Local Surface Tension Research Articles

Positional Information-Based Organization of Surfactant Droplet Swarms Emerging from Competition Between Local and Global Marangoni Effects.

Positional information is key for particles to adapt their behavior based on their position in external concentration gradients, and thereby self-organize into complex patterns. Here, position-dependent behavior of floating surfactant droplets that self-organize in a pH gradient is demonstrated, using the Marangoni effect to translate gradients of surface-active molecules into motion. First,fields of surfactant microliter-droplets are generated, in which droplets floating on water drive local, outbound Marangoni flows upon dissolution of surfactantand concomitantly grow myelin filaments. Next, a competing surfactant based on a hydrolysable amide is introduced, which is more surface active than the myelin surfactant and thereby inhibits the local Marangoni flows and myelin growth from the droplets. Upon introducing a pH gradient, the amide surfactant hydrolyses in the acidic region, so that the local Marangoni flows and myelin growth are reestablished. The resulting combination of local and global surface tension gradients produces a region of myelin-growing droplets and a region where myelin growth is suppressed, separated by a wave front of closely packed droplets, of which the position can be controlled by the pH gradient. Thereby, it is shown how "French flag"-patterns, in synthetic settings typically emerging from reaction-diffusion systems, can also be established via surfactant droplet systems.

Numerical investigation on nonlinear ship waves by LCM and WSAM

This paper investigates the nonlinear ship waves by implementing the longitudinal cut method (LCM) and wake survey analysis method (WSAM) in the computational fluid dynamics (CFD) simulation. LCM is first implemented and validated for a Series 60, Cb = 0.6 ship model to guarantee accurate prediction of the wave pattern resistance (Rwp). To illustrate the reliability, WSAM is performed for a wall-sided model, incorporating the local adaptive mesh refinement (LAMR) and surface tension models to capture nonlinear bow waves. Far and near-field wave patterns and momentum loss resistance (RML) are compared with the experiment.With the well-predicted nonlinear bow waves, the velocity discontinuity property across the nonlinear wavefront and the vortex motion beneath the nonlinear waves are clearly observed by velocity vector and Q-criteria iso-surface visualization. By LCM and WSAM analysis, the discrepancy between wave resistance (Rw) and Rwp is attributed to the nonlinearity in ship waves, and expression to evaluate this part of resistance (Rnw) is discussed and summarized. Finally, the influence of velocity and draft on Rnw and bow wave angle (β) is systematically analyzed and discussed. This study hopes to provide insights to evaluate the nonlinearity in ship waves and further understand its underlying mechanism.

Three-dimensional numerical study on wrinkling of vesicles in elongation flow based on the immersed boundary method.

We study the wrinkling dynamics of three-dimensional vesicles in a time-dependent elongation flow by utilizing an immersed boundary method. For a quasispherical vesicle, our numerical results well match the predictions of perturbation analysis, where similar exponential relationships between wrinkles' characteristic wavelength and the flow strength are observed. Using the same parameters as in the experiments by Kantsler etal. [V. Kantsler etal., Phys. Rev. Lett. 99, 178102 (2007)0031-900710.1103/PhysRevLett.99.178102], our simulations of an elongated vesicle are in good agreement with their results. In addition, we get rich three-dimensional morphological details, which are favorable to comprehend the two-dimensional snapshots. This morphological information helps identify wrinkle patterns. We analyze the morphological evolution of wrinkles using spherical harmonics. We find discrepancies in elongated vesicle dynamics between simulations and perturbation analysis, highlighting the importance of the nonlinear effects. Finally, we investigate the unevenly distributed local surface tension, which largely determines the position of wrinkles excited on the vesicle membrane.

