Self-running droplet: emergence of regular motion from nonequilibrium noise

Spontaneous motion of an oil droplet driven by nonequilibrium chemical conditions is reported. It is shown that the droplet undergoes regular rhythmic motion under appropriately designed boundary conditions, whereas it exhibits random motion in an isotropic environment. This study is a novel manifestation on the direct energy transformation of chemical energy into regular spatial motion under isothermal conditions. A simple mathematical equation including noise reproduces the essential feature of the transition from irregularity into periodic regular motion. Our results will inspire the theoretical study on the mechanism of molecular motors in living matter, working under significant influence of thermal fluctuation.     

Premicellar and micelle formation behavior of aqueous anionic surfactants in the presence of triphenylmethane dyes: protonation of dye in ion pair micelles

The premicellar and micelle formation behaviors of four cationic triphenylmethane dyes, viz, Pararosaniline (RN), Crystal violet (CV), Ethyl violet (EV), and Malachite green (MG), in aqueous anionic surfactant solutions of sodium dodecyl sulfate (SDS), sodium dodecyl benzene sulfonate (SDBS), and sodium dodecyl sulfonate (SDSN) have been studied by spectral and surface tension measurements. The study was carried out within a pH range where the dyes are stable in their quinoid forms. The dyes have been found to form dye–surfactant ion pairs (DSIPs) with the surfactants, at the surfactant concentrations well below their critical micelle concentration, CMC*. The DSIPs behave like nonionic surfactants and form an air–water interfacial monolayer. The DSIPs have a lower critical micelle concentration (CMC_IP), greater efficiency, and lower effectiveness than the corresponding pure surfactants. As the surfactant concentration is increased below the CMC*, the DSIPs start forming micelles of their own where the dye gets protonated and exists as a protonated dye–surfactant ion pair (PDSIP) in the ion pair micelles. As the concentration of the surfactant exceeds the CMC* of the pure surfactant, the protonation reverses gradually with the dye remaining in the micelles in solubilized form and the DSIPs in the air–water interfacial monolayer are replaced by pure surfactants. The distorted helical isomeric form (isomer B) of the dyes is favored in the PDSIPs. Copyright © 2009 John Wiley & Sons, Ltd.     

阳离子表面活性剂三甲基溴化铵与硝酸铵相互作用的表面和热力学研究

本文系统研究了阳离子表面活性剂三甲基溴化铵和硝酸铵盐的表面现象和自聚集行为. 采用电导法和表面张力法研究在不同温度下阳离子表面活性剂三甲基溴化铵的表面性质和热力学性质. 通过表面张力测定得到临界胶束浓度、吸附自由能、胶束化的自由能、最小分子面积和表面过量浓度. 该研究表明,胶束化过程是自发放热反应. 电导测定结果确定了临界胶束浓度、电离程度和反离子结合度. 加入硝酸铵盐至表面活性剂溶液后,临界胶束浓度降低,电离程度和反离子结合度增加,更加有利于胶束化过程的自发. 该研究对进一步理解电解质和表面活性剂之间相互作用具有重要意义.     

Stability of cellulose lyotropic liquid crystal emulsions

We studied a new kind of W/O emulsions based on a lyotropic liquid crystal as the aqueous droplet phase. The cholesteric phase, a solution hydroxypropyl cellulose in water was dispersed in the continuous oil matrix, paraffin oil or heptane. We made a specific choice of surfactant in order to impose director anchoring conditions at the oil-water interface and orient the liquid crystal inside the droplet. The strong anchoring conditions resulted in a topological defect inside the droplets of size above the critical value R^*. The defect elastic energy creates a barrier against droplet coalescence, the effect of topological size selection. We have studied the orientation of the director inside the droplets and their size distribution.     

Computer simulations of the fission process of charged nanometre droplets

The process of fission of charged liquid droplets is an important stage of multiply charged ion formation in the electrospray ionization (ESI) process. ESI is currently the most powerful ionization method in the mass spectrometry of large molecules such as biopolymers. Fission plays a crucial role in the ion formation essentially in the range of nanosized droplets, since it determines the charge states of product ions. Usually the Rayleigh equation is used to determine critical conditions, at which the fission process takes place. This equation gives the value of the critical radius of the charged droplet as a function of its charge and specific surface energy. The Rayleigh equation does not give us the opportunity to determine charges and sizes of the fission fragments. In the present work we propose a mathematical model that describes the fission process of the charged liquid droplet in an external electrostatic field. The model is based on the quasi-equilibrium assumption that the most probable shape of the droplet corresponds to the minimum of the free energy of the system. The change in the internal kinetic energy and dissipative losses for the viscous liquid are also taken into account in the model.     

Interface dynamics under nonequilibrium conditions: From a self-propelled droplet to dynamic pattern evolution

In this article, we describe the instability of a contact line under nonequilibrium conditions mainly based on the results of our recent studies. Two experimental examples are presented: the self-propelled motion of a liquid droplet and spontaneous dynamic pattern formation. For the self-propelled motion of a droplet, we introduce an experiment in which a droplet of aniline sitting on an aqueous layer moves spontaneously at an air-water interface. The spontaneous symmetry breaking of Marangoni-driven spreading causes regular motion. In a circular Petri dish, the droplet exhibits either beeline motion or circular motion. On the other hand, we show the emergence of a dynamic labyrinthine pattern caused by dewetting of a metastable thin film from the air-water interface. The contact line between the organic phase and the aqueous phase forms a unique spatio-temporal pattern characterized as a dynamic labyrinth. Motion of the contact line is controlled by diffusion processes. We propose a theoretical model to interpret essential aspects of the observed dynamic behavior.     

表面活性剂对气-液界面纳米颗粒吸附规律的影响

通过测定及分析纳米颗粒和表面活性剂-纳米颗粒复配体系在自由吸附过程与动态收缩过程中表面张力的变化,总结了纳米颗粒在气-液界面的吸附排布规律以及表面活性剂对其吸附规律的影响.实验结果表明,自由吸附过程中,随矿化度增加、阳离子活性剂浓度增加,平衡表面张力降低,这与颗粒吸附密度增加及颗粒润湿性改变有关.浓度低于临界胶束浓度(CMC)时,阳离子活性剂体系与混合体系的表面张力差异证明了阳离子活性剂可以通过静电作用吸附于纳米颗粒表面,进而部分溶解于水相;而阴离子活性剂与纳米颗粒相互作用力较弱,对表面张力影响较小.纳米颗粒体系在液滴收缩过程中,表面张力从自由吸附平衡态进一步降低大约9 m N/m,说明自由吸附过程中纳米颗粒不能达到紧密排布;同时表面张力呈现为缓慢降低、快速降低和达到平衡三部分,表面压缩模量可达70 m N/m,满足了液膜Gibbs稳定准则,这将有助于提高泡沫或者乳液稳定性.纳米颗粒-表面活性剂体系在液滴收缩过程中表面张力降低值随活性剂浓度增加而减小;表面压缩模量由高到低依次为:纳米颗粒>阳离子活性剂-纳米颗粒>阴离子-纳米颗粒>表面活性剂.     

油滴撞击油膜层内气泡的变形与破裂过程的数值模拟

旋转工作的机械零部件和机械设备的润滑系统工作过程中普遍存在着油滴和油膜的碰撞行为,这一行为易引起气泡夹带现象.气泡将对油滴撞击油膜时的运动过程和附壁油膜层的形成质量造成不可忽视的影响.基于耦合的水平集-体积分数方法,对油滴撞击含气泡油膜的行为进行数值模拟研究,考察油膜层内气泡的变形运动过程,分析气泡大小和位置等因素对撞击过程中气泡变形特征参数的影响规律,并探讨气泡破裂的动力学机制.研究表明,随着气泡直径的增大,油滴撞击含气泡油膜后气泡会依次出现自由表面破裂、稳定变形以及油膜内部破裂等现象;直径d=20μm的气泡能较稳定地存在于油膜层内,同时该值也是气泡发生自由表面破裂和油膜内部破裂的临界值.此外,气泡所在位置同样对气泡变形历程有一定影响,气泡越接近油膜表面,其变形量越大;位于油膜底层的气泡会附着在壁面上.在自由表面破裂和油膜内部破裂过程中,气泡破裂是由气-液界面不稳定引起的,表面张力对这两种现象起重要作用;而黏性剪切力对油膜内部破裂现象也有着不可忽视的影响.     

Ultrasonic emulsification of food-grade nanoemulsion formulation and evaluation of its bactericidal activity

Basil oil (Ocimum basilicum) nanoemulsion was formulated using non-ionic surfactant Tween80 and water by ultrasonic emulsification method. Process of nanoemulsion development was optimized for parameters such as surfactant concentration and emulsification time to achieve minimum droplet diameter with high physical stability. Surfactant concentration was found to have a negative correlation with droplet diameter, whereas emulsification time had a positive correlation with droplet diameter and also with intrinsic stability of the emulsion. Stable basil oil nanoemulsion with droplet diameter 29.3 nm was formulated by ultrasonic emulsification for 15 min. Formulated nanoemulsion was evaluated for antibacterial activity against Escherichia coli by kinetics of killing experiment. Fluorescence microscopy and FT-IR results showed that nanoemulsion treatment resulted alteration in permeability and surface features of bacterial cell membrane.     

Phase-field modeling droplet dynamics with soluble surfactants

Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence.     

Total Internal Reflection Fluorescence Spectroscopy for Investigating the Adsorption of a Porphyrin at the Glass/Water Interface in the Presence of a Cationic Surfactant Below the Critical Micelle Concentration

Total internal reflection fluorescence (TIRF) spectroscopy was used to investigate the adsorption behavior of meso-tetrakis(p-sulfonatophenyl)porphyrin (TPPS) at the glass/water interface in the presence of a cationic surfactant (cetyltrimethylammonium bromide, CTAB) far below the critical micelle concentration. The adsorption model of TPPS at the glass/water interface in the presence of low concentration of CTAB was proposed, which was different from the adsorption of TPPS in the presence of micelles of CTAB at the glass/water interface. TPPS and CTAB did not form stable complex at the interface in dilute system. The interfacial species of TPPS were analyzed by comparing the spectra of TPPS at the glass/water interface and in the aqueous phase. The influences of the TPPS concentration, the CTAB concentration, and the pH values on the interfacial fluorescence spectra and intensities were studied. It was demonstrated that electrostatic interaction and hydrophobicity performed an important role on the adsorption of TPPS in the presence of CTAB. The different effects of TPPS concentration on the adsorption behaviour of TPPS at different pH were observed for the first time. It was found that the adsorption isotherms of TPPS at glass/water interface could fit Freundlich equation at pH 7.1.     

Minimising oil droplet size using ultrasonic emulsification

The efficient production of nanoemulsions, with oil droplet sizes of less than 100 nm would facilitate the inclusion of oil soluble bio-active agents into a range of water based foods. Small droplet sizes lead to transparent emulsions so that product appearance is not altered by the addition of an oil phase. In this paper, we demonstrate that it is possible to create remarkably small transparent O/W nanoemulsions with average diameters as low as 40 nm from sunflower oil. This is achieved using ultrasound or high shear homogenization and a surfactant/co-surfactant/oil system that is well optimised. The minimum droplet size of 40 nm, was only obtained when both droplet deformability (surfactant design) and the applied shear (equipment geometry) were optimal. The time required to achieve the minimum droplet size was also clearly affected by the equipment configuration. Results at atmospheric pressure fitted an expected exponential relationship with the total energy density. However, we found that this relationship changes when an overpressure of up to 400 kPa is applied to the sonication vessel, leading to more efficient emulsion production. Oil stability is unaffected by the sonication process.     

