Thermal Marangoni Flow Research Articles

Droplet evaporation on curved surfaces: transients of internal and external transport phenomena

We explore the transient evolution of thermo-fluid-dynamics of evaporating sessile droplets over curved substrates in the liquid and gaseous domains. A computational model using the Arbitrary Lagrangian-Eulerian framework is adopted. The governing equations in both liquid and gaseous domains are solved in a fully coupled manner, considering coupled effects of evaporative cooling and heat advection due to bulk fluid motion. This bulk motion in the liquid domain is caused by natural advection due to thermal actuations such as thermal Marangoni flow and buoyancy-driven convection. For the gaseous domain, the additional effects of solutal convection (due to vapour-concentration variation), Stefan flow and interfacial viscous stresses are also considered. To depict a generalized role of substrate curvature, both concave and convex surfaces with curvatures over a wide range are studied. The surface wettability effects are also explored by varying the true contact angle of the droplets. Computational predictions on evaporation rate and internal flow field are validated against experimental results from literature. The interplay of wetting state and substrate curvature is noted to substantially affect the evaporation process and its thermo-fluidics. The convex curvature significantly augments internal advection while the same is weakened over concave substrates due to altered mass loss rate. Consequently, the duration of multi-vortex Marangoni flows in the development stages of evaporation and the advection in the external gaseous domain is markedly different for different curvatures. Further, on superhydrophobic curved surfaces, the effects of re-distributed evaporative fluxes play a major role. In such cases, the reduced mass flux over a large interfacial area near the periphery expedites the stable state Marangoni and external flow features.

External Stefan and Internal Marangoni Thermo-Fluid Dynamics for Evaporating Capillary Bridges.

We probe the evaporation mechanisms of wettability-moderated, confined capillary bridges and bulges. For the first time, we explore the internal Marangoni hydrodynamics and external Stefan advection dynamics in the surrounding gaseous domain due to evaporative effects. A transient simulation approach based on the level set (LS) method and the Arbitrary Lagrangian-Eulerian (ALE) framework was adopted to computationally model the capillary bridge profiles and evaporation phenomenon with generic contact line dynamics (both CCR and CCA modes). The governing equations corresponding to the transport processes in both the liquid and gaseous domains are simulated in a fully coupled manner with appropriate boundary conditions to precisely trace the liquid-vapor interface and the three-phase contact point during evaporation. The effect of the bridge confinement phenomenon, i.e., the extent of confined ambient surrounding the liquid-vapor interface between the solid surfaces, is explored. Also, the role of wetting state and contact line dynamics during CCR and CCA modes of evaporation were probed, and good agreement with experimental observations was noted. Results show that the evaporation rate is primarily dictated by the confinement phenomenon, and wettability effects play a marginal role. A higher confinement curtails the evaporation rate due to an increased local vapor concentration around the liquid bridges. However, the wetting state substantially affects the internal Marangoni effect dynamics and the Stefan advection dynamics due to its explicit influence on the nonuniform evaporative flux along the liquid-vapor interface. Between superhydrophobic confinements, the contact lines are confined in the wedge-shaped region, thereby locally augmenting the vapor concentration. As a result, the large evaporative flux near the bulge region develops a higher temperature gradient, thereby inducing upscaled thermal Marangoni flow compared to hydrophilic confinements. These findings may have significant implications for the efficient designing and development of thermofluidic systems involving thermal transport, mixing, and deposition of dissolved particles in liquid bridges.

Solution-Processable Route for Large-Area Uniform 2D Semiconductor Nanofilms.