Multiple Marangoni flows in a binary mixture sessile droplet

A multicomponent droplet evaporation problem has widely been investigated due to diverse industrial applications, including ink-jet printing, surface coating and patterning, medical diagnosis, spraying cooling, and fuel combustion. During evaporation, the Marangoni flow caused by selective evaporation should be observed, and it plays an important role in determining the drying process and the final dried deposit pattern. However, most of the works focused on measuring the internal flow field although the Marangoni flow mainly occurred near the liquid–gas interface. In this study, using particle image velocimetry, we tried to measure the interfacial Marangoni flows where the measurement focal plane was set in the vicinity of the apex of the binary mixture droplet. We observed distinctive multiple Marangoni flows in time, such as (i) directional circulating flow, (ii) complicated mixing flow, and (iii) spontaneous bursting flow. Finally, we found that the Reynolds number is different for each case. Based on the flow field measurement result and dimensionless number analysis, we considered a stress balance model that qualitatively described the local surface tension gradient and Marangoni stress.

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.

Study on Tensile and Compressive Bending Deformation Sensor Based on Surface Acoustic Wave

SAW sensors are becoming interesting in the field of strain and stress detection applications. The strain of complex structures can be divided into a combination of local surface tension and compression, hence it is pretty important that study the detection of tension and compression for the analysis of complex structures. Here, we fabricated two SAW sensors based ST-cut quartz (78.65 MHz and 157.1 MHz) through photo-lithography and wet-etching processes and focused on their comparative analysis for the bending displacement and strain testing with the performance of the sensor sensitivity studied. The SAW-IDT10 and SAW-IDT5 sensor showed the maximum bending displacement sensitivity of ∼1.9369 kHz mm−1 and ∼4.3887 kHz mm−1, respectively. Additionally, the SAW-IDT5 sensor exhibited up to 2 times higher sensitivity (1570 kHz/%) than that of SAW-IDT10 sensor (786 kHz/%) under the same bending strain conditions. And the SAW-IDT5 and the SAW-IDT10 have both 0.99 and 1 tensile and compression strain gauge factors. Thus SAW sensors with high operating frequency have a higher frequency shift response in detecting micro-strain. Meanwhile, negative frequency shift response to tension and positive frequency shift response to compression of SAW sensors can be used to classify structural deformation in a complex environment in the future.

Interpreting contact angles of surfactant solutions on microporous hydrophobic membranes

Almost every single experimental study regarding membranes involves the measurement of contact angle (CA) to quantify the membrane wetting property. However, the interpretation of CA can sometimes be tricky. In this study, we investigate an interesting phenomenon about the CA of a surfactant solution on a microporous hydrophobic membrane. Specifically, a surfactant solution with a very low surface tension can have an unexpectedly high CA on a microporous hydrophobic membrane. In contrast, a water/ethanol mixture with the same surface tension completely wicks the membrane (i.e., zero CA). The drastic difference in CA between the two types of liquid of the same surface tension results from the rapid adsorption of surfactants at the wetting frontier which substantially reduces the local surfactant concentration and increases the local surface tension. The same theory can also be applied to explain the striking difference between the two liquids in capillary rise and liquid entry pressure. The results from this study cast significant doubt on the role of surface tension in understanding the wetting behavior of surfactant solutions when they are in contact with solid with large specific area and raise important questions regarding the utility of measuring CA for surfactant solutions on microporous hydrophobic membranes.

