Droplet retraction in the presence of nanoparticles with different surface modifications

We studied the influence of nanoparticles with different surface modifications on the interfacial tension and relaxation of model polymer blend after cessation of different strains. The droplet retraction experiments were carried out on a model system composed of polydimethylsiloxane (PDMS) as the suspending fluid and polyisobutylene (PIB) as droplet at room temperature in the presence of hydrophobic and hydrophilic nanosilica. Different weight fractions of particles were dispersed in the PIB droplet before forming a dispersed droplet by using a microsyringe in shear cell. We found that applied strain, nanoparticle concentration and their thermodynamically preferred localization affect both nominal interfacial tension and droplet retraction process. By addition of nanoparticles at a concentration as low as 0.2%wt, the nominal interfacial tension decreases from 3.12?±?0.15 mN/m for neat PIB-PDMS interface depending on the surface characteristics of nanosilica. Hydrophilic nanosilica has the most effect on nominal interfacial tension and decreases it as low as 0.2?±?0.21 mN/m at 1 wt.% loading under a strain of 7. The results show that the retraction process in this system is mainly controlled by interfacial phenomena rather than bulk rheological properties. Additionally, the shape evolution of droplets changes and the retraction rate slows down in the presence of nanoparticles.     

Direct numerical simulation of surfactant-stabilized emulsions

A 3D lattice Boltzmann model for two-phase flow with amphiphilic surfactant was used to investigate the evolution of emulsion morphology and shear stress in starting shear flow. The interfacial contributions were analyzed for low and high volume fractions and varying surfactant activity. A transient viscoelastic contribution to the emulsion rheology under constant strain rate conditions was attributed to the interfacial stress. For droplet volume fractions below 0.3 and an average capillary number of about 0.25, highly elliptical droplets formed. Consistent with affine deformation models, gradual elongation of the droplets increased the shear stress at early times and reduced it at later times. Lower interfacial tension with increased surfactant activity counterbalanced the effect of increased interfacial area, and the net shear stress did not change significantly. For higher volume fractions, co-continuous phases with a complex topology were formed. The surfactant decreased the interfacial shear stress due mainly to advection of surfactant to higher curvature areas. Our results are in qualitative agreement with experimental data for polymer blends in terms of transient interfacial stresses and limited enhancement of the emulsion viscosity at larger volume fractions where the phases are co-continuous.     

Abnormal rotation of a deformed liquid crystal droplet immersed in an isotropic fluid after transient flow

The morphology evolution of liquid crystal droplets immersed in an isotropic fluid in flow field is found to be different from flexible polymer droplets. In this paper, we investigated the retraction of a liquid crystal droplet after transient flow. It is found that the liquid crystal droplet will rotate during the shape recovery, which has never been observed for an isotropic droplet. The factors that influence the rotational angle of a single liquid crystal droplet during retraction progress were studied, including the temperature, the dimension of the droplets, the time of shear flow, the shear rate, the flow type, and the properties of liquid crystal molecules. The rotation of liquid crystal droplet during shape recovery is ascribed to both the bulk elasticity of liquid crystal droplets and the anisotropic properties of the interface between liquid crystal and isotropic fluid.     

The influence of matrix viscoelasticity on the rheology of polymer blends

We examine the effects of matrix phase viscoelasticity on the rheological modeling of polymer blends with a droplet morphology. Two contravariant, second-rank tensor variables are adopted along with the translational momentum density of the fluid to account for viscoelasticity of the matrix phase and the ellipsoidal droplet shapes. The first microstructural variable is a conformation tensor describing the average extension and orientation of the molecules in the matrix phase. The other microstructural variable is a configuration tensor to account for the average shape and orientation of constant-volume droplets. A Hamiltonian framework of non-equilibrium thermodynamics is then adopted to derive a set of continuum equations for the system variables. This set of equations accounts for local conformational changes of the matrix molecules due to droplet deformation and vice versa. The model is intended for dilute blends of both oblate and prolate droplets, and droplet breakup and coalescence are not taken into account. Only the matrix phase is considered as viscoelastic; i.e., the droplets are assumed to be Newtonian. The model equations are solved for various types of homogeneous deformations, and microstructure/rheology relationships are discussed for transient and steady-state conditions. A comparison with other constrained-volume rheological models and experimental data is made as well.     