The semiconductor thin film engineering technique plays a key role in the development of advanced electronics. Printing uniform nanofilms on freeform surfaces with high efficiency and low cost is significant for actual industrialization in electronics. Herein, a high-throughput colloidal printing (HTCP) strategy is reported for fabricating large-area and uniform semiconductor nanofilms on freeform surfaces. High-throughput and uniform printing rely on the balance of atomization and evaporation, as well as the introduced thermal Marangoni flows of colloidal dispersion, that suppresses outward capillary flows. Colloidal printing with in situ heating enables the fast fabrication of large-area semiconductor nanofilms on freeform surfaces, such as SiO2/Si, Al2O3, quartz glass, poly(ethylene terephthalate) (PET), Al foil, plastic tube, and Ni foam, expanding their technological applications where substrates are essential. The printed SnS2 nanofilms are integrated into thin-film semiconductor gas sensors with one of the fastest responses (8 s) while maintaining the highest sensitivity (Rg/Ra = 21) (toward 10ppm NO2), as well as an ultralow limit of detection (LOD) of 46 ppt. The ability to print uniform semiconductor nanofilms on freeform surfaces with high-throughput promises the development of next-generation electronics with low cost and high efficiency.

Particle deposition dynamics in evaporating droplets using lattice Boltzmann and magnetic particle simulation

Herein, a simulation model is proposed that combines the lattice Boltzmann method (LBM) and a magnetic particle model to observe particle ring patterns in evaporating sessile droplets, controlling them using a magnetic field. Brownian dynamics and van der Waals force models are applied to the nanoparticles. The interactions between the magnetic particles are simulated using the magnetic particle model, which is validated using previous experimental particle distribution results. The particle deposition patterns are compared according to the substrate wetting conditions. The distribution exhibited a clear coffee-ring pattern as the pinning time of the contact line increased. In the case of a non-pinned droplet, the thermal Marangoni flow was maintained, and the adhesion of the particles was delayed by the vortex. A thick, uniform ring pattern was formed when a magnetic field was applied to the particles. The particle bundles formed by the magnetic field were resistant to flow. To verify this result, the average particle velocity was measured. Consequently, particle transfer was classified into three stages. In Stage I, capillary force dominates, Marangoni flow develops in Stage II, and particle adhesion occurs in Stage III. With an increase in the magnetic strength, the velocity change exhibited a decrease across all stages.

Laser Controlled Manipulation of Microbubbles on a Surface with Silica-Coated Gold Nanoparticle Array.

Microbubble generation and manipulation play critical roles in diverse applications such as microfluidic mixing, pumping, and microrobot propulsion. However, existing methods are typically limited to lateral movements on customized substrates or rely on specific liquids with particular properties or designed concentration gradients, thereby hindering their practical applications. To address this challenge, this paperpresents a method that enables robust vertical manipulation of microbubbles. By focusing a resonant laser on hydrophilic silica-coated gold nanoparticle arrays immersed in water, plasmonic microbubbles are generated and detach from the substrates immediately upon cessation of laser irradiation. Using simple laser pulse control, it can achieve an adjustable size and frequency of bubble bouncing, which is governed by the movement of the three-phase contact line during surface wetting. Furthermore, it demonstrates that rising bubbles can be pulled back by laser irradiation induced thermal Marangoni flow, which is verified by particle image velocimetry measurements and numerical simulations. This study provides novel insights into flexible bubble manipulation and integration in microfluidics, with significant implications for various applications including mixing, drug delivery, and the development of soft actuators.

Pinning and Depinning Dynamics of an Evaporating Sessile Droplet Containing Mono- and Bidispersed Colloidal Particles on a Nonheated/Heated Hydrophobic Substrate

The present study is primarily focused on the coupled effects of substrate heating, colloidal dispersion, and particle size variation on the contact line (CL) pinning-depinning dynamics of evaporating droplets containing mono- (3/4.5 μm) and bidispersed (3 and 4.5 μm) polystyrene colloidal particles on poly(dimethylsiloxane) (PDMS) substrates. Experimental techniques such as high-speed visualization, optical microscopy, infrared thermography, and scanning electron microscopy are implemented to discover the plausible causes dictating the underlying physics. In the case of the nonheated substrate, there exists a significant delay in the CL depinning for the evaporating droplets containing bidispersed particles, as opposed to the monodispersed cases. A first-order model is illustrated for the determination of the net horizontal force acting on the particles near the CL. Interestingly, the model's findings revealed that due to the difference of particle size in the case of the bidispersed suspension, the interparticle contact force gets modified, thus enhancing the CL pinning. For the heated substrate cases, droplets with monodispersed particles (3 μm) exhibit a substantial delay in the CL depinning, whereas a nearly complete pinning of the CL is witnessed for the case of bidispersed colloidal suspension droplets. It is mainly due to the augmentation of particle deposition near the CL because of the circulatory thermal Marangoni and outward capillary flows. Thus, the mobility of the CL is inhibited, which is further reinforced by the presence of different-sized particles. Eventually, a ring-like deposition is observed, as opposed to an inner deposit commonly observed from the evaporation of colloidal droplets on hydrophobic substrates.