Numerical simulation of particle deposition patterns in evaporating droplets

Nanostructures are used for various chemical, biological, and even volatile organic compound (VOC) sensor applications, in which the inkjet printer provides an easy and convenient fabrication method. In particular, nanoparticles in injected droplets form various self-assembled nanostructures after evaporation such as flat films, rings, and domes, whose patterns are largely influenced by the flow fields within those droplets, temperature, humidity, and substrate wettability. In addition, the temperature at the liquid–gas interface of the droplets governs the local surface tension and evaporation flux, thereby determining the convection fluid flow and particle movement. In this study, we investigate four particle deposition patterns via numerical simulations. First, we reveal the formation of monolayered flat-films on a superhydrophilic substrate in the constant contact angle (CCA) mode during evaporation. Second, we confirm that particles in evaporated droplets usually form coffee-ring patterns on a hydrophilic substrate, which are mainly governed by capillary flows. Interestingly, we find that the coffee rings with low aspect ratios appear to be well-ordered in the constant contact radius mode, while those with high aspect ratios appear to be non-uniformly self-assembled in the CCA mode in an amorphous structure. Third, we prove that the Marangoni flow generated on a hydrophobic substrate accumulates particles at the center of the droplet, forming well-ordered dome-shaped patterns. Furthermore, we experimentally demonstrate four different particle deposition patterns to validate our simulation results and confirm that both sets of results are in reasonable agreement with each other. Hence, we believe that these theoretical model and simulation results can help to develop various nanostructure-based sensor applications by enhancing their performance.

Deducing a Variational Principle with Minimal A Priori Assumptions

We study the well-known variational and large deviation principle for graph homomorphisms from $\mathbb{Z}^m$ to $\mathbb{Z}$. We provide a robust method to deduce those principles under minimal a priori assumptions. The only ingredient specific to the model is a discrete Kirszbraun theorem i.e. an extension theorem for graph homomorphisms. All other ingredients are of a general nature not specific to the model. They include elementary combinatorics, the compactness of Lipschitz functions, and a simplicial Rademacher theorem. Compared to the literature, our proof does not need any other preliminary results like e.g. concentration or strict convexity of the local surface tension. Therefore, the method is very robust and extends to more complex and subtle models, as e.g. the homogenization of limit shapes or graph-homomorphisms to a regular tree.

A note on the synergistic effect of surfactants and nanoparticles on rising bubble hydrodynamics

Various mixtures of surfactants and nanosilica particles were investigated to assess their influence on rising bubble hydrodynamics. For this purpose, local velocities of rising bubbles were measured experimentally. Also, the effects of concentration of three types of surface-modified silica nanoparticles on density, viscosity, and surface tension of surfactant solutions were determined. Experimental results revealed that the simultaneous presence of nanoparticles and surfactant molecules led to the decrease of local velocities of rising bubbles. The presence of nanoparticles in surfactant solutions leads to a more reduction of bubble local velocity. This could be caused by the formation of surfactant-nanoparticle complexes and their adsorption at the gas-liquid interface. However, the increase of concentration of nanoparticles from 0.02 to 0.04 %wt led to an increase in bubble local velocities. That effect may be related to adsorption of surfactants to nanoparticle-liquid interfaces i.e. low surface coverage of surfactant, may increase local surface tension and lead to increasing the mobility of bubble surface.

Inkjet jettability and physical characterization of water–ethanol solutions of low molecular weight sodium polyacrylate and poly-diallyl dimethyl ammonium chloride (polyDADMAC)

Polyelectrolytes are water-soluble polymers having repeat units carrying electrolyte groups. As polyionic molecules having like charge units, they are self-repelling with a rod-like conformation in solution. Inkjet applications of polyelectrolytes include particle dispersing, surface modification, and multilayer structures. This work investigates the physical properties of low molecular weight sodium polyacrylate (NaPA) and poly-diallyl dimethyl ammonium chloride (polyDADMAC) polyelectrolyte solutions in the water–ethanol mixture in relation to their behavior in inkjet deposition. In rotational rheometry measurements, the solutions are found to behave in a Newtonian fashion once the effects of experimental artifacts are taken into account. The range of NaPA concentrations that could be studied was limited to 1 wt./wt. % by the poor solubility of NaPA in the presence of ethanol, and at these concentrations, the addition of NaPA to the solvent did not have a significant effect on the jetting behavior. PolyDADMAC had good solubility, and concentrations up to 10 wt./wt. % were studied and jetted successfully. While an increase in polyelectrolyte concentration resulted in a slow increase in ink viscosity, this was not found to have a significant effect on the required jetting voltage or maximum stable jetting frequency, though drop detachment and satellite droplet formation times were found to increase. As a practical limitation of polyDADMAC inks, solvent evaporation was found to lead to idle nozzles becoming non-jetting, with the allowed idle time decreasing rapidly as ink polyDADMAC concentration increased. This non-jetting behavior is likely due to residence time at the nozzle exit leading to the local surface tension and/or viscosity increase, differing from the bulk ink properties.