Shear cell rupture of nematic liquid crystal droplets in viscous fluids

We model the hydrodynamics of a shear cell experiment with an immiscible nematic liquid crystal droplet in a viscous fluid using an energetic variational approach and phase-field methods [86]. The model includes the coupled system for the flow field for each phase, a phase-field function for the diffuse interface and the orientational director field of the liquid crystal phase. An efficient numerical scheme is implemented for the two-dimensional evolution of the shear cell experiment for this initial data. The same model reduces to an immiscible viscous droplet in a viscous fluid, which we simulate first to compare with other numerical and experimental behavior. Then we simulate drop deformation by varying capillary number (independent of liquid crystal physics), liquid crystal interfacial anchoring energy and Oseen–Frank distortional elastic energy. We show the number of eventual droplets (one to several) and “beads on a string” behavior are tunable with these three physical parameters. All stable droplets possess signature quadrupolar shear and normal stress distributions. The liquid crystal droplets always possess a global surface defect structure, called a boojum, when tangential surface anchoring is imposed. Boojums [79], [32] consist of degree +1/2 and ?1/2 surface defects within a bipolar global orientational structure.     

Dynamics of the capillary breakup of a bridge in an elastic fluid

The tension of self-thinning filaments occurring upon the capillary breakup of liquid bridges in viscoelastic fluids is measured. The solution of high-molecular polymers with the concentration of 0.1 to 1% are studied. The stresses occurring in the filaments are determined and the effect of the hydrodynamic interaction between the filaments and the adjoining macroscopic volume (droplet) is evaluated. A theoretical analysis of the fluid inflow into the droplet shows that in the case of filament extension the rheology of the polymer liquids under consideration is different from that under the singleaxis compression in droplet flow.     

Dynamic rheology of the immiscible blends of liquid crystalline polymers and flexible chain polymers

Immiscible blends containing liquid crystalline polymers (LCP) as dispersed phases show different dynamic rheological properties than those composed of flexible polymers. The widely used Palierne’s model was shown by many authors to be insufficient to describe the frequency dependence of dynamic modulus of such blends. A new model was presented to describe the dynamic rheology of the immiscible blend containing LCP as a dispersed phase. The flexible chain polymer matrix was assumed to be a linear viscoelastic material under small amplitude oscillatory shear flow, and the LCP was assumed to be an Ericksen’s transversely isotropic fluid. The Rapini-Papoular equation of anisotropic interfacial energy was used to account for the effect of nematic orientation on the interfacial tension. It was found that the orientation of the director and the anchoring energy greatly influenced the storage modulus at the “shoulder” regime. The overall dynamic modulus of the blend can be well described by the model with suitable choice of the orientation of the director and anchoring energy of LCP.     

Effect of fumed silica nanoparticles on the morphology and rheology of immiscible polymer blends

We examined the effect of interfacially active particles on the morphology and rheology of droplet/matrix blends of two immiscible homopolymers. Experiments were conducted on polybutadiene/polydimethylsiloxane (10/90) blend and the inverse system. The effects of fumed silica nanoparticles, at low particle loadings (0.1–2.0 wt%), were examined by direct flow visualization and by rheology. Fumed silica nanoparticles were found to significantly affect the morphology of polymer blends, inducing droplet cluster structure and decreasing the droplet size, regardless of which phase wets the particles preferentially. This is surprising in light of much past research that shows that particles are capable of bridging and thus induce droplet cluster structure in droplet/matrix systems only when they are preferentially wetted by the continuous phase. Therefore, there should exist other possible mechanisms responsible for these droplet cluster structures except for the bridging mechanism. We proposed a particle-flocculating mechanism based on the fact that fumed silica particles readily flocculate due to their high aspect ratio, fractal-like shape, or interparticle attractions. Optical microscopy also reveals that the clustering structure becomes more extensive, and the droplet sizes in the clusters become smaller when the particle loading is increased. Rheologically, the chief effect of particles is to change the flow behavior from a liquid-like rheology to gel-like behavior. This gel-like behavior can be attributed to droplet clustering. Moreover, it should be emphasized that such gel-like behavior can be seen in the blends regardless of which phase wets the particles preferentially, suggesting that, once again, bridging is not the only cause of droplet clustering.     

Oldroyd-B黏弹性液滴碰撞过程的数值模拟

复杂的流变特性使凝胶推进剂的雾化过程存在一定困难,这制约了它的发展.聚合物胶凝剂的加入使凝胶推进剂具有黏弹性,从而在雾化时会产生黏弹性液滴,因此为了进一步认识凝胶推进剂的雾化机理、提高凝胶推进剂的雾化性能,对黏弹性液滴的碰撞行为进行数值模拟研究.针对凝胶推进剂雾化过程中出现的液滴撞击现象,考虑流体具有的黏弹性效应,采用...     

Modeling surface tension of a two‐dimensional droplet using smoothed particle hydrodynamics

Surface tension plays a significant role at the dynamic interface of free‐surface flows especially at the microscale in capillary‐dominated flows. A model for accurately predicting the formation of two‐dimensional viscous droplets in vacuum or gas of negligible density and viscosity resulting from axisymmetric oscillation due to surface tension is solved using smoothed particle hydrodynamics composed of the Navier‐Stokes system and appropriate interfacial conditions for the free‐surface boundaries. The evolution of the droplet and its free‐surface interface is tracked over time to investigate the effects of surface tension forces implemented using a modified continuous surface force method and is compared with those performed using interparticle interaction force. The dynamic viscous fluid and surface tension interactions are investigated via a controlled curvature model and test cases of nonsteady oscillating droplets; attention is focused here on droplet oscillation that is released from an initial static deformation. Accuracy of the results is attested by demonstrating that (i) the curvature of the droplet that is controlled; (ii) uniform distribution of fluid particles; (iii) clean asymmetric forces acting on the free surface; and (iv) nonsteady oscillating droplets compare well with analytical and published experiment findings. The advantage of the proposed continuous surface force method only requires the use of physical properties of the fluid, whereas the interparticle interaction force method is restricted by the requirement of tuning parameters.     

Application of maximum entropy method for droplet size distribution prediction using instability analysis of liquid sheet

This paper describes the implementation of the instability analysis of wave growth on liquid jet surface, and maximum entropy principle (MEP) for prediction of droplet diameter distribution in primary breakup region. The early stage of the primary breakup, which contains the growth of wave on liquid–gas interface, is deterministic; whereas the droplet formation stage at the end of primary breakup is random and stochastic. The stage of droplet formation after the liquid bulk breakup can be modeled by statistical means based on the maximum entropy principle. The MEP provides a formulation that predicts the atomization process while satisfying constraint equations based on conservations of mass, momentum and energy. The deterministic aspect considers the instability of wave motion on jet surface before the liquid bulk breakup using the linear instability analysis, which provides information of the maximum growth rate and corresponding wavelength of instabilities in breakup zone. The two sub-models are coupled together using momentum source term and mean diameter of droplets. This model is also capable of considering drag force on droplets through gas–liquid interaction. The predicted results compared favorably with the experimentally measured droplet size distributions for hollow-cone sprays.     

An Eulerian–Lagrangian hybrid model for the coarse-grid simulation of turbulent liquid jet breakup

In this paper we present a numerical model for the coarse-grid simulation of turbulent liquid jet breakup using an Eulerian–Lagrangian coupling. To picture the unresolved droplet formation near the liquid jet interface in the case of coarse grids we considered a theoretical model to describe the unresolved flow instabilities leading to turbulent breakup. These entrained droplets are then represented by an Eulerian–Lagrangian hybrid concept. On the one hand, we used a volume of fluid method (VOF) to characterize the global spreading and the initiation of droplet formation; one the other hand, Lagrangian droplets are released at the liquid–gas interface according to the theoretical model balancing consolidating and disruptive energies. Here, a numerical coupling was required between Eulerian liquid core and Lagrangian droplets using mass and momentum source terms. The presented methodology was tested for different liquid jets in Rayleigh, wind-induced and atomization regimes and validated against literature data. This comparison reveals fairly good qualitative agreement in the cases of jet spreading, jet instability and jet breakup as well as relatively accurate size distribution and Sauter mean diameter (SMD) of the droplets. Furthermore, the model was able to capture the regime transitions from Rayleigh instability to atomization appropriately. Finally, the presented sub-grid model predicts the effect of the gas-phase pressure on the droplet sizes very well.     

Impact dynamics of drops on thin films of viscoelastic wormlike micelle solutions

The impact dynamics of water drops on thin films of viscoelastic wormlike micelle solutions is experimentally studied using a high-speed digital video camera at frame rates up to 4000 frame/s. The composition and thickness of the thin film is modified to investigate the effect of fluid rheology on the evolution of crown growth, the formation of satellite droplets and the formation of the Worthington jet. The experiments are performed using a series of wormlike micelle solutions composed of a surfactant, cetyltrimethylammonium bromide (CTAB), and a salt, sodium salicylate (NaSal), in deionized water. The linear viscoelastic shear rheology of the wormlike micelle solutions is well described by a Maxwell model with a single relaxation time while the steady shear rheology is found to shear thin quite heavily. In transient homogeneous uniaxial extension, the wormlike micelle solutions demonstrate significant strain hardening. The size and velocity of the impacting drop is varied to study the relative importance of Weber, Ohnesorge, and Deborah numbers on the impact dynamics. The addition of elasticity to the thin film fluid is found to suppress the crown growth and the formation of satellite drops with the largest effects observed at small film thicknesses. A new form of the splashing threshold is postulated which accounts for the effects of viscoelasticity and collapses the satellite droplet data onto a single master curve dependent only on dimensionless film thickness and the underlying surface roughness. Additionally, a plateau is observed in the growth of the maximum height of the Worthington jet height with increasing impact velocity. It is postulated that the complex behavior of the Worthington jet growth is the result of a dissipative mechanism stemming from the scission of wormlike micelles.     

Modeling of complex interfaces for pendant drop experiments

Interfaces of fluid-fluid systems play an important role in the stability of foams and emulsions in chemistry, biology, consumer products, and foods. For most applications, surface active agents are added and adsorbed onto the interface to enhance stability, making the rheological behavior of the interface more complex. To understand the phenomena of these complex interfaces, various techniques are used to determine the interfacial properties. One of the most popular methods is the pendant drop technique. From the equilibrium state of the pendant drop, the interfacial tension of a system can be obtained quite easily in the absence of surface active agents. But when complex viscoelastic interfacial characteristics are considered, in particular in oscillatory measurements, interfacial constitutive relations need to be defined. Interfaces containing proteins, particles or Langmuir monolayers formed by insoluble low weight surfactants appear to act like viscoelastic solid membranes. In this work, a two-dimensional axisymmetric finite element model is designed to study the behavior of complex interfaces in pendant drop experiments. The bulk fluid consists of a Newtonian fluid, while the interface behaves according to the Kelvin-Voigt model as elastic interfacial forces dominate. To be able to capture large deformations, the Kelvin-Voigt constitutive model is made quasi-linear by using a combination of two non-linear strain tensors. A parameter study is performed to investigate the influence of the five model parameters of the quasi-linear Kelvin-Voigt equation. To demonstrate the applicability of the numerical model, a small amplitude oscillatory measurement is simulated.     

Viscosity of a Newtonian fluid calculated from the deformation of droplets covered with a surfactant under a linear shear flow

The viscosity of small fluid droplets covered with a surfactant is determined using drop deformation techniques. This method, proposed by Hu and Lips, is here extended to the case of the presence of a surface-active adsorpted at the liquid–liquid interface, to consider more general scenarios. In these experiments, a droplet is sheared by another immiscible fluid of known viscosity, both Newtonian liquids. From the steady-state deformation and retraction mechanisms, the droplet viscosity is calculated using an equation derived from the theories of Taylor and Rallison. Although these theories were expressed for surfactant-free interfaces, they can be applied when a surfactant is present in the system if the sheared droplet reaches reliable steady-state deformations and the surfactant attains its equilibrium adsorption concentration. These determinations are compared to bulk viscosities measured in a rheometer for systems with different viscosity ratios and surfactant concentrations. Very good agreement between both determinations is found for drops more viscous than the continuous phase.     

基于SPH方法的湿润性固壁边界条件模拟研究

固体壁面由于表面特殊结构和材料属性,时常表现出对交界面上水体的吸附作用,而这一特征对微小水体作用尤为明显。本文提出了一种湿润性固壁边界条件的计算方法,即假设壁面粒子的亲水性以及毛细吸附作用统一表现为对支持域内流体粒子的吸附力。基于光滑粒子流体动力学（SPH）方法,模拟了静态液滴在不同湿润性壁面上的变形至稳定过程。模拟了液滴撞击疏水壁面的过程,将液滴的运动过程分为碰撞、铺展、回缩和回弹四个阶段,分析各阶段壁面受力分布情况。研究表明：根据模拟液滴静态接触角的变化特点,本文湿润性固壁边界条件可以较好的反映出壁面湿润性;液滴撞击输水表面的模拟数据与试验结果趋势上吻合良好;壁面压力波伴随着液滴的铺展和回缩传播并衰减;只有在回弹后期液滴即将脱离壁面时壁面拉力起主导作用,其余各时刻壁面均以压力为主。     

Rheology of a suspension of particles in viscoelastic fluids

In this paper we study the bulk stress of a suspension of rigid particles in viscoelastic fluids. We first apply the theoretical framework provided by Batchelor [J. Fluid Mech. 41 (1970) 545] to derive an analytical expression for the bulk stress of a suspension of rigid particles in a second-order fluid under the limit of dilute and creeping flow conditions. The application of the suspension balance model using this analytical expression leads to the prediction of the migration of particles towards the centerline of the channel in pressure-driven flows. This is in agreement with experimental observations. We next examine the effects of inertia (or flow Reynolds number) on the rheology of dilute suspensions in Oldroyd-B fluids by two-dimensional direct numerical simulations. Simulation results are verified by comparing them with the analytical expression in the creeping flow limit. It is seen that the particle contribution to the first normal stress difference is positive and increases with the elasticity of the fluid and the Reynolds number. The ratio of the first normal stress coefficient of the suspension and the suspending fluid decreases as the Reynolds number is increased. The effective viscosity of the suspension shows a shear-thinning behavior (in spite of a non-shear-thinning suspending fluid) which becomes more pronounced as the fluid elasticity increases.     

Numerical analysis of secondary droplets characteristics due to drop impacting on 3D cylinders considering dynamic contact angle

This study is investigating three-dimensional numerical simulation of a Newtonian droplet impact and break on two square cylinders based on dynamic contact angle of droplet at the spatial interface between two solid–fluid phases. The droplet impact details and morphology studied in the present work could provide ideas for the spray wall impingement modeling in the simulation of many industrial applications, such as spray painting and liquid cooling of surfaces. The droplet impact is investigated on two square cylinders in 9 different modes with different droplet diameters and physical conditions such as different positions of droplet. The volume of fluid (VOF) method was used with open-source software. The results have been compared and validated quantitatively and qualitatively with the experimental results. Results represent droplet diameter into cylinder dimension and velocity profiles are affected on number of broken droplets, break times and droplet deformation. Also, mean velocities of droplet after impact on two square cylinders at first break time were 0, 0.025, 0.12, 0.47, 0.11, 0.08, 0.2, 0.012, 0.19 m/s for cases 1–9, respectively. Moreover, in case 7 that droplet diameter into cylinder dimension was 2, the maximum number of break-up into secondary droplets was 10 drops that occurred for 4 times.

     

基于LS-DYNA的热成型钢断裂失效预测研究

固体壁面由于表面特殊结构和材料属性,时常表现出对交界面上水体的吸附作用,而这一特征对微小水体作用尤为明显。本文提出了一种湿润性固壁边界条件的计算方法,即假设壁面粒子的亲水性以及毛细吸附作用统一表现为对支持域内流体粒子的吸附力。基于光滑粒子流体动力学（SPH）方法,模拟了静态液滴在不同湿润性壁面上的变形至稳定过程。模拟了液滴撞击疏水壁面的过程,将液滴的运动过程分为碰撞、铺展、回缩和回弹四个阶段,分析各阶段壁面受力分布情况。研究表明：根据模拟液滴静态接触角的变化特点,本文湿润性固壁边界条件可以较好的反映出壁面湿润性;液滴撞击输水表面的模拟数据与试验结果趋势上吻合良好;壁面压力波伴随着液滴的铺展和回缩传播并衰减;只有在回弹后期液滴即将脱离壁面时壁面拉力起主导作用,其余各时刻壁面均以压力为主。