Droplet transportation on photosensitive lubricant-impregnated slippery surfaces in response to the light induced Marangoni effect and asymmetrical wetting ridges.

Flexible control of droplet transportation is crucial in various applications but is constrained by liquid-solid friction. The development of biomimetic lubricant-impregnated slippery surfaces provides a new solution for flexible manipulation of droplet transportation. Herein, a light strategy is reported for flexibly controlling droplet transportation on photosensitive lubricant-impregnated slippery surfaces. Owing to the localized heating effect of a focused laser beam via photothermal conversion, the resultant thermal Marangoni flow and horizontal component of the surface tension associated with the asymmetric wetting ridges are together responsible for actuating droplet transportation. It is found that the asymmetry of the wetting ridge is dominated by the thickness of the infused oil layer, which directly affects the droplet transportation. The feasibility of this light strategy is also demonstrated by uphill movement, droplet coalescence, and chemical reaction. This study provides a new design for potential applications in open droplet microfluidics, analytical chemistry, diagnosis, etc.

Probing Into the Drying Pattern Dynamics of a Ferrofluid Droplet Under the Actuation of Magnetic Field

Evaporation of liquids, especially colloids, is a subject of research interest since decades. Evaporation patterns of colloidal particles can determine key factors about the liquid properties and the underlying physics. Particle deposition, self-assembly, and inkjet printing are various applications, where the control of droplet evaporation and its patterns can be useful. Here, kerosene-based ferrofluid droplets were allowed to evaporate in the presence of static magnetic field. Earlier, the evaporation pattern of the same fluid in ambient conditions was reported, where ring pattern with central accumulation was observed. This was attributed to thermal Marangoni flow. In this case, magnetic field helps in circumventing this pattern, and directional dependence on magnetic field in the final patterns was also observed. Magnetic field parallel to the substrate created chain structures in the direction of the field, whereas magnetic field perpendicular to the substrate resulted in completely uniform pattern. For higher volume fraction of the chosen samples, the influence of external magnetic field was seen earlier than the samples of lower volume fraction. Effect of substrate wettability was observed under similar conditions for glass substrate and Polydimethylsiloxane (PDMS) substrate. These experimental results are compared/supported by the available existing theoretical results/theories. The inferences obtained from this analysis are expected to be useful in the optimization of particle deposition of magnetic colloids, typically of demanding significance in fields, such as nanochromatography, lithography, surface engineering, self-assembly, inkjet printing, and so on.

Delaying dynamic wetting failure using thermal Marangoni flow

We develop a parallel-plate hydrodynamic model to study the influence of thermal Marangoni flow on dynamic wetting failure. We show that flow toward the dynamic contact line delays wetting failure to a higher critical capillary number by changing stress gradients in the vicinity of the contact line. Through this work, we provide a potential framework for developing faster coating processes using thermal Marangoni flow.

