Journal articles: 'Marangoni Flow in Droplets'

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Che, Yuzeng, Zishuo Cai, Wenbo Li, Ja Ma, Heng Wang, Shifeng Xu, Aocheng Zhang, et al. "Research on Spontaneous Diffusion and Fragmentation of Liquid Droplets Caused by Marangoni Effect." Advances in Engineering Technology Research 5, no. 1 (April 14, 2023): 135. http://dx.doi.org/10.56028/aetr.5.1.135.2023.

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The Marangoni effect is important to drying silicon wafers, the fields of welding and improving engine liquid fuel efficiency. In this paper, we investigate the Marangoni flow caused by the evaporation of droplets of alcohol solution, which eventually causes the droplet "atomization" phenomenon. The Marangoni convection phenomenon was studied in terms of temperature and droplet concentration, and the changes of droplet diffusion and the degree of droplet "atomization" were investigated after droplets of different volume concentrations of Isopropyl Alcohol (IPA) were added to different solutions.

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Morozov, Matvey, and Sébastien Michelin. "Self-propulsion near the onset of Marangoni instability of deformable active droplets." Journal of Fluid Mechanics 860 (December 11, 2018): 711–38. http://dx.doi.org/10.1017/jfm.2018.853.

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Experimental observations indicate that chemically active droplets suspended in a surfactant-laden fluid can self-propel spontaneously. The onset of this motion is attributed to a symmetry-breaking Marangoni instability resulting from the nonlinear advective coupling of the distribution of surfactant to the hydrodynamic flow generated by Marangoni stresses at the droplet’s surface. Here, we use a weakly nonlinear analysis to characterize the self-propulsion near the instability threshold and the influence of the droplet’s deformability. We report that, in the vicinity of the threshold, deformability enhances self-propulsion of viscous droplets, but hinders propulsion of drops that are roughly less viscous than the surrounding fluid. Our asymptotics further reveals that droplet deformability may alter the type of bifurcation leading to symmetry breaking: for moderately deformable droplets, the onset of self-propulsion is transcritical and a regime of steady self-propulsion is stable; while in the case of highly deformable drops, no steady flows can be found within the asymptotic limit considered in this paper, suggesting that the bifurcation is subcritical.

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Farhadi, Jafar, and Vahid Bazargan. "Marangoni flow and surfactant transport in evaporating sessile droplets: A lattice Boltzmann study." Physics of Fluids 34, no. 3 (March 2022): 032115. http://dx.doi.org/10.1063/5.0086141.

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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.

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Nerger, Bryan A., P. T. Brun, and Celeste M. Nelson. "Marangoni flows drive the alignment of fibrillar cell-laden hydrogels." Science Advances 6, no. 24 (June 2020): eaaz7748. http://dx.doi.org/10.1126/sciadv.aaz7748.

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When a sessile droplet containing a solute in a volatile solvent evaporates, flow in the droplet can transport and assemble solute particles into complex patterns. Transport in evaporating sessile droplets has largely been examined in solvents that undergo complete evaporation. Here, we demonstrate that flow in evaporating aqueous sessile droplets containing type I collagen—a self-assembling polymer—can be harnessed to engineer hydrated networks of aligned collagen fibers. We find that Marangoni flows direct collagen fiber assembly over millimeter-scale areas in a manner that depends on the rate of self-assembly, the relative humidity of the surrounding environment, and the geometry of the droplet. Skeletal muscle cells that are incorporated into and cultured within these evaporating droplets collectively orient and subsequently differentiate into myotubes in response to aligned networks of collagen. Our findings demonstrate a simple, tunable, and high-throughput approach to engineer aligned fibrillar hydrogels and cell-laden biomimetic materials.

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Karlsson, Linn, Anna-Lena Ljung, and T. Staffan Lundström. "Comparing Internal Flow in Freezing and Evaporating Water Droplets Using PIV." Water 12, no. 5 (May 23, 2020): 1489. http://dx.doi.org/10.3390/w12051489.

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The study of evaporation and freezing of droplets is important in, e.g., spray cooling, surface coating, ink-jet printing, and when dealing with icing on wind turbines, airplane wings, and roads. Due to the complex nature of the flow within droplets, a wide range of temperatures, from freezing temperatures to heating temperatures, have to be taken into account in order to increase the understanding of the flow behavior. This study aimed to reveal if natural convection and/or Marangoni convection influence the flow in freezing and evaporating droplets. Droplets were released on cold and warm surfaces using similar experimental techniques and setups, and the internal flow within freezing and evaporating water droplets were then investigated and compared to one another using Particle Image Velocimetry. It was shown that, for both freezing and evaporating droplets, a shift in flow direction occurs early in the processes. For the freezing droplets, this effect could be traced to the Marangoni convection, but this could not be concluded for the evaporating droplets. For both evaporating and freezing droplets, after the shift in flow direction, natural convection dominates the flow. In the end of the freezing process, conduction seems to be the only contributing factor for the flow.

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Liu, Jiangyu, Xinyu Guo, Yong Xu, and Xuemin Wu. "Spreading of Oil Droplets Containing Surfactants and Pesticides on Water Surface Based on the Marangoni Effect." Molecules 26, no. 5 (March 5, 2021): 1408. http://dx.doi.org/10.3390/molecules26051408.

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Oil droplets containing surfactants and pesticides are expected to spread on a water surface, under the Marangoni effect, depending on the surfactant. Pesticides are transported into water through this phenomenon. A high-speed video camera was used to measure the movement of Marangoni ridges. Gas chromatography with an electron capture detector was used to analyze the concentration of the pesticide in water at different times. Oil droplets containing the surfactant and pesticide spread quickly on the water surface by Marangoni flow, forming an oil film and promoting emulsification of the oil–water interface, which enabled even transport of the pesticide into water, where it was then absorbed by weeds. Surfactants can decrease the surface tension of the water subphase after deposition, thereby enhancing the Marangoni effect in pesticide-containing oil droplets. The time and labor required for applying pesticides in rice fields can be greatly reduced by using the Marangoni effect to transport pesticides to the target.

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Pearlman, Stephanie I., Eric M. Tang, Yuankai K. Tao, and Frederick R. Haselton. "Controlling Droplet Marangoni Flows to Improve Microscopy-Based TB Diagnosis." Diagnostics 11, no. 11 (November 21, 2021): 2155. http://dx.doi.org/10.3390/diagnostics11112155.

