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.      

大尺寸液桥热毛细对流失稳性地面实验研究

开展大尺寸液桥浮力-热毛细对流地面实验, 探究流场转捩的临界条件及临界状态附近的流动情况. 通过粒子图像测速方法(PIV) 获得流体速度场, 研究液桥内部定常和转捩后的流场结构以及流体运动规律;并用红外热像仪测量液桥自由面温度分布, 研究流体流动的时空演化和温度振荡. 实验发现大尺寸半浮区液桥浮力-热毛细对流临界值与几何参数有关, 在大普朗特(Prandtl) 数情况下, 流场存在由稳定态向不稳定态再到混沌的转捩过程, 在临界马兰哥尼(Marangoni) 数附近, 流场内会出现行波现象, 流动模式也会随高径比的变化而发生变化;当继续增大马兰哥尼数, 流动会进入混沌状态.      

钟摆状态下湿颗粒坍塌流动行为及其动力相似性

基于建立的湿颗粒离散动力学模型,本文系统研究了钟摆状态下湿颗粒柱在重力驱动下的坍塌流动过程,主要考虑了颗粒粒径、液体表面张力系数和液体含量等参数对系统坍塌流动模式和动力学行为的影响。研究发现,在湿颗粒系统中,颗粒粒径和液体表面张力系数会改变颗粒间的毛细力大小,引起系统发生不同的坍塌流动模式,而液体含量仅定量影响颗粒坍塌后的堆积形态。在此基础上,进一步探讨了不同模式下系统坍塌流动行为与模型参数的相关性,发现无量纲Bond数是决定钟摆状态下湿颗粒物质坍塌流动动力学行为的本质因素。     

被均匀流缓慢调制的有限水深毛细重力波

非线性的存在会产生高次谐波,这些谐波又反作用于原来的低次谐波,使波幅发生缓慢变化,从而产生缓慢调制现象.这里从考虑均匀流作用下的毛细重力水波基本方程出发,在不可压缩、无旋、无黏条件假设下,使用多重尺度分析方法推导出了在均匀流影响下有限深水毛细重力波振幅所满足的非线性Schr¨odinger方程(NLSE).分析了NLSE解的调制不稳定性.给出了毛细重力波调制不稳定的条件和钟型孤立波产生的条件.分析了无量纲最大不稳定增长率随无量纲水深和表面张力的变化趋势.同时给出了无量纲不稳定增长率随无量纲微扰动波数变化的曲线,呈现出了先增大后减小的趋势.最后指出均匀顺流减小了无量纲不稳定增长率及最大增长率,逆流增大了它们.由表面张力作用产生的毛细波及重力与表面张力共同作用产生的毛细重力波,与流的相互作用可以改变海表粗糙度和海洋上层流场结构,进而影响海气界面动量、热量及水汽的交换.了解海表这些短波动力机制,对卫星遥感的精确测量、海气相互作用的研究及海气耦合模式的改进等有重要意义.     

被均匀流缓慢调制的有限水深毛细重力波

非线性的存在会产生高次谐波,这些谐波又反作用于原来的低次谐波,使波幅发生缓慢变化,从而产生缓慢调制现象．这里从考虑均匀流作用下的毛细重力水波基本方程出发,在不可压缩、无旋、无黏条件假设下,使用多重尺度分析方法推导出了在均匀流影响下有限深水毛细重力波振幅所满足的非线性Schr?dinger方程(NLSE)．分析了NLSE解的调制不稳定性．给出了毛细重力波调制不稳定的条件和钟型孤立波产生的条件．分析了无量纲最大不稳定增长率随无量纲水深和表面张力的变化趋势．同时给出了无量纲不稳定增长率随无量纲微扰动波数变化的曲线,呈现出了先增大后减小的趋势．最后指出均匀顺流减小了无量纲不稳定增长率及最大增长率,逆流增大了它们．由表面张力作用产生的毛细波及重力与表面张力共同作用产生的毛细重力波,与流的相互作用可以改变海表粗糙度和海洋上层流场结构,进而影响海气界面动量、热量及水汽的交换．了解海表这些短波动力机制,对卫星遥感的精确测量、海气相互作用的研究及海气耦合模式的改进等有重要意义．      

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.     

液桥内热质耦合对流不稳定性及旋转磁场法控制

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SixGe1-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.     

饱和蒸发和热毛细力作用下低雷诺数液膜在波纹竖壁上的流动

考虑表面蒸发压力和热毛细力作用情况下,对饱和蒸发状态下低雷诺数自由降落液膜在小波幅正弦型波纹壁面上的流动进行理论分析。对控制微分方程及边界条件进行量纲一化并引入流函数,对微分方程及边界条件进行摄动展开,得到了这种情况下液膜流动的简化分析模型,求出了近似解析解。讨论了壁面波纹、表面张力、蒸发压力、热毛细力对液膜流动的影响。研究表明:液膜的波动幅度随蒸发强度和热毛细力的增大而增大;液膜波动与壁面波纹的相位差随蒸发强度增大而增大,随热毛细力增大而减小。     

环形浅池内硅熔体中的热流体波

为了了解工业Czochralski炉内硅熔体表面轮型的基本特征,对环形浅池内硅熔体的热毛细-浮力对流进行了三维数值模拟,硅熔池内径为15 mm,外径为50 mm,深度为3 mm,熔池外壁被加热,内壁被冷却,底部固壁和顶部自由表面均绝热或者允许一个垂直方向的传热。模拟结果表明,当径向温差较小时,熔池内会产生稳定的单胞热毛细-浮力流动,随着温差的增大,流动将转变为三维振荡流动,在熔体自由表面会出现沿周向运动的轮型,小的垂直方向的热流密度(3W/cm2)对这种振荡流动没有大的影响。同时,讨论了流动和温度波动的特征,并确定了振荡流动的临界条件。     

Flow focusing and jet instability

流动聚焦是一种有效的微细射流产生方法,其原理可以描述为从毛细管流出的流体由另一种高速运动的流体驱动,经小孔聚焦后形成稳定的锥–射流结构,射流因不稳定性破碎成单分散的液滴.自从1998年流动聚焦被提出以来,陆续发展了单轴流动聚焦、电流动聚焦、复合流动聚焦和微流控流动聚焦等毛细流动技术.这些技术稳定、易操作、没有苛刻的环境条件的要求,能够制备单分散性较好的微纳米量级的液滴、颗粒和胶囊,在科学研究和实际应用中具有重要价值.流动聚焦涉及了多尺度、多界面和多场耦合的复杂流体力学问题,其中稳定的锥形是形成稳定射流的先决条件,过程参数是影响射流界面扰动发展的关键因素,而射流不稳定性分析是揭示射流破碎的最主要理论工具.该文回顾了近二十年来不同结构流动聚焦的研究进展,概述这些技术涉及的过程控制、流动模式、尺度律和不稳定性分析等关键力学问题,总结射流不稳定性的研究方法和已取得的成果,最后展望流动聚焦的研究方向和应用前景.     

Spinodal surface instability of soft elastic thin films

When the thicknesses of thin films reduce to microns or even nanometers, surface energy and surface interaction often play a significant role in their deformation behavior and surface morphology. The spinodal surface instability induced by the van der Waals force in a soft elastic thin film perfectly bonded to a rigid substrate is investigated theoretically using the bifurcation theory of elastic structures. The analytical solution is derived for the critical condition of spinodal surface morphology instability by accounting for the competition of the van der Waals interaction energy, elastic strain energy and surface energy. Detailed examinations on the effect of surface energy, thickness and elastic properties of the film show that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range from 0.749 to 1.0. The theoretical solution has a good agreement with relevant experiment results.     

Experimental Investigation of Thermocapillary Convection Induced by a Local Temperature Inhomogeneity near the Liquid Surface. 1. Solid Source of Heat

The structure and stability of a thermocapillary flow from a concentrated source of heat located near the free surface of the liquid filling a deep reservoir are experimentally studied. For a certain power of the heat source, oscillatory instability leading to formation of surface waves is observed. Possible mechanisms of the observed instability are discussed.     

Swell-induced surface instability of hydrogel layers with material properties varying in thickness direction

Upon swelling in a solvent, a thin hydrogel layer on a rigid substrate may become unstable, developing various surface patterns. Recent experimental studies have explored the possibilities to generate controllable surface patterns by chemically modifying the molecular structures of the hydrogel near the surface. In this paper, we present a theoretical stability analysis for swelling of hydrogel layers with material properties varying in the thickness direction. As a specialization of the general procedure, hydrogel bilayers with different combinations of the material properties are examined in details. For a soft-on-hard bilayer, the onset of surface instability is determined by the short-wave limit, similar to a homogeneous layer. In contrast, for a hard-on-soft bilayer, a long-wave mode with a finite wavelength emerges as the critical mode at the onset of surface instability, similar to wrinkling of an elastic thin film on a compliant substrate, and the critical swelling ratio is much lower than that for a homogeneous hydrogel layer. A smooth transition of the critical mode is predicted as the volume fraction of the top layer changes, linking surface instability of a homogeneous layer to thin film wrinkling as two limiting cases. The results from the present study suggest that both the critical condition and the instability mode depend sensitively on the variation of the material properties in the thickness direction of the hydrogel layer.     

超弹性薄膜与可压缩基底双层结构表面失稳分析

当上层超弹性硬质薄膜和下层可膨胀基底构成的双层结构受压时,薄膜的自由表面可通过形成褶皱降低系统能量.研究表明,上下两层的模量比不同时,上层弹性硬质薄膜将表现出不同的表面失稳模式.本文提出了一种新颖的方法可有效抑制双层软材料的表面失稳,即改变基底材料的泊松比,这种方法同时适用于不具有应变硬化的软材料.首先基于Neo-Hookean模型发展了小变形条件下双层结构表面失稳的理论模型,通过半解析的方法得到了表面失稳的临界应变;然后通过有限元计算与模拟,进一步验证了负泊松比基底可延缓表面失稳.结果表明:(1)当双层结构基底泊松比为正且趋于0.5(不可压缩)时,双层结构在较小的压缩应变下出现表面失稳;(2)当基底的泊松比为负且趋于-1时,可被压缩至46%而不出现表面失稳,即可膨胀基底能有效抑制薄膜的表面失稳.本文发展的方法及主要结果可为延展性电子器件的设计提供指导.     

Spontaneous instability of soft thin films on curved substrates due to van der Waals interaction

The linear bifurcation theory is used to investigate the stability of soft thin films bonded to curved substrates. It is found that such a film can spontaneously lose its stability due to van der Waals or electrostatic interaction when its thickness reduces to the order of microns or nanometers. We first present the generic method for analyzing the surface stability of a thin film interacting with the substrate and then discuss several important geometric configurations with either a positive or negative mean curvature. The critical conditions for the onset of spontaneous instability in these representative examples are established analytically. Besides the surface energy and Poisson's ratio of the thin film, the curvature of the substrate is demonstrated to have a significant influence on the wrinkling behavior of the film. The results suggest that one may fabricate nanopatterns or enhance the surface stability of soft thin films on curved solid surfaces by modulating the mechanical properties of the films and/or such geometrical properties as film thickness and substrate curvature. This study can also help to understand various phenomena associated with surface instability.     

Thin liquid film morphology driven by electro-static field

The development of stationary patterns on a thin polymer surface subject to an electric field is studied by means of the hexagonal-planform weakly nonlinear stability analysis and numerical simulations.The time evolution of the interface between the air and the polymer film on the unbounded spatial domain is described by a thin film equation,incorporating the electric driving force and the surface diffusion.The nonlinear interfacial growth includes the amplitude equations and superposition of one-dimensional structures at regular orientations.The pattern selection is driven by the subcritical instability mechanism in which the relative thickness of the polymer film plays a critical role.     

Seed bubbles stabilize flow and heat transfer in parallel microchannels

Seed bubbles are generated on microheaters located at the microchannel upstream and driven by a pulse voltage signal, to improve flow and heat transfer performance in microchannels. The present study investigates how seed bubbles stabilize flow and heat transfer in micro-boiling systems. For the forced convection flow, when heat flux at the wall surface is continuously increased, flow instability is self-sustained in microchannels with large oscillation amplitudes and long periods. Introduction of seed bubbles in time sequence improves flow and heat transfer performance significantly. Low frequency (∼10 Hz) seed bubbles not only decrease oscillation amplitudes of pressure drops, fluid inlet and outlet temperatures and heating surface temperatures, but also shorten oscillation cycle periods. High frequency (∼100 Hz or high) seed bubbles completely suppress the flow instability and the heat transfer system displays stable parameters of pressure drops, fluid inlet and outlet temperatures and heating surface temperatures. Flow visualizations show that a quasi-stable boundary interface from spheric bubble to elongated bubble is maintained in a very narrow distance range at any time. The seed bubble technique almost does not increase the pressure drop across microsystems, which is thoroughly different from those reported in the literature. The higher the seed bubble frequency, the more decreased heating surface temperatures are. A saturation seed bubble frequency of 1000–2000 Hz can be reached, at which heat transfer enhancement attains the maximum degree, inferring a complete thermal equilibrium of vapor and liquid phases in microchannels. Benefits of the seed bubble technique are the stabilization of flow and heat transfer, decreasing heating surface temperatures and improving temperature uniformity of the heating surface.     

Formation of radially expanding liquid sheet by impinging two round jets

A thin circular liquid sheet can be formed by impinging two identical round jets against each other. The liquid sheet expands to a certain critical radial distance and breaks. The unsteady process of the formation and breakup of the liquid sheet in the ambient gas is simulated numerically. Both liquid and gas are treated as incompressible Newtonian fluids. The flow considered is axisymmetric. The liquid-gas interface is modeled with a level set function. A finite difference scheme is used to solve the governing Navier-Stokes equations with physical boundary conditions. The numerical results show how a thin circular sheet can be formed and break at its circular edge in slow motion. The sheet continues to thin as it expands radially. Hence, the Weber number decreases radially. The Weber number is defined as ρu 2 h/σ, where ρ and σ are, respectively, the liquid density and the surface tension, and u and h are, respectively, the average velocity and the half sheet thickness at a local radial location in the liquid sheet. The numerical results show that the sheet indeed terminates at a radial location, where the Weber number reaches one as observed in experiments. The spatio-temporal linear theory predicts that the breakup is initiated by the sinuous mode at the critical Weber number We c =1, below which the absolute instability occurs. The other independent mode called the varicose mode grows more slowly than the sinuous mode according to the linear theory. However, our numerical results show that the varicose mode actually overtakes the sinuous mode during the nonlinear evolution, and is responsible for the final breakup. The linear theory predicts the nature of disturbance waves correctly only at the onset of the instability, but cannot predict the exact consequence of the instability.     

Computational study of the axial instability of rimming flow using Arnoldi method

Axial instability of rimming flow has been investigated by solving a linear generalized eigenvalue problem that governs the evolution of perturbations of two‐dimensional base flow. Using the Galerkin finite element method, full Navier–Stokes equations were solved to calculate base flow and this base flow was perturbed with three‐dimensional disturbances. The generalized eigenproblem formulated from these equations was solved by the implicitly restarted Arnoldi method using shift‐invert technique. This study presents instability curves to identify the critical wavelength of the neutral mode and the critical β, which measures the importance of gravity relative to viscosity. The axial instability of rimming flow is examined and three‐dimensional flow was reconstructed by using eigenvector and growth rate at a critical wave number. The critical β value in the axial instability analysis was observed to be comparable to the onset β value of the transition between the bump and the homogeneous film state in 2‐D base flow calculations. Copyright © 2006 John Wiley & Sons, Ltd.