (weak surfactants such as polyethylene glycol (PEG)), which act as "fuel" by modulating the air-water interfacial tension. For a number of different fuels, we can observe symmetry breaking and spontaneous propulsion although the alginate particle and emission are isotropic. The propulsion mechanism is similar to soap or camphor boats, which are, however, typically asymmetric in shape or emission to se…
The present study experimentally and numerically investigates the evaporation and resultant patterns of dried deposits of aqueous colloidal sessile droplets, when the droplets are initially elevated to a high temperature before being placed on a substrate held at ambient temperature. The system is then released for natural evaporation without applying any external perturbation. Infrared thermography and optical profilometry were used as essential tools for interfacial temperature measurements and quantification of the coffee-ring dimensions, respectively. Initially, a significant temperature g…
Droplet evaporation of multicomponent droplets is essential for various physiochemical applications, e.g. in inkjet printing, spray cooling and microfabrication. In this work, we observe and study phase segregation of an evaporating sessile binary droplet, consisting of a mixture of water and a surfactant-like liquid (1,2-hexanediol). The phase segregation (i.e., demixing) leads to a reduced water evaporation rate of the droplet and eventually the evaporation process ceases due to shielding of the water by the non-volatile 1,2-hexanediol. Visualizations of the flow field by particle image velo…
Surface coatings and patterning technologies are essential for various physicochemical applications. In this Letter, we describe key parameters to achieve uniform particle coatings from binary solutions: First, multiple sequential Marangoni flows, set by solute and surfactant simultaneously, prevent non-uniform particle distributions and continuously mix suspended materials during droplet evaporation. Second, we show the importance of particle-surface interactions that can be established by surface-adsorbed macromolecules. To achieve a uniform deposit in a binary mixture, a small concentration…
Droplet evaporation has been intensively investigated in past decades owing to its emerging applications in diverse fields of science and technology. Yet the role transport mechanisms has been the subject of a heated debate, especially the presence of Marangoni flow in water droplets. This work aims to draw a clear picture of the switching transport mechanisms inside a drying pinned sessile water droplet in both the presence and absence of thermocapillarity by developing a comprehensive model that accounts for all pertinent physics in both phases as well as interfacial phenomena at the interfa…
Soap bubbles occupy the rare position of delighting and fascinating both young children and scientific minds alike. Sir Isaac Newton, Joseph Plateau, Carlo Marangoni, and Pierre-Gilles de Gennes, not to mention countless others, have discovered remarkable results in optics, molecular forces and fluid dynamics from investigating this seemingly simple system. We present here a compilation of curiosity-driven experiments that systematically investigate the surface flows on a rising soap bubble. From childhood experience, we are familiar with the vibrant colors and mesmerizing display of chaotic f…
Unsteady simulations of horizontal ribbon growth of silicon were performed that included both Marangoni and buoyancy effects. A chaotic flow was observed dominated by strong Marangoni-driven jets emerging near the local temperature minima on the free surface. This oscillatory flow caused the vertical position of the leading edge of the sheet to fluctuate, resulting in corrugations on the top surface of the ribbon. Additionally, larger amplitude and wavelength nonuniformities appeared on the bottom of the sheet resulting in a sheet with varying thickness. Lastly, the unsteady flow caused tempor…
The Greek aperitif Ouzo is not only famous for its specific anise-flavored taste, but also for its ability to turn from a transparent miscible liquid to a milky-white colored emulsion when water is added. Recently, it has been shown that this so-called Ouzo effect, i.e. the spontaneous emulsification of oil microdroplets, can also be triggered by the preferential evaporation of ethanol in an evaporating sessile Ouzo drop, leading to an amazingly rich drying process with multiple phase transitions [H. Tan et al., Proc. Natl. Acad. Sci. USA 113(31) (2016) 8642]. Due to the enhanced evaporation n…
The evaporation of multi-component droplets is relevant to various applications but challenging to study due to the complex physicochemical dynamics. Recently, Li (2018) reported evaporation-triggered segregation in 1,2-hexanediol-water binary droplets. In this present work, we added 0.5 wt% silicone oil into the 1,2-hexanediol-water binary solution. This minute silicone oil concentration dramatically modifies the evaporation process as it triggers an early extraction of the 1,2-hexanediol from the mixture. Surprisingly, we observe that the segregation of 1,2-hexanediol forms plumes, rising up…
We present a theory for the self-propulsion of symmetric, half spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air-water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion-advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary cond…
An efficient way to precisely pattern particles on solid surfaces is to dispense and evaporate colloidal drops, as for bioassays. The dried deposits often exhibit complex structures exemplified by the coffee ring pattern, where most particles have accumulated at the periphery of the deposit. In this work, the formation of deposits during the drying of nanoliter colloidal drops on a flat substrate is investigated numerically and experimentally. A finite-element numerical model is developed that solves the Navier-Stokes, heat and mass transport equations in a Lagrangian framework. The diffusion …
Hidden in plain sight: How evaporation impacts the pendant drop method
Canon Production Printing Netherlands B.V.（荷兰佳能生产打印有限公司）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；University of Twente（特温特大学）
We consider the evaporation of a thin liquid layer which consists of a binary mixture of volatile liquids. The mixture is on top of a heated substrate and in contact with the gas phase that consists of the same vapour as the binary mixture. The effect of thermocapillarity, solutocapillarity and the van der Waals interactions are considered. We derive the long-wave evolution equations for the free interface and the volume fraction that govern the two-dimensional stability of the layer subject to the above coupled mechanisms and perform a linear stability analysis. Our results demonstrate two mo…
In practical applications of inkjet printing the nozzles in a printhead have intermittent idle periods, during which ink can evaporate from the nozzle exit. Inks are usually multicomponent where each component has its own characteristic evaporation rate resulting in concentration gradients within the ink. These gradients may directly and indirectly (via Marangoni flows) alter the jetting process and thereby its reproducibility and the resulting print quality. In the present work, we study selective evaporation from an inkjet nozzle for water-glycerol mixtures. Through experiments, analytical m…
A Sharp and Conservative VOF Method for Multicomponent Liquid--Gas Mass Transfer: Bubble Dissolution and Droplet Evaporation
School of Engineering Science, University of Chinese Academy of Sciences（中国科学院大学工程科学学院）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University（西安交通大学航空航天学院机械结构强度与振动国家重点实验室）
Motived by recent ground-based and microgravity experiments investigating the interfacial dynamics of a volatile liquid (FC-72, $Pr=12.34$) contained in a heated cylindrical cell, we numerically study the thermocapillary-driven flow in such an evaporating liquid layer. Particular attention is given to the prediction of the transition of the axisymmetric flow to fully three-dimensional patterns when the applied temperature increases. The numerical simulations rely on an improved one-sided model of evaporation by including heat and mass transfer through the gas phase via the heat transfer Biot n…
The present article experimentally and theoretically probes the evaporation kinetics of sessile saline droplets. Observations reveal that presence of solvated ions leads to modulated evaporation kinetics, which is further a function of surface wettability. On hydrophilic surfaces, increasing salt concentration leads to enhanced evaporation rates, whereas on superhydrophobic surfaces, it first enhances and reduces with concentration. Also, the nature and extents of the evaporation regimes constant contact angle or constant contact radius are dependent on the salt concentration. The reduced evap…
Understanding the mechanics of detrimental convective instabilities in drying polymer solutions is crucial in many applications such as the production of film coatings. It is well known that solvent evaporation in polymer solutions can lead to Rayleigh-Bénard or Marangoni-type instabilities. Here we reveal another mechanism, namely that evaporation can cause the interface to display Rayleigh-Taylor instabilities due to the build-up of a dense layer at the air-liquid interface. We study experimentally the onset time ($t_p$) of the instability as a function of the macroscopic properties of aqueo…
Purpose: To determine whether evaporation, tangential flow, or a combination of the two cause tear film breakup in a variety of instances; to estimate related breakup parameters that cannot be measured in breakup during subject trials; and to validate our procedure against previous work. Methods: Five ordinary differential equation models for tear film thinning were designed that model evaporation, osmosis, and various types of flow. Eight tear film breakup instances of five healthy subjects that were identified in fluorescence images in previous work were fit with these five models. The fitti…
A theoretical framework is established to model the evaporation from continuously fed droplets, promising tools in the thermal management of high heat flux electronics. Using the framework, a comprehensive model is developed for a hemispherical water droplet resting on a heated flat substrate incorporating all of the relevant transport mechanisms: buoyant and thermocapillary convection inside the droplet and diffusive and convective transport of vapor in the gas domain. At the interface, mass, momentum, and thermal coupling of the phases are also made accounting for all pertinent physical aspe…
Unexpectedly distinct patterns in evaporation were observed over heated water. Although the patterns had chaotic aspects, they often showed geometric patterns. These patterns bore strong resemblance to the infrared emission patterns observable with a mid-infrared camera focused on the water surface. This similarity puts constraints on the mechanism of evaporation, and leads to a general hypothesis as to the nature of the evaporative process.
Self-driven nanofluidic flow at the liquid-air interface is a non-intuitive phenomenon. This flow behaviour was not driven by classical pressure difference or evaporation only. Depending on the position of the nanofluidic pore we can observe flow and no-flow with chaotic behaviour. In this paper, we study the nonlinear dynamics of a confined nanopore system at the liquid-air interface. The finite-range interactions between the interacting species are quantified with a corresponding critical velocity of the system. This is visualised using the finite element method and analysed mathematically w…
This article deals with the numerical modeling of the pulsating heat pipe (PHP) and is based on the film evaporation/condensation model recently applied to the single-bubble PHP (Das et al., 2010, "Thermally Induced Two-Phase Oscillating Flow Inside a Capillary Tube," Int. J. Heat Mass Transfer, 53(19--20), pp. 3905--3913). The described numerical code can treat the PHP of an arbitrary number of bubbles and branches. Several phenomena that occur inside the PHP are taken into account: coalescence of liquid plugs, film junction or rupture, etc. The model reproduces some of the experimentally obs…