Dynamic surface tension of xylem sap lipids.

The surface tension of xylem sap has been traditionally assumed to be close to that of the pure water because decreasing surface tension is thought to increase vulnerability to air seeding and embolism. However, xylem sap contains insoluble lipid-based surfactants, which also coat vessel and pit membrane surfaces, where gas bubbles can enter xylem under negative pressure in the process known as air seeding. Because of the insolubility of amphiphilic lipids, the surface tension influencing air seeding in pit pores is not the equilibrium surface tension of extracted bulk sap but the local surface tension at gas-liquid interfaces, which depends dynamically on the local concentration of lipids per surface area. To estimate the dynamic surface tension in lipid layers that line surfaces in the xylem apoplast, we studied the time-dependent and surface area-regulated surface tensions of apoplastic lipids extracted from xylem sap of four woody angiosperm plants using constrained drop surfactometry. Xylem lipids were found to demonstrate potent surface activity, with surface tensions reaching an equilibrium at ~25 mN m-1 and varying between a minimum of 19 mN m-1 and a maximum of 68 mN m-1 when changing the surface area between 50 and 160% around the equilibrium surface area. It is concluded that xylem lipid films in natural conditions most likely range from nonequilibrium metastable conditions of a supersaturated compression state to an undersaturated expansion state, depending on the local surface areas of gas-liquid interfaces. Together with findings that maximum pore constrictions in angiosperm pit membranes are much smaller than previously assumed, low dynamic surface tension in xylem turns out to be entirely compatible with the cohesion-tension and air-seeding theories, as well as with the existence of lipid-coated nanobubbles in xylem sap, and with the range of vulnerabilities to embolism observed in plants.

Control of solutal Marangoni-driven vortical flows and enhancement of mixing efficiency

HypothesisIn droplet microfluidics applications, flow control and mixing in a small volume without any active external devices is a challenge. Vapor-mediated solutal Marangoni flows can be effectively generated by applying the vapor of a volatile liquid, which can be possibly controlled, and can eventually be used in a mixing enhancement device. ExperimentsWe investigated and controlled vapor-mediated solutal Marangoni flows by varying the local surface tension. We systematically tested the effects of different volatile liquids and their vapor concentration on the flow pattern. Furthermore, by varying the number of vapor sources, we generated and controlled multiple vortices, and analyzed them by particle image velocimetry (PIV). The proposed method was applied to a mixing enhancement application. FindingsWe show that in addition to the surface tension of the volatile liquid, the vapor concentration also influenced the local surface tension along the interface, which in turn changed the internal flow velocity. To predict the flow velocity and oscillatory frequency of the solutal Marangoni flow, we developed a theoretical model based on scaling analysis that showed a good agreement with the experimental results. We believe that the current study will motivate low-cost and portable sample flow control and mixing systems in the near future.

Dynamic self-assembly of block copolymers regulated by time-varying building block composition via reversible chemical reaction

