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.     

Self-motion of an oil droplet: a simple physicochemical model of active Brownian motion

The self-motion of an oil droplet in an aqueous phase on a glass surface is reported. The aqueous phase contains a cationic surfactant, which tends to be adsorbed onto the glass surface. The oil droplet contains potassium iodide and iodine, which prefers to make an ion pair with the cationic surfactant. Since the ion pair is soluble in the oil droplet, dissolution of the surfactant into the oil droplet is promoted, i.e., the system is far from equilibrium with regard to surfactant concentration. The oil droplet is self-driven in a reactive manner by the spatial gradient of the glass surface tension. We discuss the intrinsic nature of this self-motion by developing a simple mathematical model that incorporates adsorption and desorption of the surfactant on the glass surface. Using this mathematical model we were able to construct an equation of motion that reproduces the observed self-motion of an oil droplet. This equation describes active Brownian motion. Theoretical considerations were used to predict the generation of the regular mode of oil-droplet motion, which was subsequently confirmed by experiments.     

A conservative SPH method for surfactant dynamics

In this paper, a Lagrangian particle method is proposed for the simulation of multiphase flows with surfactant. The model is based on the multiphase smoothed particle hydrodynamics (SPH) framework of Hu and Adams (2006) [1]. Surface-active agents (surfactants) are incorporated into our method by a scalar quantity describing the local concentration of molecules in the bulk phase and on the interface. The surfactant dynamics are written in conservative form, thus global mass of surfactant is conserved exactly. The transport model of the surfactant accounts for advection and diffusion. Within our method, we can simulate insoluble surfactant on an arbitrary interface geometry as well as interfacial transport such as adsorption or desorption. The flow-field dynamics and the surfactant dynamics are coupled through a constitutive equation, which relates the local surfactant concentration to the local surface-tension coefficient. Hence, the surface-tension model includes capillary and Marangoni-forces. The present numerical method is validated by comparison with analytic solutions for diffusion and for surfactant dynamics. More complex simulations of an oscillating bubble, the bubble deformation in a shear flow, and of a Marangoni-force driven bubble show the capabilities of our method to simulate interfacial flows with surfactants.     

Droplets breakup via a splitting microchannel

On the basis of a volume of fluid(VOF) liquid/liquid interface tracking method, we apply a two-dimensional model to investigate the dynamic behaviors of droplet breakup through a splitting microchannel. The feasibility and applicability of the theoretical model are experimentally validated. Four flow regimes are observed in the splitting microchannel, that is, breakup with permanent obstruction, breakup with temporary obstruction, breakup with tunnels, and non-breakup. The results indicate that the increase of the capillary number Ca provides considerable upstream pressure to accelerate the droplet deformation, which is favorable for the droplet breakup. The decrease of the droplet size contributes to its shape changing from the plug to the sphere, which results in weakening droplet deformation ability and generating the nonbreakup flow regime.     

表面活性剂浓度对球形气泡界面和尾流的影响

发展了一种研究气泡界面污染程度的数值模型,并用其对流场中不同表面活性剂浓度下、上浮气泡的界面参量和周围流场进行了模拟研究。该模型假设吸附于气泡界面的表面活性剂分布在毗邻气液界面的薄吸附层中,且气泡界面上表面活性剂的吸附与解吸过程也发生于此;界面切应力为界面浓度的函数。研究发现:气泡界面的流动性会因表面活性剂的吸附而降低,该现象会增大气泡周围流域中切向速度在界面法向上的变化量,从而对界面性质和周围流场产生影响;由于对流的作用和吸附-解吸动态平衡的存在,气泡前部界面不完全干净,且受污染界面的流动性也不完全为零。     

Novel surface tension isotherm for surfactants based on local density functional theory

In this Letter we report a new general method for calculating of surface tension isotherms in the presence of surfactants, based on a local density functional. We illustrate this method by deriving the interfacial tension isotherm for nonionic surfactants at an air-water or oil-water interface by using the self-consistent field theory of polymer brushes. We consider a particular case of local density functional to calculate explicitly how the interfacial tension and the surfactant adsorption depend on the surfactant bulk concentration. Experimental data for the surface tension and the surfactant adsorption isotherm for nonionic surfactants were interpreted with the help of the new isotherm. Very good agreement between the adsorption of n-dodecyl pentaoxyethylene glycol ether (C12E5) at an air-water interface, calculated from the surface tension isotherm and small-angle neutron-scattering is obtained.     

Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations

The three-dimensional, moving mesh interface tracking (MMIT) method coupled with local mesh adaptations by Quan and Schmidt [S.P. Quan, D.P. Schmidt, A moving mesh interface tracking method for 3D incompressible two-phase flows, J. Comput. Phys. 221 (2007) 761–780] demonstrated the capability to accurately simulate multiphase flows, to handle large deformation, and also to perform interface pinch-off for some specific cases. However, another challenge, i.e. how to handle interface merging (such as droplet coalescence) has not been addressed. In this paper, we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup. These two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region. After the conversion, the newly created interface is usually ragged, and a local projection method is employed to smooth the interface. Extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes. Simulations of droplet pair collisions including both head-on and off-center coalescences show that the mesh adaptations are capable of resolving very small length scales, and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows. The potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed.     

激波诱导液滴变形和破碎现象实验研究

本文介绍了用于激波诱导液滴变形和破碎现象研究的实验系统及方法,详细分析了激波与液滴相互作用以及液滴加速、变形和破碎过程,为进一步研究激波诱导的液滴内流场性质及气液相间相互作用对液滴变形和破碎的影响机制提供了基础实验数据。     

激波诱导的液滴变形和破碎

 建立液滴变形与破碎的模型,提出初始雾化时间概念,由此分析激波后液滴变形和破碎雾化的特征。液滴变形率、完全破碎时间的数值分析结果与实验结果基本一致。     

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.     

The droplet breakup model and characteristics of pH-shifted peanut protein isolate-high methoxyl pectin stabilised emulsions under ultrasound

The effect of pH on the occurrence states of peanut protein isolate (PPI) and high methoxyl pectin (HMP), and droplet breakup model of the emulsions under ultrasound were studied. Particle size distribution and scanning electron microscopy results showed that PPI-HMP existed a soluble complex at pH 5.0, had no interaction at pH 7.0, and was co-soluble at pH 9.0. Droplet breakup model results revealed that the characteristics of emulsion stabilised by PPI-HMP treated at pH 5.0 was different from that at pH 7.0 and 9.0. The average diameter of the droplet well satisfied the model. According to rheological properties, interface tension, and microstructure, the formation mechanism and characteristics of emulsion stabilised by PPI-HMP treated at pH 5.0 was different from that at pH 7.0 and pH 9.0. The research provided a reference for constructing emulsions using pH-shifted PPI-HMP under ultrasound.     

Y型微通道内双重乳液流动破裂机理

基于体积分数法建立了Y型微通道中双重乳液流动非稳态理论模型,数值模拟研究了Y型微通道内双重乳液破裂情况,详细分析了双重乳液流经Y型微通道时的流场信息以及双重乳液形变参数演化特性,定量地给出了双重乳液流动破裂的驱动以及阻碍作用,揭示了双重乳液破裂流型的内在机理.研究结果表明:流经Y型微通道时,双重乳液受上游压力驱动产生形变,形变过程中乳液两端界面张力差阻碍双重乳液形变破裂,两者正相关;隧道的出现将减缓双重乳液外液滴颈部收缩速率以及沿流向拉伸的速率,并减缓了内液滴沿流向拉伸的速率,其对于内液滴颈部收缩速率影响不大;隧道破裂和不破裂工况临界线可以采用幂律关系式l~*=βCa~b进行预测,隧道破裂和阻塞破裂工况临界线可以采用线性关系l~*=α描述;与单乳液运动相图相比,双重乳液运动相图各工况的分界线关系式系数α和β均相应增大.     

等直径微液滴碰撞过程的改进光滑粒子动力学模拟

运用一种改进光滑粒子动力学(SPH)方法模拟了相溶和不相溶两种情况下的等直径微液滴碰撞动力学过程. 为提高传统SPH方法的数值精度和稳定性, 采用一种不涉及核导数计算的核梯度改进形式; 为处理液滴界面张力采用修正的van der Waals表面张力模型. 通过模拟牛顿液滴碰撞聚并变形过程并与相关文献或试验结果进行对比, 验证了改进SPH 方法模拟微液滴碰撞过程的可靠性. 随后, 研究了基于van der Waals模型相溶聚合物微液滴碰撞聚并变形过程及不相溶微液滴碰撞后的反弹、分离过程, 讨论了碰撞过程中碰撞速度、碰撞角度、密度比等参数对碰撞变形过程的影响, 分析了流体桥、旋转角度等因素的变化情况. 关键词： 光滑粒子动力学 微液滴 聚合物液滴 碰撞     

