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.     

Experimental techniques in natural convection

Experimental techniques in natural convection heat transfer employed in the author's laboratory are introduced. The techniques are mostly related to visualization of flow, temperature field, and heat flux distribution in fluids. Three topics are presented, the first being natural convection in a horizontal rectangular liquid layer driven by surface tension and buoyancy. The patterns of flow were visualized by suspending fine aluminum flakes in the liquid. At the same time, the distribution of the temperature gradient in the liquid was visualized by an optical method making use of the refraction of light. The second topic is the onset of oscillatory convection in the Czochralski growth melt. In this case a forced flow due to rotation of the crystal and the vessel is superimposed on the buoyancy convection, resulting in an oscillatory flow under certain circumstances. The flow pattern and the temperature distribution in the liquid were visualized simultaneously by suspending in the liquid a microencapsulated temperature-sensitive liquid crystal. Periodical oscillation of the flow and the temperature was clearly recognized. The third topic is the rollover of double liquid layers that were stratified stably due to a density difference. A small-scale experiment was carried out to clarify the basic mechanism of rollover. The tracer method was used to visualize boundary layer flow along the vertical side wall and the shadowgraph technique to visualize the density distribution in the liquid layers. The article emphasizes the importance of visual observation in the investigation of natural convection phenomena.     

半浮区液桥热毛细振荡流

采用非定常、三维直接数值模拟方法研究大Pr数半浮区液桥热毛细对流从定常流向振荡流的过渡过程．文中详细描述了热毛细振荡流的起振和振荡特征,给出了液桥横截面上振荡流的流场和温度分布．在地面引力场条件下计算的结果与地面实验的结果进行比较,得出液桥水平截面上的流场和温度分布图样以一定的速度旋转,自由表面固定点处流体的环向流速正、负交替变化的一致结论．     

Flow and temperature field measurements of thermal convection in a small vertical gap using liquid crystals

Thermal convection in a small vertical gap is studied experimentally applying digital particle image velocimetry/thermometry. This optical method enables the simultaneous measurement of two-dimensional flow and temperature fields in a liquid. The principle is based on seeding the liquid flow medium with thermochromic liquid crystal particles. The temperature is measured by the crystal particles which change their reflected colour as function of temperature. The flow velocity is measured by using the same particles as flow tracers. The investigation shall contribute to the understanding of the fluid mechanical behaviour of biological liquids within micro reactor systems. However, the problem is also of fundamental interest as far as heat and mass transfer is concerned. Measured temperature and flow velocity fields are presented and discussed. Presented in part at the 4th Chemnitz/Hamburger Colloquium (CHC) on Microflows, Hamburg, Germany, November 2004.     

Equalizing calculus in Trefftz method for solving two-dimensional temperature field of FC-72 flowing along the minichannel

The paper focuses on the numerical solution to two-dimensional temperature field of boiling liquid flowing along a vertical, asymmetrically heated minichannel with a rectangular cross-section. One of the walls of a minichannel is DC supplied single-sided enhanced foil with mini-recesses distributed unevenly in the selected area. The parallel walls are made of glass panes for thermal insulation and they are intended for observation of the two-phase flow and the void fraction. The thin layer of thermosensitive liquid crystal paint on the outer side of the foil enabled to record two-dimensional temperature distribution of outer foil surface. The paper described computations based on Trefftz method for finding two-dimensional temperature field of boiling liquid flowing along the minichannel. The presented research is limited only to the liquid phase of the two-phase mixture observed in the minichannel. The velocity of liquid flowing through the minichannel is represented by a piecewise linear approximating function. To solve energy equation for liquid phase, Trefftz functions specially generated for this purpose were employed. Temperature field in the fluid was approximated by a linear combination of Trefftz functions. Equalizing calculus was applied to the Trefftz method to smooth temperature measurements and reduce measurement errors. Temperature at the interface between working fluid and foil amounts to the saturation temperature. Temperature distribution in the foil and the glass pane was also computed using proper Trefftz functions.     