Dynamic self-assembly processes occurring out of thermodynamic equilibrium underlie many forms of adaptive and intelligent behaviors in natural systems. Because of the continuous input of energy, the dynamic self-assembly provides the opportunity for creating structures that are unattainable in equilibrium state. In this paper, we propose a strategy in the dynamic self-assembly of amphiphilic block copolymers regulated by reversible chemical reaction. By time-dependently tuning the reaction direction in the simulations, the amphiphilicity of building block keeps changing periodically. Relying on this dynamic process, we can obtain exotic self-assembled vesicle with surface pores which is otherwise metastable in an equilibrium state. The effects induced by the type of chemical reaction and the reaction period are discussed. Only at short reaction period in suitable reversible reaction, novel self-assembly structure emerges. It is attributed to the competition of reaction and diffusion in the dynamic process, by which the local component of building blocks alters a lot, leading to large local surface tension resulting in the formation of perforated vesicle. In order to predict the assembled structure in a dynamic process, we build up the relationship between component ratio P , the diffusion effect parameter P diff and assembled structures. The dynamic self-assembly regulated by chemical reaction holds great promise as a rational strategy to realize exotic functional materials that are not easily obtained in equilibrium.

Role of Surfactant in Evaporation and Deposition of Bisolvent Biopolymer Droplets.

Inkjet printing of biopolymer droplets is gaining popularity because of its potential applications in regenerative medicine, particularly the fabrication of tissue-regenerative scaffolds. The quality of bioprinting, which affects cellular behaviors and the subsequent tissue formation, is determined by the solvent evaporation and deposition processes of biopolymer droplets, during which instantaneous local viscosity and surface tension changes occur because of the redistribution of the biopolymer inside the drop. Such dynamics is complex and not well understood. Most biopolymer inks also contain multiple solvents of distinct evaporation rates, further complicating the system dynamics. Using high-speed interferometry, we directly observe in real time the instantaneous drop shape of inkjet-printed picoliter gelatin drops containing glycerol and water. It is observed that, for bisolvent gelatin drops with surfactants, highly viscous gelatin and glycerol accumulated near the pinned contact line at an early stage suppress the evaporation-driven outward flow and create a stagnation zone near the contact line region. Lower surface tension at the contact line, because of its high local surfactant concentration, as compared to the drop apex induces a strong Marangoni recirculation, which in conjunction with a stagnation zone in the contact line region causes the instantaneous drop shape to transition from a spherical cap to a volcano shape during evaporation and resulting in a volcano-like deposition profile. In contrast, the suppressed evaporation outward flow together with a weak Marangoni flow leads to a domelike deposition for the case without surfactant. The role of surfactant in polymer drop deposition with water-only solvent is also investigated and compared against that of bisolvent drops. For the single-solvent case, the deposition profile is found to shift from a coffee-eye shape in the presence of surfactant to a uniform deposition without surfactant. The results reveal new insight into the complex role surfactant plays during polymer drop evaporation and deposition processes.

Thermal Marangoni-driven dynamics of spinning liquid films

Spin coating of thin films of viscous liquids on a rotating substrate is a core technological component of semiconductor microchip fabrication. The thinning dynamics is influenced by many physical processes. Specifically temperature gradients affect thin liquid films through their influence on the local fluid surface tension. We show here experimentally and numerically that adding a static temperature gradient has a significant effect on the equilibrium film thickness and height profile reached in spin coating. Our results suggest that thermal gradients can be used to control film height profile dynamics.

High vapour pressure nanofuel droplet combustion and heat transfer: Insights into droplet burning time scale, secondary atomisation and coupling of droplet deformations and heat release

Combustion characteristics of ethanol-water (EW) droplets laden with ceria nanoparticles are investigated. The present experimental study focuses on three facets of droplet combustion (i) burning time scale of droplets with and without NPs, (ii) pathways of secondary atomisation due to interface deformations and (iii) coupling of droplet shape deformations and flame heat release. A theoretical vaporisation timescale is advocated which considers natural convection-based evaporation, mass loss due to daughter droplet ejections, and flow through porous media. Droplets seeded with ceria nanoparticles, exhibit arrested surface undulations although internal ebullition is discernibly enhanced as compared to EW droplets without NPs. Deformations and formation of surface craters in EW droplets are traced to the imbalance between local vapour recoil (due to rapid ethanol vaporisation) and surface tension. Such craters collapse and form high-speed ligaments which eventually break at the tip through Rayleigh–Plateau mechanism. This pathway of secondary atomisation of EW droplets has been elucidated using a modified local weber number. On the contrary, for nanofuels, bubble rupture is the mechanism behind the surface crater formation. Proper orthogonal decomposition (POD) technique is utilised for investigating the droplet shape and flame heat release coupling. EW droplet shape and HR are found to be a synced system with a phase lag arising from the flame response timescale. However, a weak coupling is detected for nanofuel droplets.

Self-sustained movement of condensate drop on uniform temperature surface during Marangoni dropwise condensation

During the condensation of some binary vapor mixtures so-called ‘positive system’, in which the more volatile component has the higher surface tension (e.g., water–ethanol), Marangoni dropwise condensation occurs owing to the temperature-induced local concentration and surface tension instability. It was found that the spontaneous movement of condensate drops occurred from the low- to high-temperature side of the heat transfer surface due to the concentration and surface tension difference around the drops, which are induced by the bulk temperature gradient. In this study, it was newly discovered that the spontaneous movement of condensate drops could be ‘self-sustained’ even without the presence of a bulk temperature gradient on the heat transfer surface. By applying the neighboring temperature gradient region and uniform temperature region on the condensing surface, two different modes of drop behaviors were observed during the experiments: (1) For the condensate drops with notable initial velocities in the temperature gradient region, the spontaneous movement was sustained in the uniform temperature region; (2) for the condensate drops initially formed in the uniform temperature region, the spontaneous movement did not occur owing to the lack of initial velocity. The reason for self-sustained movement of condensate drops can thus be inferred to be the presence of a self-formed temperature gradient around the moving condensate drops.

Directional and Rotational Motions of Nanoparticles on Plasma Membranes as Local Probes of Surface Tension Propagation.

Mechanical heterogeneity is ubiquitous in plasma membranes and of essential importance to cellular functioning. As a feedback of mechanical stimuli, local surface tension can be readily changed and immediately propagated through the membrane, influencing structures and dynamics of both inclusions and membrane-associated proteins. Using the nonequilibrium coarse-grained membrane simulation, here we investigate the inter-related processes of tension propagation, lipid diffusion, and transport of nanoparticles (NPs) adhering on the membrane of constant tension gradient, mimicking that of migrating cells or cells under prolonged stimulation. Our results demonstrate that the lipid bilayer membrane can by itself propagate surface tension in defined rates and pathways to reach a dynamic equilibrium state where surface tension is linearly distributed along the gradient maintained by the directional flow-like motion of lipids. Such lipid flow exerts shearing forces to transport adhesive NPs toward the region of a larger surface tension. Under certain conditions, the shearing force can generate nonzero torques driving the rotational motion of NPs, with the direction of the NP rotation determined by the NP-membrane interaction state as functions of both NP property and local membrane surface tension. Such features endow NPs with promising applications ranging from biosensing to targeted drug delivery.

Alignment of Thermally Conducting Nanotubes Making High-Performance Light-Driving Motors

Light-actuating devices that can produce selective motions at small scales are highly desired for on-demand manipulation. For conventional photothermal motors that mostly encounter the homogenous light-induced heat diffusion at the liquid/air interface, it is challenging to effectively control the actuating direction and enhance the actuating speed. To this end, here, we explore aligned thermally conducting one-dimensional nanomaterials to make light-driving motors where the light-induced heat can be transmitted to the water surface along the length direction of the aligned one-dimensional nanomaterials to generate a localized surface tension gradient for high spatial resolution propulsion. When multiwalled carbon nanotubes were studied as a demonstration, the aligned active layer generated sufficient propulsion to drive a centimeter-sized motor that was 10 000 times higher in mass of the actuating layer on water. In addition, the actuating direction had been accurately controlled by varying the illuminated region of the active aligned nanotube layer. The resulting light-driving motors can move as fast as 4.19 cm/s (or 5.2 body length per second), which exceeded the previous motors based on the light activation.