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In developing countries, the most common diagnostic method for tuberculosis (TB) is microscopic examination sputum smears. Current assessment requires time-intensive inspection across the microscope slide area, and this contributes to its poor diagnostic sensitivity of ≈50%. Spatially concentrating TB bacteria in a smaller area is one potential approach to improve visual detection and potentially increase sensitivity. We hypothesized that a combination of magnetic concentration and induced droplet Marangoni flow would spatially concentrate Mycobacterium tuberculosis on the slide surface by preferential deposition of beads and TB–bead complexes in the center of an evaporating droplet. To this end, slide substrate and droplet solvent thermal conductivities and solvent surface tension, variables known to impact microfluidic flow patterns in evaporating droplets, were varied to select the most appropriate slide surface coating. Optimization in a model system used goniometry, optical coherence tomography, and microscope images of the final deposition pattern to observe the droplet flows and maximize central deposition of 1 μm fluorescent polystyrene particles and 200 nm nanoparticles (NPs) in 2 μL droplets. Rain-X® polysiloxane glass coating was identified as the best substrate material, with a PBS-Tween droplet solvent. The use of smaller, 200 nm magnetic NPs instead of larger 1 μm beads allowed for bright field imaging of bacteria. Using these optimized components, we compared standard smear methods to the Marangoni-based spatial concentration system, which was paired with magnetic enrichment using iron oxide NPs, isolating M. bovis BCG (BCG) from samples containing 0 and 103 to 106 bacilli/mL. Compared to standard smear preparation, paired analysis demonstrated a combined volumetric and spatial sample enrichment of 100-fold. With further refinement, this magnetic/Marangoni flow concentration approach is expected to improve whole-pathogen microscopy-based diagnosis of TB and other infectious diseases.

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Diddens, Christian, Huanshu Tan, Pengyu Lv, Michel Versluis, J. G. M. Kuerten, Xuehua Zhang, and Detlef Lohse. "Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking." Journal of Fluid Mechanics 823 (June 20, 2017): 470–97. http://dx.doi.org/10.1017/jfm.2017.312.

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The Greek aperitif Ouzo is not only famous for its specific anise-flavoured taste, but also for its ability to turn from a transparent miscible liquid to a milky-white coloured 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 (Tan et al., Proc. Natl Acad. Sci. USA, vol. 113 (31), 2016, pp. 8642–8647). Due to the enhanced evaporation near the contact line, the nucleation of oil droplets starts at the rim which results in an oil ring encircling the drop. Furthermore, the oil droplets are advected through the Ouzo drop by a fast solutal Marangoni flow. In this article, we investigate the evaporation of mixture droplets in more detail, by successively increasing the mixture complexity from pure water over a binary water–ethanol mixture to the ternary Ouzo mixture (water, ethanol and anise oil). In particular, axisymmetric and full three-dimensional finite element method simulations have been performed on these droplets to discuss thermal effects and the complicated flow in the droplet driven by an interplay of preferential evaporation, evaporative cooling and solutal and thermal Marangoni flow. By using image analysis techniques and micro-particle-image-velocimetry measurements, we are able to compare the numerically predicted volume evolutions and velocity fields with experimental data. The Ouzo droplet is furthermore investigated by confocal microscopy. It is shown that the oil ring predominantly emerges due to coalescence.

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Matsuda, Kazuki, Tenshin Oyama, Hirotaka Ishizuka, Shuji Hironaka, and Jun Fukai. "Effect of Marangoni Convection in a Droplet Containing Surfactant on Thin Film Shape." MATEC Web of Conferences 333 (2021): 03002. http://dx.doi.org/10.1051/matecconf/202133303002.

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In printed electronics, uniform and solute film formation by the inkjet method is very important. This study aims to clarify the relationship between Marangoni convection generated by adding surfactant and thinning of solute film. First, four types of surfactants were added one by one to the anisole-polystyrene solution with varying concentrations, and then a little amount of fluorescent polymer was added as tracer to each solution. Next, each solution was dropped on a hydrophilic substrate with a droplet diameter of 80 micrometers using an inkjet method, and the flow in the evaporation process and the shape of the solute film after drying were observed. As a result, Marangoni convection occurred when any surfactant was added at a certain concentration or more, and the solute film after drying of the droplets to which two kinds of surfactants were added became thin and approached a uniform shape. In addition, the measurement of surface tension showed that the visualized flow is the Marangoni convection.

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Matsuda, Kazuki, Tenshin Oyama, Hirotaka Ishizuka, Shuji Hironaka, and Jun Fukai. "Effect of Marangoni Convection in a Droplet Containing Surfactant on Thin Film Shape." MATEC Web of Conferences 333 (2021): 03002. http://dx.doi.org/10.1051/matecconf/202133303002.

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In printed electronics, uniform and solute film formation by the inkjet method is very important. This study aims to clarify the relationship between Marangoni convection generated by adding surfactant and thinning of solute film. First, four types of surfactants were added one by one to the anisole-polystyrene solution with varying concentrations, and then a little amount of fluorescent polymer was added as tracer to each solution. Next, each solution was dropped on a hydrophilic substrate with a droplet diameter of 80 micrometers using an inkjet method, and the flow in the evaporation process and the shape of the solute film after drying were observed. As a result, Marangoni convection occurred when any surfactant was added at a certain concentration or more, and the solute film after drying of the droplets to which two kinds of surfactants were added became thin and approached a uniform shape. In addition, the measurement of surface tension showed that the visualized flow is the Marangoni convection.

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11

Soligo, Giovanni, Alessio Roccon, and Alfredo Soldati. "Breakage, coalescence and size distribution of surfactant-laden droplets in turbulent flow." Journal of Fluid Mechanics 881 (October 24, 2019): 244–82. http://dx.doi.org/10.1017/jfm.2019.772.

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In this work, we compute numerically breakage/coalescence rates and size distribution of surfactant-laden droplets in turbulent flow. We use direct numerical simulation of turbulence coupled with a two-order-parameter phase-field method to describe droplets and surfactant dynamics. We consider two different values of the surface tension (i.e. two values for the Weber number, $We$, the ratio between inertial and surface tension forces) and four types of surfactant (i.e. four values of the elasticity number, $\unicode[STIX]{x1D6FD}_{s}$, which defines the strength of the surfactant). Stretching, breakage and merging of droplet interfaces are controlled by the complex interplay among shear stresses, surface tension and surfactant distribution, which are deeply intertwined. Shear stresses deform the interface, changing the local curvature and thus surface tension forces, but also advect surfactant over the interface. In turn, local increases of surfactant concentration reduce surface tension, changing the interface deformability and producing tangential (Marangoni) stresses. Finally, the interface feeds back to the local shear stresses via the capillary stresses, and changes the local surfactant distribution as it deforms, breaks and merges. We find that Marangoni stresses have a major role in restoring a uniform surfactant distribution over the interface, contrasting, in particular, the action of shear stresses: this restoring effect is proportional to the elasticity number and is stronger for smaller droplets. We also find that lower surface tension (higher $We$ or higher $\unicode[STIX]{x1D6FD}_{s}$) increases the number of breakage events, as expected, but also the number of coalescence events, more unexpected. The increase of the number of coalescence events can be traced back to two main factors: the higher probability of inter-droplet collisions, favoured by the larger number of available droplets, and the decreased deformability of smaller droplets. Finally, we show that, for all investigated cases, the steady-state droplet size distribution is in good agreement with the $-10/3$ power-law scaling (Garrett et al., J. Phys. Oceanogr., vol. 30 (9), 2000, pp. 2163–2171), conforming to previous experimental observations (Deane & Stokes, Nature, vol. 418 (6900), 2002, p. 839) and numerical simulations (Skartlien et al., J. Chem. Phys., vol. 139 (17), 2013).

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Mokbel, Marcel, Karin Schwarzenberger, Sebastian Aland, and Kerstin Eckert. "Information transmission by Marangoni-driven relaxation oscillations at droplets." Soft Matter 14, no. 45 (2018): 9250–62. http://dx.doi.org/10.1039/c8sm01720d.

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Liu, Haihu, Yan Ba, Lei Wu, Zhen Li, Guang Xi, and Yonghao Zhang. "A hybrid lattice Boltzmann and finite difference method for droplet dynamics with insoluble surfactants." Journal of Fluid Mechanics 837 (December 21, 2017): 381–412. http://dx.doi.org/10.1017/jfm.2017.859.

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Droplet dynamics in microfluidic applications is significantly influenced by surfactants. It remains a research challenge to model and simulate droplet behaviour including deformation, breakup and coalescence, especially in the confined microfluidic environment. Here, we propose a hybrid method to simulate interfacial flows with insoluble surfactants. The immiscible two-phase flow is solved by an improved lattice Boltzmann colour-gradient model which incorporates a Marangoni stress resulting from non-uniform interfacial tension, while the convection–diffusion equation which describes the evolution of surfactant concentration in the entire fluid domain is solved by a finite difference method. The lattice Boltzmann and finite difference simulations are coupled through an equation of state, which describes how surfactant concentration influences interfacial tension. Our method is first validated for the surfactant-laden droplet deformation in a three-dimensional (3D) extensional flow and a 2D shear flow, and then applied to investigate the effect of surfactants on droplet dynamics in a 3D shear flow. Numerical results show that, at low capillary numbers, surfactants increase droplet deformation, due to reduced interfacial tension by the average surfactant concentration, and non-uniform effects from non-uniform capillary pressure and Marangoni stresses. The role of surfactants on the critical capillary number ($Ca_{cr}$) of droplet breakup is investigated for various confinements (defined as the ratio of droplet diameter to wall separation) and Reynolds numbers. For clean droplets,$Ca_{cr}$first decreases and then increases with confinement, and the minimum value of$Ca_{cr}$is reached at a confinement of 0.5; for surfactant-laden droplets,$Ca_{cr}$exhibits the same variation in trend for confinements lower than 0.7, but, for higher confinements,$Ca_{cr}$is almost a constant. The presence of surfactants decreases$Ca_{cr}$for each confinement, and the decrease is also attributed to the reduction in average interfacial tension and non-uniform effects, which are found to prevent droplet breakup at low confinements but promote breakup at high confinements. In either clean or surfactant-laden cases,$Ca_{cr}$first remains almost unchanged and then decreases with increasing Reynolds number, and a higher confinement or Reynolds number favours ternary breakup. Finally, we study the collision of two equal-sized droplets in a shear flow in both surfactant-free and surfactant-contaminated systems with the same effective capillary numbers. It is identified that the non-uniform effects in the near-contact interfacial region immobilize the interfaces when two droplets are approaching each other and thus inhibit their coalescence.

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Huang, Bingyao, Haodong Zhang, Zundi Liu, Xiaoyuan Yang, Wei Li, and Yuyang Li. "Characterizing Internal Flow Field in Binary Solution Droplet Combustion with Micro-Particle Image Velocimetry." Applied Sciences 13, no. 9 (May 6, 2023): 5752. http://dx.doi.org/10.3390/app13095752.

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Droplet internal flow participates in liquid-phase mass transfer during multicomponent solution droplet combustion. In this work, internal flow fields in the binary droplet combustion of two polyoxymethylene dimethyl ethers (CH3O(CH2O)nCH3, n ≥ 1, abbreviated as PODEn), i.e., PODE2 and PODE4, are characterized using micro-particle image velocimetry (Micro-PIV). The buoyancy-driven upward vapor flow around the droplet is found to initiate two opposite radial flows in the droplet, which form two vortex cores near the surface, while the gravitational effect and Marangoni effect resulting from the content and temperature gradients in the binary droplets can induce disturbance to the two flows. The binary droplets have comparable spatially averaged flow velocities at the stable evaporation stage to those of pure droplets, which are around 3 mm/s. The velocity curves are more fluctuant and tend to slightly increase and reach the peak values at around 250 ms, and then decrease until droplet atomization. The flow velocities in the droplet interior are generally higher than those near the droplet surface, forming a parabolic velocity profile along the horizontal radial direction. The peak velocity first increases to 5–9 mm/s as the radial flow and vortex structure start to form and then decreases to around 3 mm/s until droplet atomization. The radial flow with a spatially averaged velocity of 3 mm/s can run around one lap during the stable evaporation stage, which implies that the convection-induced mass transfer is relatively weak, and consequently, the content gradient of the binary droplet is still mainly controlled by mass diffusion.

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Wu, Zi-Yi, Li-Tao Yang, Shao-Fei Zheng, Shu-Rong Gao, Yan-Ru Yang, Tian Gao, Bengt Sunden, and Xiao-Dong Wang. "Convective transport characteristics of condensing droplets in moist air flow." Physics of Fluids 35, no. 2 (February 2023): 027111. http://dx.doi.org/10.1063/5.0134579.

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Condensation of convective moist air flow is a crucial physical process and is directly related to various industries. It is essential to understand the underlying growth mechanism of condensing droplets, while past studies have commonly considered convective transport with a negligible/simplified approach. In this work, a three-dimensional transient multiphysics coupling model was developed to investigate the transport characteristics of condensing droplets in convective moist air flow. This model typically interconnects heat transfer with vapor–liquid phase change, mass transport, and fluid flow. The results reveal that convective flow significantly dominates heat and mass transport during condensation. On the gas side, the incoming flow thins the diffusion layer at the windward part with a large concentration gradient. However, a low vapor-concentration zone behind the droplet is formed due to the resulting rear-side vortex, which presents an increased influence as the contact angle increases. By forcing molecular diffusion with convection transport, vapor transport from surroundings to the condensing interface is enhanced several times depending on the Reynolds number. Within the droplet, the flow shearing at the interface is principally responsible for the strong internal convection, while the Marangoni effect is negligible. The internal flow greatly affects the droplet temperature profile with a large gradient close to the base. Finally, convective flow contributes to over 3.3 times higher overall heat transfer coefficient than the quiescent environment. In addition, in interaction-governed growth, transport characteristics depend on not only the size and space distributions of droplets but also the interaction between droplets and convective flow.

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TAM, DANIEL, VOLKMAR von ARNIM, G. H. McKINLEY, and A. E. HOSOI. "Marangoni convection in droplets on superhydrophobic surfaces." Journal of Fluid Mechanics 624 (April 10, 2009): 101–23. http://dx.doi.org/10.1017/s0022112008005053.

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We consider a small droplet of water sitting on top of a heated superhydrophobic surface. A toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the interior towards the liquid/solid contact point. The internal dynamics arise due to the presence of a vertical temperature gradient; this leads to a gradient in surface tension which in turn drives fluid away from the contact point along the interface. We develop a solution to this thermocapillary-driven Marangoni flow analytically in terms of streamfunctions. Quantitative comparisons between analytical and experimental results, as well as effective heat transfer coefficients, are presented.

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Chen, Chang, XiuMei Xu, Yi Li, Hilde Jans, Pieter Neutens, Sarp Kerman, Guy Vereecke, et al. "Full wetting of plasmonic nanopores through two-component droplets." Chemical Science 6, no. 11 (2015): 6564–71. http://dx.doi.org/10.1039/c5sc02338f.

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By placing a drop of wine near the sub-10 nm gold nanopore to generate a Marangoni flow, we can finally overcome the wetting problem and make the nanopore perform excellently for molecular sensing in aqueous solutions.

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Antritter, Thomas, Peter Hachmann, Tatiana Gambaryan-Roisman, Bernhard Buck, and Peter Stephan. "Spreading of Micrometer-Sized Droplets under the Influence of Insoluble and Soluble Surfactants: A Numerical Study." Colloids and Interfaces 3, no. 3 (August 9, 2019): 56. http://dx.doi.org/10.3390/colloids3030056.

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Wetting and spreading of surfactant solutions play an important role in many technical applications. In printing processes, the size of individual droplets is typically on the order of a few tens of microns. The purpose of this study is to develop a better understanding of the interaction between spreading and surfactant transport on these small length and related time scales. Therefore, numerical simulations based on the volume-of-fluid method including Marangoni stresses and transport of an insoluble or soluble surfactant are performed. The results for an insoluble surfactant show competing effects of Marangoni flow on the one hand, and a decreasing surfactant concentration as the droplet spreads on the other hand. Even in the case of a soluble surfactant, adsorption and desorption could only partly mitigate these effects, demonstrating the importance of the sorption kinetics for fast, small scale wetting processes.

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Cai, Y., and B. m. Zhang Newby. "Polymeric microstructure arrays consequence of Marangoni flow-induced water droplets." Applied Physics A 100, no. 4 (July 1, 2010): 1221–29. http://dx.doi.org/10.1007/s00339-010-5882-y.

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Narsimhan, Vivek. "Shape and rheology of droplets with viscous surface moduli." Journal of Fluid Mechanics 862 (January 11, 2019): 385–420. http://dx.doi.org/10.1017/jfm.2018.930.

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We develop perturbation theories to describe the flow dynamics of a droplet with a thin layer of insoluble surfactant whose mechanics are described by interfacial viscosity, i.e. a Boussinesq–Scriven constitutive law. The theories quantify droplet deformation in the limit of small capillary number, large viscosity ratio, or large shear Boussinesq number, to a sufficient level of approximation where one can extract information about nonlinear rheology and droplet breakup. In the first part of this manuscript, we quantify the Taylor deformation parameter and inclination angle in shear and extensional flows, developing expressions that resolve discrepancies between current analytical theories and boundary element simulations. Interestingly, the theories we develop appear to accurately describe the inclination angle of a clean droplet over a wider range of viscosity ratios and capillary numbers than previous works. In the second part of the manuscript, we calculate how interfacial viscosity alters the extra stress of a dilute suspension of droplets, in particular the shear stress, normal stress differences, shear thinning and extensional thickening. The normal stresses are intimately related to the lateral migration of droplets in wall-bound shear flow, and we explore the influence of interfacial viscosity on this phenomenon. We conclude by discussing how one can use these theories to describe droplet breakup, and how one can incorporate additional effects into the perturbation theories such as viscoelastic membranes and/or Marangoni flows.

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Masoudi, Saeed, and Hendrik C. Kuhlmann. "Axisymmetric buoyant–thermocapillary flow in sessile and hanging droplets." Journal of Fluid Mechanics 826 (August 15, 2017): 1066–95. http://dx.doi.org/10.1017/jfm.2017.479.

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The steady axisymmetric incompressible flow in a droplet sitting on or hanging from a flat plate is calculated numerically. In the limit of large mean surface tension the liquid–gas interface is spherical which allows the use of boundary-fitted toroidal coordinates. The flow is driven by thermocapillary and buoyant forces induced by a linear variation of the ambient temperature normal to the perfectly conducting wall. We present benchmark-quality results for the streamfunction and temperature fields, varying the contact angle, the thermocapillary Reynolds number, the Prandtl number, the Grashof number and the interfacial heat-transfer coefficient including the latent heat of evaporation. Scaling laws for the strength of the flow are provided for asymptotically large Marangoni numbers.

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Zhu, Ji-Long, and Wan-Yuan Shi. "Instability patterns of Marangoni flow in evaporating droplets on lyophobic surface." International Communications in Heat and Mass Transfer 141 (February 2023): 106598. http://dx.doi.org/10.1016/j.icheatmasstransfer.2022.106598.

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Foudhil, Walid, Costanza Aricò, Patrick Perré, and Sadok Ben Jabrallah. "Use of Heating Configuration to Control Marangoni Circulation during Droplet Evaporation." Water 14, no. 10 (May 22, 2022): 1653. http://dx.doi.org/10.3390/w14101653.

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The present work presents a numerical study of the evaporation of a sessile liquid droplet deposited on a substrate and subjected to different heating configurations. The physical formulation accounts for evaporation, the Marangoni effect, conductive transfer in the support, radiative heating, and diffusion–convection in the droplet itself. The moving interface is solved using the Arbitrary Lagrangian–Eulerian (ALE) method. Simulations were performed using COMSOL Multiphysics. Different configurations were performed to investigate the effect of the heating conditions on the shape and intensity of the Marangoni circulations. A droplet can be heated by the substrate (different natures and thicknesses were tested) and/or by a heat flux supplied at the top of the droplet. The results show that the Marangoni flow can be controlled by the heating configuration. An upward Marangoni flow was obtained for a heated substrate and a downward Marangoni flow for a flux imposed at the top of the droplet. Using both heat sources generated two vortices with an upward flow from the bottom and a downward flow from the top. The position of the stagnation zone depended on the respective intensities of the heating fluxes. Controlling the circulation in the droplet might have interesting applications, such as the control of the deposition of microparticles in suspension in the liquid, the deposition of the solved constituent, and the enhancement of the evaporation rate.

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Huo, Y., S. P. Song, and B. Q. Li. "Droplet Deformation and 2-D/3-D Marangoni Flow Phenomena in Droplets Levitated by Electric Fields." Materials and Manufacturing Processes 19, no. 4 (October 2004): 761–75. http://dx.doi.org/10.1081/amp-200028126.

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SCHLEIZER, ANTHONY D., and ROGER T. BONNECAZE. "Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows." Journal of Fluid Mechanics 383 (March 25, 1999): 29–54. http://dx.doi.org/10.1017/s0022112098003462.

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The dynamic behaviour and stability of a two-dimensional immiscible droplet subject to shear or pressure-driven flow between parallel plates is studied under conditions of negligible inertial and gravitational forces. The droplet is attached to the lower plate and forms two contact lines that are either fixed or mobile. The boundary-integral method is used to numerically determine the flow along and dynamics of the free surface. For surfactant-free interfaces with fixed contact lines, the deformation of the interface is determined for a range of capillary numbers, droplet to displacing fluid viscosity ratios, droplet sizes and flow type. It is shown that as the capillary number or viscosity ratio or size of the droplet increases, the deformation of the interface increases and above critical values of the capillary number no steady shape exists. For small droplets, and at low capillary numbers, shear and pressure-driven flows are shown to yield similar steady droplet shapes. The effect of surfactants is studied assuming a fixed amount of surfactant that is subject to convective–diffusive transport along the interface and no transport to or from the bulk fluids. Increasing the surface Péclet number, the ratio of convective to diffusive transport, leads to an accumulation of surfactant at the downstream end of the droplet and creates Marangoni stresses that immobilize the interface and reduce deformation. The no-slip boundary condition is then relaxed and an integral form of the Navier-slip model is used to examine the effects of allowing the droplet to slip along the solid surface in a pressure-driven flow. For contact angles less than or equal to 90°, a stable droplet spreads along the wall until a steady shape is reached, when the droplet translates across the wall at a constant velocity. The critical capillary number is larger for these droplets compared to those with pinned contact lines. For contact angles greater than 90°, the wetted area between a stable droplet and the wall decreases until a steady shape is reached. The critical capillary number for these droplets is less than that for pinned droplets. Above the critical capillary number the droplet completely detaches for a contact angle of 120°, or part of it is pinched off leaving behind a smaller attached droplet for contact angles less than or equal to 90°.

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Liu, Haiting, and Jiewen Deng. "Influence of Marangoni Effect on Heat and Mass Transfer during Evaporation of Sessile Microdroplets." Micromachines 13, no. 11 (November 13, 2022): 1968. http://dx.doi.org/10.3390/mi13111968.

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Evaporative cooling is an important method for controlling the temperature of micro devices, and heat and mass transfer from the microdroplets in the evaporation process directly affect the cooling performance. In order to study the droplet heat and mass transfer law in the droplet evaporation process, this paper builds a coupled thermal mass model of droplet evaporation and tests the accuracy of the numerical model through theoretical results. In order to study the influence of the Marangoni effect on the droplet evaporation process and the effects of different initial droplet radius and ambient temperature on the temperature and flow, fields within the droplet are compared. From this result, it can be seen that the droplet volume is 20 μL, and the maximum flow velocity in the droplet is 0.34 mm/s, without taking into account the Marangoni effect. When the Marangoni effect is taken into account, the maximum flow velocity increases by almost 100 times. The Marangoni effect can cause the convection in the droplet to change direction, and the formation of the Marangoni flow may affect the temperature distribution within the droplet, thereby increasing the evaporation efficiency by 2.5%. The evaporation process will increase the velocity of the air close to the surface of the liquid, but the increase in air velocity close to the liquid surface is not sufficient to reinforce evaporation. There is a non-linear relationship between increasing ambient temperature and increasing evaporation efficiency. For every 5 °C increase in ambient temperature, the maximum increase in the rate of evaporation is approximately 22.7%.

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Al-Sharafi, Abdullah, Ahmet Z. Sahin, Bekir S. Yilbas, and S. Z. Shuja. "Marangoni convection flow and heat transfer characteristics of water–CNT nanofluid droplets." Numerical Heat Transfer, Part A: Applications 69, no. 7 (January 4, 2016): 763–80. http://dx.doi.org/10.1080/10407782.2015.1090809.

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Huo, Y., and B. Q. Li. "Three-dimensional Marangoni convection in electrostatically positioned droplets under microgravity." International Journal of Heat and Mass Transfer 47, no. 14-16 (July 2004): 3533–47. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2004.01.021.

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Zeng, Binglin, Kai Leong Chong, Yuliang Wang, Christian Diddens, Xiaolai Li, Marvin Detert, Harold J. W. Zandvliet, and Detlef Lohse. "Periodic bouncing of a plasmonic bubble in a binary liquid by competing solutal and thermal Marangoni forces." Proceedings of the National Academy of Sciences 118, no. 23 (June 4, 2021): e2103215118. http://dx.doi.org/10.1073/pnas.2103215118.

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The physicochemical hydrodynamics of bubbles and droplets out of equilibrium, in particular with phase transitions, display surprisingly rich and often counterintuitive phenomena. Here we experimentally and theoretically study the nucleation and early evolution of plasmonic bubbles in a binary liquid consisting of water and ethanol. Remarkably, the submillimeter plasmonic bubble is found to be periodically attracted to and repelled from the nanoparticle-decorated substrate, with frequencies of around a few kilohertz. We identify the competition between solutal and thermal Marangoni forces as the origin of the periodic bouncing. The former arises due to the selective vaporization of ethanol at the substrate’s side of the bubble, leading to a solutal Marangoni flow toward the hot substrate, which pushes the bubble away. The latter arises due to the temperature gradient across the bubble, leading to a thermal Marangoni flow away from the substrate, which sucks the bubble toward it. We study the dependence of the frequency of the bouncing phenomenon from the control parameters of the system, namely the ethanol fraction and the laser power for the plasmonic heating. Our findings can be generalized to boiling and electrolytically or catalytically generated bubbles in multicomponent liquids.

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Wegener, M., and A. R. Paschedag. "Mass transfer enhancement at deformable droplets due to Marangoni convection." International Journal of Multiphase Flow 37, no. 1 (January 2011): 76–83. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2010.08.005.

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Ng, Vi-Vie, Mathieu Sellier, and Volker Nock. "Marangoni-induced actuation of miscible liquid droplets on an incline." International Journal of Multiphase Flow 82 (June 2016): 27–34. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2016.02.013.

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Moezzi, Mahsa, Mozhdeh Sajjadi, and S. Hossein Hejazi. "Thermally driven Marangoni effects on the spreading dynamics of droplets." International Journal of Multiphase Flow 159 (February 2023): 104335. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2022.104335.

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Li, Weihua, and Satish Kumar. "Three-dimensional surfactant-covered flows of thin liquid films on rotating cylinders." Journal of Fluid Mechanics 844 (April 3, 2018): 61–91. http://dx.doi.org/10.1017/jfm.2018.153.

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The coating of discrete objects is an important but poorly understood step in the manufacturing of a broad variety of products. An important model problem is the flow of a thin liquid film on a rotating cylinder, where instabilities can arise and compromise coating uniformity. In this work, we use lubrication theory and flow visualization experiments to study the influence of surfactant on these flows. Two coupled evolution equations describing the variation of film thickness and concentration of insoluble surfactant as a function of time, the angular coordinate and the axial coordinate are solved numerically. The results show that surface-tension forces arising from both axial and angular variations in the angular curvature drive flows in the axial direction that tend to smooth out free-surface perturbations and lead to a stable speed window in which axial perturbations do not grow. The presence of surfactant leads to Marangoni stresses that can cause the stable speed window to disappear by driving flow that opposes the stabilizing flow. In addition, Marangoni stresses tend to reduce the spacing between droplets that form at low rotation rates, and reduce the growth rate of rings that form at high rotation rates. Flow visualization experiments yield observations that are qualitatively consistent with predictions from linear stability analysis and the simulation results. The visualizations also indicate that surfactants tend to suppress dripping, slow the development of free-surface perturbations, and reduce the shifting and merging of rings and droplets, allowing more time for solidifying coatings in practical applications.

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Abo Jabal, M., E. Homede, L. M. Pismen, H. Haick, and A. M. Leshansky. "Controlling Marangoni flow directionality: patterning nano-materials using sessile and sliding volatile droplets." European Physical Journal Special Topics 226, no. 6 (April 2017): 1307–24. http://dx.doi.org/10.1140/epjst/e2016-60404-x.

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Huo, Y., and B. Q. Li. "A mathematical model for marangoni flow and mass transfer in electrostatically positioned droplets." Metallurgical and Materials Transactions B 36, no. 2 (April 2005): 271–81. http://dx.doi.org/10.1007/s11663-005-0029-9.

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Tang, Jian She, Wei Lu, Bo Xi, Eli Martinez, Fred Li, Alex Ko, Craig Todd, and John T. C. Lee. "Marangoni Dryer Integrated High Performance Cleaner for Cu/Low k Post Strip Clean for 45nm Technology Node and Beyond." Solid State Phenomena 134 (November 2007): 337–40. http://dx.doi.org/10.4028/www.scientific.net/ssp.134.337.

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To address the water mark issue from hydrophobic film drying, and the stringent particle removal requirements for the 45nm technology node and beyond, we developed a cleaner with an innovative single wafer Marangoni dryer. The single wafer Marangoni dryer design features and process characterization data are presented in this paper. The major results can be summarized as: (1) With the immersion type Marangoni dryer, as the wafer is lifted out of a DIW bath, a stable and uniform meniscus can be easily maintained, making the single-wafer Marangoni dryer ideal for drying hydrophilic, hydrophobic or hydrophobic/hydrophilic mixed patterned wafers; (2) The new Marangoni dryer leaves ~14nm [1] water film on the wafer after drying, therefore any dissolved or suspended materials contained inside the water film, and potentially left on the wafer surface after water evaporation, is less than 14nm in diameter. This feature is critical for the 45nm technology node and beyond because 23nm particle could be killer defects at these nodes [2]; (3) Because of the strong Marangoni flow effect, high aspect ratio features can be completely dried without leaving any water droplets inside the trenches; therefore copper corrosion can be prevented; (4) The Marangoni dryer uses N2 as the carrier gas, so when a wafer is lifted out of the degasified DIW bath through the N2/IPA spray zone, it is thoroughly dried in an oxygen-free environment before exposure to the ambient environment; (5) The Marangoni dryer is free of electrostatic charge and centrifugal force because of the slow (2mm/s~20mm/s) wafer linear lifting speed compared to linear speed at wafer edge during SRD.

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Korenchenko, Anna E., and Anna A. Zhukova. "Sessile droplet evaporation in the atmosphere of different gases under forced convection." Physics of Fluids 34, no. 4 (April 2022): 042102. http://dx.doi.org/10.1063/5.0084830.

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The phenomenon of evaporation from the surface of a liquid droplet into a neutral noncondensible gas was numerically studied by taking forced convection gaseous flow into account. The mathematical model considers the effects of surface tension, gravitational force, viscosity of both liquid and gaseous media, as well as the Stefan flow from the droplet surface, possible free gravitational convection, and the Marangoni convection in droplets, and it is designed to describe diffusion-limited evaporation. We consider the diffusion-limited evaporation process when the diffusive gas flux to the droplet surface is compensated by the convective Stefan flow from the surface. The results indicate an interaction of the liquid and gaseous media. Convective gas flows cause the liquid to move and a vortex to occur in the droplet. The flow velocities in a vortex are 103 times less than the characteristic velocity of forced convection flow in air. The droplet surrounded by gaseous flow changes its shape and oscillates, which causes a gas-density wave. Calculations have shown that the diffusion-limited evaporation rate does not change in the presence of forced convection, which contradicts most of the known experimental works. The possible reason for this discrepancy is the presence of non-equilibrium conditions at the liquid–gas interface in experiments. This leads to a consequent change of the evaporation mode to non-diffusive, while the numerical model postulates the Stefan condition and diffusion-limited evaporation.

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Xu, Xuefeng, and Jianbin Luo. "Marangoni flow in an evaporating water droplet." Applied Physics Letters 91, no. 12 (September 17, 2007): 124102. http://dx.doi.org/10.1063/1.2789402.

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Liu, Jiazheng, Jialing Yu, Xuemei Chen, and Zhenhai Pan. "Evaporation of vertical and pendant ethanol droplets and internal Marangoni convections." International Journal of Heat and Mass Transfer 214 (November 2023): 124338. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2023.124338.

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Das, Sayan, Shubhadeep Mandal, and Suman Chakraborty. "Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow." Journal of Fluid Mechanics 835 (November 27, 2017): 170–216. http://dx.doi.org/10.1017/jfm.2017.750.

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The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactant-laden droplet. The droplet speed and direction of motion are strongly influenced by the interfacial transport of surfactant, which is governed by surface Péclet number. The present study is focused on the following two limiting situations of surfactant transport: (i) surface-diffusion-dominated surfactant transport considering small surface Péclet number, and (ii) surface-convection-dominated surfactant transport considering high surface Péclet number. Thermocapillary-induced Marangoni stress, the strength of which relative to viscous stress is represented by the thermal Marangoni number, has a strong influence on the distribution of surfactant on the droplet surface. The present study shows that the motion of a surfactant-laden droplet in the combined presence of temperature and imposed Poiseuille flow cannot be obtained by a simple superposition of the following two independent results: migration of a surfactant-free droplet in a temperature gradient, and the motion of a surfactant-laden droplet in a Poiseuille flow. The temperature field not only affects the axial velocity of the droplet, but also has a non-trivial effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of the Poiseuille flow, the droplet migrates towards the flow centreline. The magnitude of both axial and cross-stream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of the Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centreline or away from it. The present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centreline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow, for which the droplet always moves towards the flow centreline. Interestingly, we show that the above picture may become significantly altered in the case where the droplet is not a neutrally buoyant one. When the droplet is less dense than the suspending medium, the presence of gravity in the direction of the Poiseuille flow can lead to cross-stream motion of the droplet away from the flow centreline even when the temperature increases in the direction of the Poiseuille flow. These results may bear far-reaching consequences in various emulsification techniques in microfluidic devices, as well as in biomolecule synthesis, vesicle dynamics, single-cell analysis and nanoparticle synthesis.

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Perrin, Lionel, Andrew Akanno, Eduardo Guzman, Francisco Ortega, and Ramon G. Rubio. "Pattern Formation upon Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers." International Journal of Molecular Sciences 22, no. 15 (July 26, 2021): 7953. http://dx.doi.org/10.3390/ijms22157953.

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The formation of coffee-ring deposits upon evaporation of sessile droplets containing mixtures of poly(diallyldimethylammonium chloride) (PDADMAC) and two different anionic surfactants were studied. This process is driven by the Marangoni stresses resulting from the formation of surface-active polyelectrolyte–surfactant complexes in solution and the salt arising from the release of counterions. The morphologies of the deposits appear to be dependent on the surfactant concentration, independent of their chemical nature, and consist of a peripheral coffee ring composed of PDADMAC and PDADMAC–surfactant complexes, and a secondary region of dendrite-like structures of pure NaCl at the interior of the residue formed at the end of the evaporation. This is compatible with a hydrodynamic flow associated with the Marangoni stress from the apex of the drop to the three-phase contact line for those cases in which the concentration of the complexes dominates the surface tension, whereas it is reversed when most of the PDADMAC and the complexes have been deposited at the rim and the bulk contains mainly salt.

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Huo, Y., and B. Q. Li. "Surface Deformation and Convection in Electrostatically-Positioned Droplets of Immiscible Liquids Under Microgravity." Journal of Heat Transfer 128, no. 6 (November 30, 2005): 520–29. http://dx.doi.org/10.1115/1.2188460.

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A numerical study is presented of the free surface deformation and Marangoni convection in immiscible droplets positioned by an electrostatic field and heated by laser beams under microgravity. The boundary element and the weighted residuals methods are applied to iteratively solve for the electric field distribution and for the unknown free surface shapes, while the Galerkin finite element method for the thermal and fluid flow field in both the transient and steady states. Results show that the inner interface demarking the two immiscible fluids in an electrically conducting droplet maintains its sphericity in microgravity. The free surface of the droplet, however, deforms into an oval shape in an electric field, owing to the pulling action of the normal component of the Maxwell stress. The thermal and fluid flow distributions are rather complex in an immiscible droplet, with conduction being the main mechanism for the thermal transport. The non-uniform temperature along the free surface induces the flow in the outer layer, whereas the competition between the interfacial surface tension gradient and the inertia force in the outer layer is responsible for the flows in the inner core and near the immiscible interface. As the droplet cools into an undercooled state, surface radiation causes a reversal of the surface temperature gradients along the free surface, which in turn reverses the surface tension driven flow in the outer layer. The flow near the interfacial region, on the other hand, is driven by a complimentary mechanism between the interfacial and the inertia forces during the time when the thermal gradient on the free surface has been reversed while that on the interface has not yet. After the completion of the interfacial thermal gradient reversal, however, the interfacial flows are largely driven by the inertia forces of the outer layer fluid.

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Mac Intyre, J. R., J. M. Gomba, Carlos Alberto Perazzo, P. G. Correa, and M. Sellier. "Thermocapillary migration of droplets under molecular and gravitational forces." Journal of Fluid Mechanics 847 (May 17, 2018): 1–27. http://dx.doi.org/10.1017/jfm.2018.306.

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We study the thermocapillary migration of two-dimensional droplets of partially wetting liquids on a non-uniformly heated surface. The effect of a non-zero contact angle is imposed through a disjoining–conjoining pressure term. The numerical results for two different molecular interactions are compared: on the one hand, London–van der Waals and ionic–electrostatics molecular interactions that account for polar liquids; on the other hand, long- and short-range molecular forces that model molecular interactions of non-polar fluids. In addition, the effect of gravity on the velocity of the drop is analysed. We find that for small contact angles, the long-time dynamics is independent of the molecular potential, and the footprint of the droplet increases with the square root of time. For intermediate contact angles we observe that polar droplets are more likely to break up into smaller volumes than non-polar ones. A linear stability analysis allows us to predict the number of droplets after breakup occurs. In this regime, the effect of gravity is stabilizing: it reduces the growth rates of the unstable modes and increases the shortest unstable wavelength. When breakup is not observed, the droplet moves steadily with a profile that consists in a capillary ridge followed by a film of constant thickness, for which we find power law dependencies with the cross-sectional area of the droplet, the contact angle and the temperature gradients. For large contact angles, non-polar liquids move faster than polar ones, and the velocity is proportional to the Marangoni stress. We find power law dependencies for the velocity for the different regimes of flow. The numerical results allow us to shed light on experimental facts such as the origin of the elongation of droplets and the existence of saturation velocity.

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Hasegawa, K., and Y. Manzaki. "Marangoni fireworks: Atomization dynamics of binary droplets on an oil pool." Physics of Fluids 33, no. 3 (March 2021): 034124. http://dx.doi.org/10.1063/5.0041346.

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Hu, Yin Chun, Qiong Zhou, Cui Cui Dong, and Li Shan Cui. "Micro-Flow Induced Peculiar Surface Profile of Film from Dried Droplet of Water-Poly(Ethylene Oxide) Solution." Key Engineering Materials 531-532 (December 2012): 358–61. http://dx.doi.org/10.4028/www.scientific.net/kem.531-532.358.

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We report a peculiar surface of poly(ethylene oxide) (PEO) film from droplet of water-PEO solution dried at heating substrate. The drying process contains two stages. The contact line is pinned initially. When substrate temperature reaches 60 °C, it starts to recede and continues to leave a film. The resulted film contains an edge-ring and middle-step surface profile. The rheological properties of PEO solution were studied. We found that capillary flow is dominant in the first drying stage and Marangoni flow appears because concentration gradient induced strong Marangoni effect and high temperature induced sharply decrease of viscous stress resulted in the contact line receding in the later drying stage. We confirm that the ringlike deposit is formed by outward capillary flow and the step in the middle is formed by Marangoni flow which carries solute to the inner, and these flows compete with the viscous force.

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Poddar, Antarip, Shubhadeep Mandal, Aditya Bandopadhyay, and Suman Chakraborty. "Electrical switching of a surfactant coated drop in Poiseuille flow." Journal of Fluid Mechanics 870 (May 7, 2019): 27–66. http://dx.doi.org/10.1017/jfm.2019.236.

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Electrical effects can impart a cross-stream component to drop motion in a pressure-driven flow, due to either an asymmetric charge distribution or shape deformation. However, surfactant-mediated alterations in such migration characteristics remain unexplored. By accounting for three-dimensionality in the drop motion, we analytically demonstrate here a non-trivial switching of drop migration with the aid of a surfactant coating on its surface. We establish this phenomenon as controllable by exploiting an interconnected interplay between the hydrodynamic stress, electrical stress and Marangoni stress, manifested so as to achieve a net interfacial force balance. Our results reveal that under different combinations of electrical conductivity and permittivity ratios, the relative strength of the electric stress with respect to the hydrodynamic stress, the applied electric field direction and the surfactants alter the longitudinal and cross-stream velocity components of the droplets differently. The effect of drop deformation on its speed is found to be altered with the increased sensitivity of the surface tension to the surfactant concentration, depending on the competing effects of the electrohydrodynamic flow modification and the tip stretching phenomenon. Further, with a suitable choice of electrical property ratios, the Marangoni effects can be exploited to direct the drop in reaching a final transverse position towards or away from the channel centreline. These results may turn out to be of immense consequence in providing an insight to the underlying complex physical mechanisms dictating an intricate control on the drop motion in different directions.

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Palizdan, Sepideh, Jassem Abbasi, Masoud Riazi, and Mohammad Reza Malayeri. "Impact of solutal Marangoni convection on oil recovery during chemical flooding." Petroleum Science 17, no. 5 (April 24, 2020): 1298–317. http://dx.doi.org/10.1007/s12182-020-00451-z.

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Abstract In this study, the impacts of solutal Marangoni phenomenon on multiphase flow in static and micromodel geometries have experimentally been studied and the interactions between oil droplet and two different alkaline solutions (i.e. MgSO4 and Na2CO3) were investigated. The static tests revealed that the Marangoni convection exists in the presence of the alkaline and oil which should carefully be considered in porous media. In the micromodel experiments, observations showed that in the MgSO4 flooding, the fluids stayed almost stationary, while in the Na2CO3 flooding, a spontaneous movement was detected. The changes in the distribution of fluids showed that the circular movement of fluids due to the Marangoni effects can be effective in draining of the unswept regions. The dimensional analysis for possible mechanisms showed that the viscous, gravity and diffusion forces were negligible and the other mechanisms such as capillary and Marangoni effects should be considered in the investigated experiments. The value of the new defined Marangoni/capillary dimensionless number for the Na2CO3 solution was orders of magnitude larger than the MgSO4 flooding scenario which explains the differences between the two cases and also between different micromodel regions. In conclusion, the Marangoni convection is activated by creating an ultra-low IFT condition in multiphase flow problems that can be profoundly effective in increasing the phase mixing and microscopic efficiency.

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Pan, K. L., Y. H. Tseng, J. C. Chen, K. L. Huang, C. H. Wang, and M. C. Lai. "Controlling droplet bouncing and coalescence with surfactant." Journal of Fluid Mechanics 799 (June 28, 2016): 603–36. http://dx.doi.org/10.1017/jfm.2016.381.

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The collision between aqueous drops in air typically leads to coalescence after impact. Rebounding of the droplets with similar sizes at atmospheric conditions is not generated, unless with significantly large pressure or high impact parameters exhibiting near-grazing collision. Here we demonstrate experimentally the creation of a non-coalescent regime through addition of a small amount of water-soluble surfactant. We perform a direct simulation to account for the continuum and short-range flow dynamics of the approaching interfaces, as affected by the soluble surfactant. Based on the immersed-boundary formulation, a conservative scheme is developed for solving the coupled surface-bulk convection–diffusion concentration equations, which presents excellent mass preservation in the solvent as well as conservation of total surfactant mass. We show that the Marangoni effect, caused by non-uniform distributions of surfactant on the droplet surface and surface tension, induces stresses that oppose the draining of gas in the interstitial gap, and hence prohibits merging of the interfaces. In such gas–liquid systems, the repulsion caused by the addition of surfactant, as frequently observed in liquid–liquid systems such as emulsions in the form of an electric double-layer force, was found to be too weak to dominate in the attainable range of interfacial separation distances. These results thus identify the key mechanisms governing the impact dynamics of surfactant-coated droplets in air and imply the potential of using a small amount of surfactant to manipulate impact outcomes, for example, to prevent coalescence between droplets or interfaces in gases.

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Jeong, Hwapyeong, Hyunwoo Shin, Johan Yi, Yonghyun Park, Jiyoul Lee, Yogesh Gianchandani, and Jaesung Park. "Size-based analysis of extracellular vesicles using sequential transfer of an evaporating droplet." Lab on a Chip 19, no. 19 (2019): 3326–36. http://dx.doi.org/10.1039/c9lc00526a.

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Murata, Akira, and Sadanari Mochizuki. "Motion of droplets induced by the Marangoni force on a wall with a temperature gradient." Heat Transfer?Asian Research 33, no. 2 (2004): 81–93. http://dx.doi.org/10.1002/htj.20004.

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Journal articles on the topic 'Marangoni Flow in Droplets'

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