固体火箭燃气射流驱动液柱过程的CFD分析

固体火箭燃气射流驱动液柱过程会产生一个复杂的非稳态多相流场,为了研究液柱对固体火箭发动机工作过程中射流流场的降温效果,并揭示燃气冲击液柱的流动演化和气水之间的相互作用,利用FLUENT软件中耦合了液态水汽化方程的VOF多相流计算模型对燃气与液柱之间的耦合流动及相变过程进行了数值模拟,并与无液柱情况下射流流场的计算结果进行了对比分析。计算结果表明,当有液柱平衡体时射流流场中的压力、温度、速度波动幅度均减小,减弱了射流流场中的湍流脉动强度;液柱与燃气之间的汽化以及液柱的阻碍作用减小了射流流场的轴向发展位移,尾管后的完全发展射流流场核心区域内的压力峰值降低了0.9 MPa,温度峰值降低了503 K,速度峰值降低了291 m/s,验证了实验中液柱对燃气射流流场的降温效果。     

Convection in a Horizontal Layer in a Rotating Heat Field

An asymptotic laminar-convection pattern in a plane horizontal liquid layer with a radially nonuniform temperature gradient on its boundaries is investigated. The problem arises in applications connected with modified Czochralski crystal growth technology using the heat field rotation method. An analytical model of the flow is compared with the results of experiments, specially carried out using model fluids and a technological melt. The conditions of adequacy of the model are analyzed and the restrictions on the parameter values and fluid thermophysical properties that ensure the validity of the model are found. The range of variation of the heat field rotation velocity for which the mixing of the melt in the crucible is maximum is determined.     

Digital particle image thermometry: The method and implementation

A computerized flow visualization technique capable of automatically quantifying the temperature field in a two-dimensional cross section of a flow field is described. The temperature sensors used are fast-response temperature-sensitive micro-encapsulated liquid crystal particles. Illuminating the flow by a thin sheet of white light, the reflected colors from the liquid-crystal particles were captured through a 3-chip video color camera and stored onto a videotape for subsequent data processing. The temperature field was obtained through an automatic color-temperature calibration scheme in HSI rather than RGB space, thus allowing for data processing of approximately one-third the time of RGB processing. The technique is finally applied to the study of a heated vortex-ring and some preliminary results are discussed.     

向列相溶致液晶旋转黏度研究

溶致液晶具有良好的生物相容性、无毒性、生物降解性以及光学、电磁学各向异性等, 在细胞相互作用、神经刺激传递、脂肪吸收、药物智能输运等生命活动研究、医药工程和液晶显示等领域有广泛应用. 本文采用旋转磁场法测得溶致液晶日落黄在不同温度和溶液浓度下向列相时旋转黏度, 并结合溶致液晶分子自组装过程, 理论分析了溶致液晶向列相旋转黏度随温度和溶液浓度的变化规律. 研究结果表明: 溶致液晶旋转黏度与液晶分子自组装柱状体平均长度的平方呈正比增大关系, 随溶液浓度的增大而增大, 随温度的升高表现出指数减小的规律. 构建了与向列相溶致液晶温度和浓度相关的旋转黏度经验表达式, 经验表达式计算结果与实验值吻合较好, 最大误差仅为18.56${\%}$. 提出采用旋转流变仪间接获得溶致液晶剪切能的新方法, 溶致液晶剪切能随溶液浓度的增大而增大, 但在实验温度范围内, 溶致液晶剪切能几乎不随温度而改变. 利用旋转流变仪间接获得的溶致液晶剪切能与报道的利用X-Ray检测所得的结果之间最大误差仅为3${\%}$. 成功地利用了液晶分子自组装能力随温度的变化规律来研究柱状体长径比对旋转黏度的影响规律, 创新地提出了"一步法"测量研究, 大大减少相关实验研究的成本和复杂性.      

Regime diagram and three-dimensional effects of convective interactions in the hydrodynamic Czochralski model

The generalized diagram of the critical Grashof numbers as functions of the Prandtl number is presented. The diagram shows the zones of occurrence of flow field and temperature fluctuations in the axisymmetric and three-dimensional formulations of the crystal growth model using the pulling from a melt. The structure of thermals at high Prandtl numbers and the distinctive features of the three-dimensional convection structure in the zones of stabilization and hazardous mode changeover at different Prandtl numbers are discussed. The effect of crystal rotation on the flow and temperature field patterns is estimated.     

INSTABILITY OF COUPLED THERMO-SOLUTE CAPILLARY CONVECTION IN LIQUID BRIDGE AND CONTROL BY ROTATING MAGNETIC FIELD

浮区法因具有无坩埚接触污染的生长优点而成为生长高完整性和高均匀性单晶材料的重要技术.但熔体中存在的毛细对流会给浮区法晶体生长带来极大挑战,这是由于对流的不稳定会导致晶体微观瑕疵的产生和宏观条纹等缺陷的形成.为了提高浮区法生长单晶材料的品质,研究浮区法晶体生长中毛细对流特性及如何控制其不稳定性显得尤为重要.本文采用数值模拟的方法对半浮区液桥内Si_xGe_1-x体系中存在的热质毛细对流展开研究并施加旋转磁场对其进行控制.结果表明：纯溶质毛细对流表现为二维轴对称模式,温度场主要由热扩散作用决定,而浓度场则由对流和溶质扩散共同支配;纯热毛细对流呈现三维稳态非轴对称流动,浓度分布与熔体内热毛细对流的流向密切相关,等温线在对流较大的区域发生弯曲;耦合溶质与热毛细对流则为三维周期性旋转振荡流.施加旋转磁场后,熔体周向速度沿径向向外增大,熔体内浓度场和流场均呈现二维轴对称分布.     

Experimental and numerical investigations of fluid flow and heat transfer in a cryogenic tank at loss of vacuum

The transient process of thermal stratification in liquid nitrogen (LN₂) induced by lose of vacuum in a multi-layer insulated cryogenic tank is investigated both experimentally and numerically. In the experiments, distribution and evolution of the liquid temperature is obtained using thermocouples. Then, two-dimensional numerical computations are performed, using the two-fluid model together with nucleate boiling model as the closure correlations. Comparison of the numerical results against the experimental data illustrates that the process of thermal stratification forming and weakening, as well as the liquid temperature field are satisfactorily simulated. The computed results of liquid flow field contribute to the understanding of this transient process. It is also demonstrated that the two-phase flow in the tank plays an important role on thermal stratification.     

On the stability of shear flows in nematics

A theoretical study of the effect of an applied magnetic field on the stability of the flow of nematic slabs subjected to an arbitrary shear is presented. Homeotropic boundary conditions with strong anchoring and a constant magnetic field applied perpendicular to the plates are considered. We discuss the general conditions on the control parameters under which the flow is stable, for a low molecular weight liquid crystal and for a polymer liquid crystal, and obtain estimations of the critical values.     

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.     

用胶囊式液晶粒子同时测量流场的温度和速度

胆甾相液晶在不同温度下显示不同的颜色，这一特性已被广泛地应用于固体表面或流体的温度测量．胶囊式胆甾相液晶具有粒子形态和温度－颜色反应特性，可以用来同时测量流体的速度和温度场．作者改进了粒子测速的测试精度；还标定了色度－温度关系，获得了自然对流流场中的速度和温度场     

On the influence of buoyancy on the surface tension driven flow around a bubble on a heated wall

The surface tension driven flow in the liquid vicinity of gas bubbles on a heated solid wall has been investigated both, in a reduced gravity environment aboard a sounding rocket, and in an earth-bound experiment. Both experiments deal with temperature gradients within the liquid surrounding of a bubble which cause variations of the surface tension. These, in turn, lead to a liquid flow around the bubble periphery termed thermocapillary or thermal Marangoni-convection. On Earth, this phenomenon is widely masked by buoyancy. We therefore carried out an experiment under reduced gravitational acceleration. In order to simultaneously observe and record the flow field and the temperature field liquid crystal tracers have been applied. These particles offer the feature of selectively reflecting certain wavelengths of incident white light depending on the crystals temperature. Although the bubble injection system did not perform nominally during the flight experiment, some interesting flow characteristics could be observed. Comparison of results obtained in microgravity to data measured on Earth reveal that due to the interaction of thermocapillarity and buoyancy a very compact vortex flow results on ground, while in microgravity the influence on the surface tension driven flow penetrates much deeper into the bulk. This result is of special interest regarding the production of materials in space. Dedicated to Professor Dr. Julius Siekmann on the occasion of his 70th birthday The work described herein was supported by the German space agency DARA (Deutsche Agentur für Raumfahrtangelegenheiten GmbH) through DARA Grant 50 WM 9434. The authors thank the European Space Agency (ESA) for the opportunity to conduct the TEXUS 33 sounding rocket experiment. The flight hardware has been partly built by Daimler-Benz-Aerospace which is gratefully acknowledged. Also, the authors are indebted to Mr. H.-H. Wolf for his careful evaluation of the particle images     

双自由面溶质?热毛细液层的不稳定性

溶质?热毛细对流是流体界面的浓度和温度分布不均导致的表面张力梯度驱动的流动, 它主要存在于空间微重力环境、小尺度流动等表面张力占主导的情况中, 例如晶体生长、微流控、合金浇筑凝固、有机薄液膜生长等. 对其流动进行稳定性分析具有重要意义. 本文采用线性稳定性理论研究了双自由面溶质?热毛细液层对流的不稳定性, 得到了两种负毛细力比(η)下的临界Marangoni数与Prandtl数(Pr)的函数关系, 并分析了临界模态的流场和能量机制. 研究发现: 溶质?热毛细对流和纯热毛细对流的临界模态有较大的差别, 前者是同向流向波、逆向流向波、展向稳态模态和逆向斜波, 后者是逆向斜波和逆向流向波. 在Pr较大时, Pr增加会降低流动稳定性; 在其他参数下, Pr增加会增强流动稳定性. 在中低Pr, 溶质毛细力使流动更加不稳定; 在大Pr时, 溶质毛细力的出现可能使流动更加稳定; 在其他参数下, 溶质毛细力会减弱流动稳定性. 流动稳定性不随η单调变化. 在多数情况下, 扰动浓度场与扰动温度场都是相似的. 能量分析表明: 扰动动能的主要能量来源是表面张力做功, 但其中溶质毛细力和热毛细力做功的正负性与参数有关.      

Couette flow of a nematic liquid crystal in the presence of a magnetic field

Summary We derive the equations governing helical flow of a nematic liquid crystal in the presence of a magnetic field. These equations are used to investigate Couette flow, and a study is made of the large number of possible solutions.     

Viscous effects in liquid encapsulated liquid bridges

An analytical derivation of the surface deflections and the streamfunctions for the flow inside a liquid encapsulated liquid bridge has been derived using an asymptotic expansion about a small capillary number. The model assumes an initially flat and cylindrical interface under the assumption that the densities of both fluids are equal. To simplify the analysis, the top and bottom walls are assumed to be stress-free and the Reynolds number is assumed to be negligible. Flow is generated either by a moving outer wall (shear-driven flow) or by applying a temperature difference across the top and bottom walls (Marangoni-driven flow). The resulting equations show that for the shear-driven flow, as the viscosity ratio increases, the surface deflections increase monotonically. For the Marangoni-driven flow there exist values of the viscosity ratio where the surface deflections reach a minimum and then switch signs. This investigation shows that it may be possible in more realistic systems to use an outer encapsulating liquid of the proper viscosity ratio to stabilize the liquid–liquid interface during float zone crystal growth.     

Bingham流体双自由面热毛细液层的稳定性分析

热毛细对流是流体界面温度分布不均导致的表面张力梯度驱动的流动.它主要存在于空间等微重力环境或小尺度流动等表面张力占主导的情况中.在很多工业领域,如晶体生长、聚合物加工、喷墨打印、微流控,产品质量都与热毛细对流密切相关.空间3D打印是太空制造的重要技术,可以支持空间站的在轨长期有人照料的运行和维护,实现按需制造.本文以聚合物流体的空间3D打印为应用背景,采用线性稳定性理论研究了Bingham流体双自由面热毛细液层的稳定性,得到了在不同Bingham数(B)下的临界Marangoni数(Mac)与Prandtl数(Pr)的函数关系,分析了临界模态的流场和能量机制.研究发现:该流动的临界模态包括流向波和斜波模态,与B, Bi和两界面垂直方向上的温差(Q)相关. B和Bi的增加会增强热毛细对流的稳定性.当Q=0时,扰动温度分布分成对称和反对称两种情况.当Q> 0时, Pr的增加会减弱流动稳定性.在小Pr情况下,扰动温度分布在整个流场,在大Pr情况下,扰动温度在栓塞区为零.能量分析表明:扰动动能的主要能量来源是表面张力做功,但小Pr数下基本流也有一定贡献.