Threshold onset of Marangoni convection in narrow channels

There are several experimental studies where the Marangoni convection begins only at a certain difference in the surface tension, i.e. in a threshold way. This effect contradicts a traditional point of view according to which the surface flow in Newtonian fluids should begin at an arbitrary small difference in surface tension. To explore this phenomenon in detail we investigated the initiation of the Marangoni convection at a free liquid surface caused by injection of a droplet of surfactant. It was found that the surface motion occurs in a threshold manner, i.e. when a surfactant concentration in the droplet approaches a certain critical value. The described phenomenon is more important in narrow channels and essentially depends both on the purity of the basic liquid and on the surfactant used. Based on the experimental results, a hypothesis about an important role of residual impurities contained in basic liquids which can thoroughly change a surface rheology was suggested. The theoretical model taking into account special rheological properties in the free surface is considered. The results of the numerical simulation are in a good agreement with the experimental observations.     

Self-propelled droplets

Self-propelled droplets are a special kind of self-propelled matter that are easily fabricated by standard microfluidic tools and locomote for a certain time without external sources of energy. The typical driving mechanism is a Marangoni flow due to gradients in the interfacial energy on the droplet interface. In this article we review the hydrodynamic prerequisites for self-sustained locomotion and present two examples to realize those conditions for emulsion droplets, i.e. droplets stabilized by a surfactant layer in a surrounding immiscible liquid. One possibility to achieve self-propelled motion relies on chemical reactions affecting the surface active properties of the surfactant molecules. The other relies on micellar solubilization of the droplet phase into the surrounding liquid phase. Remarkable cruising ranges can be achieved in both cases and the relative insensitivity to their own ‘exhausts’ allows to additionally study collective phenomena.     

Modeling and simulation of thermocapillary flows using lattice Boltzmann method

To understand how thermocapillary forces manipulate droplet motion in microfluidic channels, we develop a lattice Boltzmann (LB) multiphase model to simulate thermocapillary flows. The complex hydrodynamic interactions are described by an improved color-fluid LB model, in which the interfacial tension forces and the Marangoni stresses are modeled in a consistent manner using the concept of a continuum surface force. An additional convection–diffusion equation is solved in the LB framework to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. A stress-free boundary condition is also introduced to treat outflow boundary, which can conserve the total mass of an incompressible system, thus improving the numerical stability for creeping flows.The model is firstly validated against the analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of three-dimensional deformable droplet at various Marangoni numbers, and its accuracy is once again verified against the theoretical prediction in the limit of zero Marangoni number. Finally, we numerically investigate how the localized heating from a laser can block the microfluidic droplet motion through the induced thermocapillary forces. The droplet motion can be completely blocked provided that the intensity of laser exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and constant velocity. When the droplet motion is completely blocked, four steady vortices are clearly visible, and the droplet is fully filled by two internal vortices. The external vortices diminish when the intensity of laser increases.     

A molecular dynamics study of effective parameters on nano-droplet surface tension

The main purpose of this paper is to numerically study the effect of droplet radius, temperature, and surface wettability on droplet surface tension. Moreover, the validity of Young-Laplace equation (Y-L) for nano-droplet is examined. Simulations of droplet surrounded by its vapor and droplet on solid surface are carried out and the results are compared to each other in order to comprehend the role of surface wettability on droplet surface tension. The pair potential for the liquid-liquid and liquid-solid interaction is considered using Lennard-Jones model. Different numbers of atoms and surface wettabilities are employed to generate droplet of different radiuses. In addition, contact angle of droplet on solid surface is computed. Pressure tensor and density profile is locally calculated. Furthermore, liquid pressure is evaluated far from the interface using the virial theorem and gas pressure is obtained using an equation of state. In order to calculate the surface tension, two different approaches are employed; Young-Laplace equation and direct molecular dynamics (MD) simulation. The surface tension increases with increase in droplet radius and it is seen that the surface wettability does not directly influence the surface tension.     

Lattice-Boltzmann simulations of dynamic interfacial tension due to soluble amphiphilic surfactant

An amphiphilic Lattice-Boltzmann approach is adopted to model dynamic interfacial tension due to non-ionic surfactant. In the current system, the surfactant adsorption kinetics is diffusion dominated and the interface separates two immiscible fluids. A rotational relaxation time and a diffusive/viscous relaxation time are associated with the surfactant. The model results are compared with experimental data for the dynamic interfacial tension of a pendant oil droplet in water, with oil soluble surfactant. We demonstrate how to adapt and calibrate the model to capture the adsorption timescale of the surfactant and the magnitude of interfacial tension reduction due to surfactant. A scheme to overcome numerical instabilities due to the relatively low surfactant concentration, is devised. We are able to qualitatively match the Frumkin equation of state for the interfacial tension.     

Droplets sliding on fibres

We present the results of a combined experimental and theoretical investigation of oil droplets sliding on fibres. First, both the axisymmetric shape and the motion of a droplet on a vertical fibre are described. The motion is shown to result from a balance between the droplet weight and the viscous stresses. On a long-term range, the droplet loses some mass through coating the fibre, which decreases its velocity. In a second time, we rationalize the behaviour of a droplet that encounters a junction between vertical and horizontal fibres. Depending on its size, the droplet may cross the junction or remain blocked. The transition is well described by an ordinary differential equation equivalent to a damped harmonic oscillator truncated to the neighbourhood of the horizontal fibre. This simple system is the basic element for more complex fiber networks that would be useful in microfluidic applications involving droplets.     

Photophysical and Nonlinear Optical Properties of Azophloxine in Reverse Micelles

The photophysical and nonlinear optical properties of Azophloxine in Reverse micelle (RM) and dye-surfactant interaction were studied using Z-scan, spectrophotometer, and spectrofluorometer techniques. The different range of RM sizes and oil polarity is studied. RM is a mixture of water droplet in a continuous phase of oil and its polarity depends on oil polarity. The nonlinear absorption coefficient (β) and nonlinear refractive index (n₂) of Azophloxine in RM depend on the polarity of bulk. By using the NMR instrument, it was observed that the Azophloxine dye is intercalated in the reverse micelles in AOT/Water/Benzene solution and its average location corresponds with the core of the micelle close to polar groups of the surfactant. The rule of charge and length scale of surfactant on the value of β and n₂ of Azophloxine is studied. The results showed that the enhancement value of β and n₂ is due to the solubility reduction of Azophloxine with the anionic surfactant in aqueous solutions or increase of oil length scale in RM. The quantum perturbation theory was used to study the ratio of excited to ground state dipole moment of Azophloxine in RM. By using dynamic light scattering, it was observed that the size of RM reduced with an increase of dye concentration in RM.     

A coupled arbitrary Lagrangian–Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants

A finite element scheme to compute the dynamics of insoluble surfactant on a deforming free surface is presented. The free surface is tracked by the arbitrary Lagrangian–Eulerian (ALE) approach, whereas the surfactant concentration transport equation is approximated in a Lagrangian manner. Since boundary resolved moving meshes are used in the ALE approach, the surface tension, which may be a linear or nonlinear function of surfactant concentration (equation of state), and the Marangoni forces can be incorporated directly into the numerical scheme. Further, the Laplace–Beltrami operator technique, which reduces one order of differentiation associated with the curvature, is used to handle the curvature approximation. A number of 3D-axisymmetric computations are performed to validate the proposed numerical scheme. An excellent surfactant mass conservation without any additional mass correction scheme is obtained. The differences in using a linear and a nonlinear equation of state, respectively, on the flow dynamics of a freely oscillating droplet are demonstrated.