Uniaxial extensional flow behavior of immiscible and compatibilized polypropylene/liquid crystalline polymer blends

In this work liquid crystalline polymer (LCP) and thermoplastic (TP) blends with and without compatibilizer were studied with respect to their elongational flow behavior, under uniaxial extensional flow. This knowledge is important because in processes involving dominantly extensional deformations, like the case of the formation of the LCP fibrillation, transient extensional flow properties become more important than transient or steady-shear properties. In systems characterized by disperse phase morphologies (10 and 20 wt%) the LCP acts as a plasticizer, decreasing the viscosity of the system and increasing its durability with respect to that of the matrix. On the other hand, for a system in which a co-continuous morphology is present (40 wt% LCP) fibrils and droplets deformation occurs simultaneously, leading to a much higher strain hardening and durability. Moreover, the addition of compatibilizers to the blends gives rise to an increase of the strain hardening and to a decrease of the durability, which is in accordance with the mechanical properties, namely a higher Young’s modulus and lower elongation at break, in comparison with noncompatibilized systems.     

CONSTITUTIVE MODELING OF ROLLED SHAPE MEMORY ALLOY SHEETS TAKING INTO ACCOUNT PRE-TEXTURE AND ANISOTROPIC HARDENING

The drawing or rolling process endows polycrystal shape memory alloy with a crys- tallographic texture, which can result in macroscopic anisotropy. The main purpose of this work is to develop a constitutive model to predict the thermomechanical behavior of shape memory alloy sheets, which accounts for the crystallographic texture. The total macroscopic strain is decom- posed into elastic strain and macro-transformation strain under isothermal condition. Considering the transformation strain in local grains and the orientation distribution function of crystallo- graphic texture, the macro-transformation strain and the effective elastic modulus of textured polycrystal shape memory alloy are developed by using tensor expressions. The kinetic equation is established to calculate the volume fraction of the martensite transformation under given stress. Furthermore, the Hill＇s quadratic model is developed for anisotropic transformation hardening of textured SMA sheets. All the calculation results are in good agreement with experimental data, which show that the present model can accurately describe the macro-anisotropic behaviors of textured shape memory alloy sheets.     

高韦伯数条件下黏性对液滴变形过程的影响

为探究液滴黏性对变形过程的影响，深入了解液滴在冲击波作用下变形破碎的行为机制。采用高速阴影技术在水平激波管上拍摄了高韦伯数（We=1 100～4 400）条件下，3种黏性硅油液滴的变形过程。结果表明随着黏性的提升:液滴演化出相应特征所需时间增大，同时会出现新的变形特征；液滴空间及位移特征参数的生长速率降低而变形时间、最大变形高度/位移都增大，这是因为提升的黏性力降低了变形速率、耗散了更多的动能并延长了液滴的变形过程；液滴表面最不稳定的Kelvin-Helmholtz波朝着大尺度、低生长率的方向发展，从而实现黏性对变形过程的延缓作用。随着最大变形位移的增大，最大变形高度首先线性增长，之后增幅降低。     

同轴气流式液体射流分裂液滴粒径研究

针对同轴气流式液体射流分裂液滴粒径预测模型缺乏的现状,结合射流线性稳定性理论,建立了基于临界模数的同轴气流式黏性液体射流分裂液滴粒径表达式,在此基础上,分别研究了气流旋拧(气流同时存在轴向和周向运动)及流体物性(气体可压缩性、液体黏性、气液密度比和表面张力)对液滴粒径的影响规律.研究发现:周围气流轴向引射作用和同轴旋转...     

Investigation of the band texture occurring in hydroxypropylcellulose solutions using rheo-optical, rheological and small angle light scattering techniques

The band texture occurs in lyotropic and thermotropic main-chain polymers after cessation of flow. This paper begins with a review of work concerned with band texture formation following shear and is followed by the presentation of original results obtained during a recent investigation. The evolution of band texture formation in a Klucel EF, 50% hydroxypropylcellulose (HPC) water solution, has been observed using polarized optical microscopy. The relationship determined between the primary shear rate and the rate of evolution of the band texture is complex and three different behaviours have been observed corresponding to three shear rate regions. Both steady flow and dynamic rheological investigations have been conducted on the HPC solution, the results of which have been related to the optical behaviour of the band texture. Data from steady flow investigations suggest that the viscosity of the solution when the band texture is present, decreases following increasing primary shear rates, is shear thinning and increases linearly with the time following its formation. Dynamic investigations suggest a definite link between the band texture evolution and the evolution of both G′ and G′′. In addition, the perfection of the band texture versus the primary shear rate has been quantified by studying the evolution of tan(δ) following the cessation of the primary shear. Dynamic experiments show that the structure of the band texture remains longer than suggested by the optical aspect of the texture. Small angle light scattering patterns have been correlated with the development of the band texture and confirm the continuing presence of the band texture structure following its optical disappearance. Received: 2 March 1999/Accepted: 26 July 1999     

Phase structure change and ER effect in liquid crystalline polymer/dimethylsiloxane blends

The mechanism of the electrorheological (ER) effect in two types of liquid crystalline polymer (LCP)/dimethylsiloxane (DMS) blends was investigated by rheological measurements and by structure observation under electric field and shear flow. The results show that the phase structures of these immiscible blends can be categorized into slipping (low viscosity) and non-slipping (high viscosity) states. In the non-slipping state, higher viscosity LCP domains connect the electrodes. In the slipping state, on the other hand, LCP domains do not connect the electrodes and the shear is mainly confined in the lower viscosity DMS domains. The ER effect (electrically induced viscosity increase) originates from the electrically induced slipping to non-slipping transition. In one of the blends, the ER effect occurs only at high shear rate, since this blend is in non-slipping state even under no field if the shear rate is low. Received: 29 April 1997 Accepted: 3 November 1997     

Manifestation of phase separation processes in oscillatory shear: droplet-matrix systems versus co-continuous morphologies

Phase separation processes in mixtures of poly-α-methylstyrene-co-acrylonitrile (PαMSAN) and poly-methylmethacrylate (PMMA) with lower critical solution temperature (LCST) behavior have been studied, focusing on the manifestation of the interface in oscillatory shear measurements. By using blends of different composition, systems with a droplet-matrix morphology or a co-continuous structure are generated during the phase separation process. The feasibility of probing this morphology development by rheological measurements has been investigated. The development of a disperse droplet phase leads to an increase in the elasticity of the blend at low frequency, showing up as a shoulder in the plot of storage modulus versus frequency. Here, the droplet growth is unaffected by the shear amplitude up to strains of 0.2; therefore the resulting dynamic data are suitable for quantitative analysis. In contrast, for blends in which phase separation leads to a co-continuous structure, the storage modulus shows a power law behavior at low frequency and its value decreases as time proceeds. For the latter systems, effects of the dynamic measurement on the morphology development have been observed, even for strain amplitudes as low as 0.01. To probe the kinetics of morphology evolution in droplet-matrix systems, measurements of the time dependence of the dynamic moduli at fixed frequency should be performed (for a whole series of frequencies). Only from such measurements, curves of the frequency dependence of the moduli at a well defined residence time can be constructed. From fitting these curves to the emulsion model of Palierne, the droplet diameter distribution at that particular stage in the phase separation and growth process can be obtained. It is not appropriate to use a simplified version of the Palierne model containing only the average droplet size, because a morphology with too broad a size distribution is generated. Received: 15 February 1999 Accepted: 20 May 1999     

基于线性互补模型的梯度塑性连续体无网格方法

对梯度塑性连续体提出了一个归结为线性互补问题的数值分析方法. 塑性乘子与位移均为主要未知变量,并采用基于移动最小二乘的无网格方法分别在积分点与节点上插值. 联立弱形式下的平衡方程与积分点上逐点满足的非局部本构方程和屈服准则可以导出一个线性互补问题,并通过Lexico-Lemke算法求解. 构造了一个基于N-R方法的迭代方案,使得不需要形成一致性切线刚度矩阵而仍保持二阶收敛性. 一维和二维的数值算例证明了所提出的方法处理由应变软化引起的应变局部化问题的有效性.      

Modelling impingement of hollow metal droplets onto a flat surface

Despite many theoretical and experimental works dealing with the impact of dense melt droplets on the substrate during the process of thermal spray coating, the dynamics of the impingement of hollow melt droplet and the subsequent splat formation are not well addressed. In this paper a model study for the dynamic impingement of hollow droplet is presented. The hollow droplet is modelled such that it consists of a liquid shell enclosing a gas cavity. The impingement model considers the transient flow dynamics during impact, spreading and solidification of the droplet using the volume of fluid surface tracking method (VOF) coupled with a solidification model within a one-domain continuum formulation. The results for spreading, solidification and formation of splats clearly show that the impingement process of hollow droplet is distinctly different from the dense droplet. Study with different droplet void fractions and void distribution indicates that void fraction and void distribution have a significant influence on the flow dynamics during impact and on the final splat shape. The results are likely to provide insights for the less-explored behaviour of hollow melt droplets in thermal spray coating processes.     

一个综合模糊裂纹和损伤的混凝土应变软化本构模型

本文研究就变软化材料的本构关系，提出了一个考虑损伤的粘塑性模型，损伤不仅影响材料的临界应力，而且影响材料的粘塑性，为模拟材料的应变软化行为，假设受损混凝土的破坏局部区域由模糊裂纹和损伤所统治，软化模量和局部区域尺度参量依赖于模糊裂纹扩展时释放的断裂能的参变量，用文中提出的模型计算了混凝土单轴压缩时不同应变速率下的瞬时应力应变响应以及等应力长期作用下的徐变，均得到很的结果。     

Viscosity of a liquid crystalline polymer solution with a polydomain or a band texture

The viscosity of a main-chain liquid crystalline polymer (anisotropic aqueous solution of hydroxypropylcellulose) is measured in the case where the liquid crystalline polymer presents a band texture and is compared to the case of a polydomain texture.     

Strain stiffening of non-colloidal hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region

Concentrated hard sphere suspensions often show an interesting nonlinear behavior, called strain stiffening, in which the viscosity or modulus starts to increase at critical strain amplitude. Sudden increase of rheological properties is similar to shear thickening; however, the particle dynamics in the strain stiffening under oscillatory shear flow does not necessarily coincide with the mechanism of shear thickening under step shear flow. In this study, we have systematically investigated the nonlinear rheology of non-colloidal (>1???m) hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region in order to better understand the strain stiffening behavior. The suspensions near liquid-and-crystal coexistence region are known to locally form the closed packing structure. The critical strain amplitude which is the onset of strain stiffening was different for the storage and loss modulus. But they converged to each other as the suspension forms a more crystalline structure. The critical strain amplitude was independent of medium viscosity, imposed angular frequency, and particle size, but was strongly dependent upon particle volume fraction. The onset of strain stiffening was explained in terms of shear-induced collision due to particle motion in the closed packing structure. Nonlinear stress wave-forms, which reflect the micro-structural change, were observed with the onset of strain stiffening. During the strain stiffening, enhanced elastic stress before and after flow reversal was observed which originates from changes in the suspension microstructure. Nonlinearity of the shear stress in terms of Fourier intensity was extremely increased up to 0.55. Beyond the strain stiffening, the suspension responded liquid-like and the nonlinearity decreased but the elastic shear stress was still indicating the microstructure rearrangement within a cycle.     

Isothermal elongational behavior of liquid-crystalline polymers and LCPs based blends

The rheological behavior of two flexible thermoplastics, Nylon-6 (Ny) and bisphenol-A polysulfone (PSu), and two wholly aromatic liquid crystalline polymers, Vectra-A900 (VA) and Vectra-B950 (VB), as well as that of Ny/VB and PSu/VA blends with 10% LCP, has been investigated by the use of capillary viscometers equipped with cylindrical dies having different length-to-diameter ratios. The elongational viscosity of all materials was calculated, from the results of isothermal measurements carried out at 290°C, by means of the Cogswell's analysis, based on the estimation of the pressure drop due to the converging flow at the die inlet. The behavior in elongational flow was compared with the rheological behavior in shear flow conditions. It was found that the elongational viscosities of VA and VB are very large and account for a fairly marked pressure drop at the die entrance, due to the orientation of the LCP domains taking place in the converging flow zone. For these materials, the ratio of the elongational viscosity to the Newtonian shear viscosity is up to two orders of magnitude higher than the value expected on the basis of the Trouton rule. For the flexible resins, the Trouton ratio is 3 and ca. 3–10, are common values for high molar mass linear polymers. The addition of 10% LCP into the flexible resins strongly increases their elongational viscosity and makes the blends resemble neat LCPs in their extensional flow behavior. In shear flow, on the contrary, the addition of LCP was shown to induce a marked reduction of the melt viscosity, even when, as for the Ny/VB blend, the LCP is more viscous than the matrix.     

流动聚焦装置中液滴的形成:喉部尺寸的影响

在本文中,研究了液滴在一个流动聚焦微流体设备中的形成过程,分析了喉部长度和宽度以及连续相的流速和分散相的粘度对液滴尺寸的影响。在固定的分散相流速(Qd)下,连续相流速(Q_c)对于液滴尺寸有重要的影响。当Q_c0.7mL/h,液滴尺寸在喉部长度到达一个临界值之前先趋于增加,之后随着喉部尺寸的继续增加逐渐下降;当Q_c0.7mL/h,液滴尺寸随着喉部长度的增加而降低。而越大的喉部宽度会产生越大尺寸的液滴。在Q_c继续增长的过程中通常会出现从挤压模式到滴模式的转变,最终液滴尺寸呈现出随着Q_c的增加指数降低的特征。归因于流速控制破碎机制,低粘度分散相下,液滴尺寸随粘度的增加而增加。     

The dynamics of a droplet in a capillary constriction underwave excitation

The frequency dependence of the amplitude of the wave excitation mobilizing a droplet trapped in a capillary constriction is determined. The effect of droplet viscosity is analyzed. The problem of free longitudinal oscillations of a viscous-fluid droplet in a capillary constriction is considered. The influence of the surface tension, the droplet volume, and the constriction shape on the natural frequency of droplet longitudinal oscillations is studied. A formula for calculating the droplet natural frequency in the conical constriction is obtained and analyzed.     

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.     

Growth and structure of nematic spherulites under shallow thermal quenches

The growth kinetics, shape, interfacial and internal orientation texture of a submicron nematic spherulite arising during the isotropic-to-nematic liquid crystal phase transformation under shallow thermal quenches is analyzed using theory, scaling, and numerical simulations based on the Landau – de Gennes model (The Physics of Liquid Crystals, 2nd edn. Clarendon, Oxford). The numerical computations from this model yield interfacial cusp formation that relaxes through the nucleation of two disclination lines of topological charge +1/2 and subsequently leads to intra-droplet texturing and a net topological charge within the spherulite of +1. The timing of these events suggests that cusp formation at the interface is intimately associated with the interfacial defect shedding mechanism (J. Chem. Phys. 124:244902, 2006) for shallow quenches. These results are different than predictions for deep quenches (J. Chem. Phys. 124:244902, 2006) where interfacial defect shedding leads to four defects and a net topological charge of +2. A liquid crystal dynamic shape equation is derived from the Landau – de Gennes model to account for the interface shape changes in terms of surface viscosity, the driving forces due to the uniaxial nematic-isotropic free energy difference, capillary forces, and friction forces, and used to semi-quantitatively show that during cusp formation and defect shedding, gradient elasticity, capillary forces and friction play significant roles in decelerating and accelerating the surface. An interfacial eigenvalue analysis shows that during the shallow quench, disclination lines nucleate within the interface itself and then texturize the nematic droplet as they migrate from within the interface to the bulk of the growing nematic droplet. After defect shedding, the spherulite is nearly circular and grows with constant velocity, in agreement with experiments. The results shed new light on intra-spherulite texturing mechanisms in phase ordering under weak driving forces.      

Particle velocimetry inside Newtonian and non-Newtonian droplets impacting a hydrophobic surface

A particle velocimetry technique is described which enables the measurement of the fluid velocity inside impacting drops. Using high speed photography of 2 μm fluorescent tracer particles suspended in the fluid, the velocity field was measured as a function of time and radial position. The potential of the technique is illustrated using velocimetry measurements of drops of pure water and aqueous solutions of 200 ppm poly-(ethylene oxide) (PEO). Dilute solutions of PEO have been known for some time to suppress the rebound of water from hydrophobic surfaces. The dissipation has traditionally been attributed to an increased extensional viscosity as the polymers stretch in the extensional flow of the droplet. Our results enable us to infer that the extensional viscosity of PEO drops, during both the spreading and retraction phase, is similar to that of pure water. The data suggest that the true source of dissipation lies at the droplet edge. We also show, by analysing the spreading of water drops, that the Roisman-Yarin theory for a droplet spreading on a surface is valid in the bulk of the droplet prior to the final stages of spreading.     

Scaling law behaviour of the retraction of a Newtonian droplet after a strain jump in a Newtonian matrix

We performed 3D visualisation of a Newtonian droplet embedded in an immiscible Newtonian liquid after a strain jump with a home-built counter-rotating shear device. The use of different linear polyurethanes for the droplet liquid allowed us to cover almost three decades of viscosity ratios (K) and to obtain a distinct interface with PDMS matrices with the same interfacial tension for all droplet/matrix pairs. During the droplet retraction, the major axis (L) showed universal time dependence. The apparent Hencky strain of L decayed linearly at large deformations and exponentially at small deformations. After large strain steps, the droplet axis along the vorticity direction (W) deflated and then inflated and the time dependence could be well described by a log normal function. The full width at half maximum was proportional to the droplet relaxation time for all K. The amplitude and the position of the minimum of W were proportional to the affine deformation. The results revealed interesting scaling law behaviour of the droplet retraction after large strain jumps.     

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.