Rheology dictated spreading regimes of a non-isothermal sessile drop

In the present work, within the framework of thin film theory, we delineate the interaction between the interfacial dynamics of thermal Marangoni flow and non-Newtonian rheology by considering a spreading droplet over a non-isothermal substrate. The numerical simulations, performed at different equilibrium contact angles $(\theta _e)$ , dimensionless thermocapillary strengths $(\beta )$ and shear-dependent viscosities $(n)$ , reveal that the fluid rheology nonlinearly influences the mechanisms of disjoining pressure and Marangoni stress. Accordingly, three distinct spreading regimes for non-Newtonian drops arise. Results indicate that the Marangoni film regime, having an approximate linear drop shape, sustains at lower $\theta _e$ , higher $\beta$ and $n$ ranges. Also, shear-thickening drops display an early onset of thermocapillary time scale and a steeper advancing front, while their shear-thinning counterparts retain a significant curvature for a much longer time. Contrastingly, the droplet regime is identified by fixed shape and uniform speed $(U)$ at higher $\theta _e$ and lower $(\beta$ , $n)$ combinations. Here, an intricate interplay between $\beta$ and $n$ realizes a sharp increase in $U$ for shear thinning compared with its invariance for shear-thickening droplets. The transition regime appears as an intermediate regime between the other two and involves multiple ruptured droplets. In all the regimes, we observe slower (faster) spreading of shear-thinning (thickening) droplets than the Newtonian droplets. In addition, the variations in $n$ cause intense characteristic modulations to spreading attributes like droplet morphology and transient spreading behaviour, and also act as a switching mechanism between different spreading regimes. These unique results may be utilized for superior control of non-isothermal biofluid droplets in microfluidics.

Local heating effect on thermal Marangoni flow and heat transfer characteristics of an evaporating droplet

• Flow characteristics of evaporating droplets are investigated using numerical simulations. • Uniform and local heating is considered to control the internal flow of the droplets. • Flow motions are analyzed with the liquid–air interface temperature and local surface tension differences. • Flow velocity has a maximum value of 0.048 m/s at the location of the peak region of local surface tension difference. This study numerically investigated the thermal Marangoni flow and heat transfer characteristics of an evaporating droplet. Uniform and local heating methods can control the internal flow patterns of a droplet during evaporation. The present study applied the dynamic mesh method to simulate the behaviors of the liquid-air interface during evaporation. The results revealed that the flow transition inside the droplet appeared in the early stages of evaporation and occurred owing to the temperature variation at the liquid-air interface; these variations eventually yielded surface tension gradients. Moreover, nonuniform evaporation fluxes caused capillary flows that moved from the center of the droplet to the contact line along the substrate. The surface tension gradient along the liquid-air interface had a dominant effect on the internal flow, which induced the thermal Marangoni flow. For the local heating cases, different flow patterns appeared, as compared with those that appeared from uniform heating. The flow directions changed according to the local heating conditions owing to the difference in the local surface tensions at the liquid-air interface.

Droplet dissolution driven by emerging thermal gradients and Marangoni flow

The lifetime $\ensuremath{\tau}$ of an isothermal and purely diffusively dissolving droplet in a host liquid scales as $\ensuremath{\tau}\ensuremath{\sim}{R}_{0}^{2}$ with its initial radius ${R}_{0}$. Here we experimentally find and theoretically derive a completely different droplet dissolution behavior, resulting in $\ensuremath{\tau}\ensuremath{\sim}{R}_{0}^{4}$. It occurs when the dissolution dynamics is controlled by local heating of the liquid, leading to a modified solubility and a thermal Marangoni flow around the droplet.

Numerical simulation of thermo-solutal Marangoni convection in a floating half-zone with radiation effects under zero gravity

Numerical simulations of thermo-solutal Marangoni convection in a floating half SiGe zone with radiation effects under zero gravity have been carried out. In this system, thermal and solutal Marangoni flows develop along the melt free surface either in the same direction or opposite directions depending on the directions of thermal and solutal gradients. In present model of a half SiGe zone, the ambient temperature is kept constant. Radiation due to heat loss and heat gain is considered as the dominant heat transfer mechanism from the ambience. Transition mode maps, based on concentration distribution with respect to Marangoni ratio (Rσ=MaC/MaT) and ambient temperature (Ta), have been developed to investigate the effect of radiation at unequal or equal (MaC, MaT) values. The maps reveal the main concentration structures and potential transitions at various Ta values. The opposite thermo-solutal Marangoni flows give rise to more complex structures than those of the same-direction flows. Both heat loss and heat gain may alter or destabilize the concentration distribution in the melt. However, to some extent, heat loss in the opposite-direction flow case provides a stabilizing effect on the azimuthal wave pattern at a lower or higher Rσ value.

Competition between thermal and surfactant-induced Marangoni flow in evaporating sessile droplets

HypothesisThermal Marangoni flow in evaporating sessile water droplets is much weaker in experiments than predicted theoretically. Often this is attributed to surfactant contamination, but there have not been any in-depth analyses that consider the full fluid and surfactant dynamics. It is expected that more insight into this problem can be gained by using numerical models to analyze the interplay between thermal Marangoni flow and surfactant dynamics in terms of dimensionless parameters. SimulationsTwo numerical models are implemented: one dynamic model based on lubrication theory and one quasi-stationary model, that allows for arbitrary contact angles. FindingsIt is found that insoluble surfactants can suppress the thermal Marangoni flow if their concentration is sufficiently large and evaporation and diffusion are sufficiently slow. Soluble surfactants, however, either reduce or increase the interfacial velocity, depending on their sorption kinetics. Furthermore, insoluble surfactant concentrations that cause an order 0.1% surface tension reduction are sufficient to reduce the spatially averaged tangential flow velocity at the interface by a factor 100. For larger contact angles and smaller droplets this required concentration is larger (typically <1% surface tension reduction). The numerical models are mutually validated by comparing their results in cases where both are valid.

Marangoni flow and surfactant transport in evaporating sessile droplets: A lattice Boltzmann study

The circulatory Marangoni flow can alter the contact line deposition in evaporating colloidal droplets with pinned contact line. Marangoni flow can be induced by surfactants or thermal effects. Although both cases have been exclusively investigated, the combined effect of surfactant-induced and thermal Marangoni flows is still unknown. The lattice Boltzmann method is utilized to simulate droplet evaporation and corresponding Marangoni flow. Five equations for hydrodynamics, interface capturing, vapor concentration, temperature field, and surfactant transport are intrinsically coupled with each other. They are simultaneously solved in the lattice Boltzmann framework. A geometrical method is proposed to pin the contact line at the triple point. First, evaporation-induced and thermal Marangoni flows are successfully captured. By incorporating surfactant-induced effects, interesting flow patterns are observed. Considering the combined effect of surfactant and temperature gradient, maximum surfactant concentration and maximum temperature (local minima for surface tension) are found at the top and the edge of the droplet, respectively. The maximum surface tension is consequently located between them, and double-circulation flow is observed. If the thermal effect is eliminated, surfactant local concentrations intermittently converge to steady values so that the edge concentration becomes higher than the apex concentration. Until reaching the steady state, there are two patterns that the flow alternates between: one in the direction of the thermal Marangoni flow and the other in the opposite direction.

Effect of radiative heat transfer on thermal-solutal Marangoni convection in a shallow rectangular cavity with mutually perpendicular temperature and concentration gradients

A series of three-dimensional numerical simulations considering the effect of radiative heat transfer on the free surface has been carried out to examine the characteristics of thermal-solutal Marangoni convection in a shallow rectangular cavity that is subjected to mutually perpendicular temperature and concentration gradients. In the simulation, the overall contributions of thermal and solutal Marangoni flows are in the same order (Marangoni ratio Maσ=1) for all the cases considered, and the ambient temperature Θa ranges from −1.5 to 1.5, representing the transition from heat loss to heat gain in the whole system. Results show that with the increase of ambient temperature in the case of steady flow, the intensity of the thermal Marangoni effect decreases first, and then increases; furthermore, the flow structure, temperature, and concentration fields in the cavity are significantly affected by the radiative heat transfer on the free surface. When the Marangoni number exceeds a critical value, the flow stability is lost, and a three-dimensional oscillatory flow develops. The critical Marangoni number at which the flow destabilizes highly depends on thermal radiation and exhibits different variation tendencies on the stages of heat loss and gain. For the oscillatory flow, the observed wave patterns of temperature and concentration fluctuations are caused by the coupling effect of thermal-solutal Marangoni flow and radiative heat transfer. Two new types of oscillatory modes with different propagation directions appear in the cases of larger heat loss and gain due to the effect of thermal radiation. In addition, a sudden drop in the frequency is observed at a higher thermal Marangoni number.

A Numerical Study on the Exact Onset of Flow Instabilities in Thermo-Solutal Marangoni Convection Driven by Opposing Forces in a Half-Zone Liquid Bridge under Zero Gravity

The theoretical onset of the Marangoni convection instability occurring in a half-zone liquid bridge of the floating zone (FZ) growth of SixGe1–x has been investigated by numerical simulations. A half-zone model of the liquid bridge between a cold (bottom plane) and a hot (top plane) disk is considered. The highest Si concentration is on the top of the liquid bridge. Therefore, the driving forces for thermal and solutal Marangoni flows are in opposite directions in this configuration. The nonlinear equilibria and periodic orbits are obtained using the Newton–Krylov method, and their stability is analyzed with global linear stability analysis. A flow bifurcation analysis is conducted. The results show that when the solutal Marangoni number, MaC, ≤360, the primary flow bifurcation is from 2D axisymmetric to 3D steady flow. When MaC>360, the 2D axisymmetric flow becomes weakly periodic 2D axisymmetric, and eventually becomes chaotic. The critical thermal Marangoni number is monotonically increasing as MaC increases, and the flow is 2D axisymmetric when the solutal Marangoni forceis dominant. The stability evaluation for various thermal Marangoni number values at MaC=893 reveals that the onset of transition is from steady to periodic. However, the reverse transition does not occur at the same Marangoni number value. The simulation results show that the hysteresis behavior of the flow field exhibits an approximately 1% difference between two critical thermal Marangoni numbers. The present study suggests that the control parameters of FZ crystal growth should be smaller than the calculated critical values to avoid any flow-induced disturbances.

Optical Manipulation of Liquids by Thermal Marangoni Flow along the Air-Water Interfaces of a Superhydrophobic Surface.

The control of liquid motion on the micrometer scale is important for many liquid transport and biomedical applications. An efficient way to trigger liquid motion is by introducing surface tension gradients on free liquid interfaces leading to the Marangoni effect. However, a pronounced Marangoni-driven flow generally only occurs at a liquid–air or liquid–liquid interface but not at solid–liquid interfaces. Using superhydrophobic surfaces, the liquid phase stays in the Cassie state (where liquid is only in contact with the tips of the rough surface structure and air is enclosed in the indentations of the roughness) and hence provides the necessary liquid–air interface to trigger evident Marangoni flows. We use light to asymmetrically heat this interface and thereby control liquid motion near superhydrophobic surfaces. By laser scanning confocal microscopy, we determine the velocity distribution evolving through optical excitation. We show that Marangoni flow can be induced optically at structured, air-entrapping superhydrophobic surfaces. Furthermore, by comparison with numerical modeling, we demonstrate that in addition to the Marangoni flow, buoyancy-driven flow occurs. This effect has so far been neglected in similar approaches and models of thermocapillary driven flow at superhydrophobic surfaces. Our work yields insight into the physics of Marangoni flow and can help in designing new contactless, light-driven liquid transport systems, e.g., for liquid pumping or in microfluidic devices.

Thermal Marangoni Flow Impacts the Shape of Single Component Volatile Droplets on Thin, Completely Wetting Substrates.

Despite surface energies dictating complete wetting, it has been classically observed that volatile alkanes do not spread completely on glass substrates, and faster evaporation rates lead to higher contact angles. Here we investigate how substrate thickness influences this behavior. For sufficiently thin substrates, wefind alkanes evaporate slower and display higher apparent contact angles, at odds with the typical explanations involving just evaporation, capillarity, and viscous dissipation. We derive the droplet temperature distribution and use it as part of a criteria to show that thermal Marangoni contraction plays a significant role in establishing droplet shape on thin substrates.

Numerical simulation of thermo-solutal Marangoni convection in a full floating zone with radiative heat transfer under zero gravity

A numerical simulation study of thermo-solutal Marangoni convection has been carried out in a full floating zone with radiative heat transfer under zero gravity. In this system, the thermal and solutal Marangoni flows develop in the same direction and/or opposite directions along the free surface depending on the location in the zone. In the model, the ambient temperature distribution along the zone is taken as a Gaussian profile, and the radiative heat transfer is considered dominant. The characteristics of the concentration pattern in the zone vary due to the varying thermal and solutal Marangoni numbers, as well as the characteristic azimuthal wave. The flow velocity field exhibits two or four main vortices along the free surface. These vortices get stronger at higher thermal Marangoni number values.