Modeling Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking without Connectivity

Three-dimensional multiphase flow and flow with phase change are simulated using a simplified method of tracking and reconstructing the phase interface. The new level contour reconstruction technique presented here enables front tracking methods to naturally, automatically, and robustly model the merging and breakup of interfaces in three-dimensional flows. The method is designed so that the phase surface is treated as a collection of physically linked but not logically connected surface elements. Eliminating the need to bookkeep logical connections between neighboring surface elements greatly simplifies the Lagrangian tracking of interfaces, particularly for 3D flows exhibiting topology change. The motivation for this new method is the modeling of complex three-dimensional boiling flows where repeated merging and breakup are inherent features of the interface dynamics. Results of 3D film boiling simulations with multiple interacting bubbles are presented. The capabilities of the new interface reconstruction method are also tested in a variety of two-phase flows without phase change. Three-dimensional simulations of bubble merging and droplet collision, coalescence, and breakup demonstrate the new method's ability to easily handle topology change by film rupture or filamentary breakup. Validation tests are conducted for drop oscillation and bubble rise. The susceptibility of the numerical method to parasitic currents is also thoroughly assessed.     

非对称布置液滴在波纹状基底上的聚并过程

基于润滑理论建立在波纹基底上两个含表面活性剂液滴聚并的演化模型，模拟液滴位于波纹基底波峰和波谷处的聚并过程，分析液滴初始间距和基底高度对聚并的影响，并与对称布置液滴进行比较.结果表明：液滴高度随时间呈现五个阶段变化；活性剂浓度在短时间内完成三个阶段变化；初始间距的增大将延长液滴及活性剂聚并时间；增大基底高度将缩短液滴及活性剂聚并时间；非对称液滴相较于对称液滴聚并时间短，聚并速度快.     

Dependence of the Average Size of Particles Formed during Steady Mixing on their Concentration in Immiscible Polymer Blends

A linear increase in the size of ethylene-propylene rubber particles with its content in polypropylene matrix at steady mixing in a batch mixer was observed. This type of the dependence is predicted by the theory of dynamic equilibrium between the droplet breakup and coalescence. However, theoretical calculation of droplet radius extrapolated to zero concentration of EPR and slope of the dependence of droplet radius versus concentration, based on the effective shear rate (related to mixing conditions), are in strong disagreement with the experimental results. Reasons for these discrepancies between theories and experimental results are thoroughly elucidated.     

A front-tracking method for computation of interfacial flows with soluble surfactants

A finite-difference/front-tracking method is developed for computations of interfacial flows with soluble surfactants. The method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations together with the incompressible Navier–Stokes equations using a non-linear equation of state that relates interfacial surface tension to surfactant concentration at the interface. The method is validated for simple test cases and the computational results are found to be in a good agreement with the analytical solutions. The method is then applied to study the cleavage of drop by surfactant—a problem proposed as a model for cytokinesis [H.P. Greenspan, On the dynamics of cell cleavage, J. Theor. Biol. 65(1) (1977) 79; H.P. Greenspan, On fluid-mechanical simulations of cell division and movement, J. Theor. Biol., 70(1) (1978) 125]. Finally the method is used to model the effects of soluble surfactants on the motion of buoyancy-driven bubbles in a circular tube and the results are found to be in a good agreement with available experimental data.     

Numerical investigation of the effect of insoluble surfactant on drop formation in microfluidic device

Surfactants are commonly used in droplet-based microfluidics to stabilize the droplet interface. In this study, we investigate the effect of insoluble surfactant on drop formation in a capillary microfluidic device. We use a diffuse-interface method to describe the evolution of interface involving insoluble surfactant. The Navier-Stokes/Cahn-Hilliard equations and the surfactant conservation equation are solved by a finite element method along with a grid deformation method. As the surfactant has a non-uniform distribution during the drop formation in general, the surface tension has a gradient on the interface, which affects the flow field and interface evolution. The surfactant effect is discussed for dripping and jetting regimes.     

Arbitrary Lagrangian–Eulerian finite-element method for computation of two-phase flows with soluble surfactants

A finite-element scheme based on a coupled arbitrary Lagrangian–Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier–Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant.