Realistic rotating convection in a DNA suspension

In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation for realistic rigid-rigid boundary conditions. We focus our analysis in the DNA aqueous suspensions. Instability thresholds for oscillatory convection are calculated. Finally, we analyze the stabilizing effect for the onset of convection.     

分离比对混合流体Rayleigh-Bénard对流解的影响

混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一.基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解.然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富.由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4时的对流解不同.     

黑腔冷冻靶传热与自然对流的数值模拟研究

惯性约束聚变的设计要求在靶丸内形成均匀光滑的氘氚冰层, 靶丸周围的热环境对冰层的质量特别是低阶粗糙度有很大的影响. 本文对自主研发的黑腔冷冻靶实验装置中的热物理问题展开了数值模拟, 重点考察了黑腔冷冻靶的传热和流体力学特性. 通过参数分析得到了自然对流对靶丸温度均匀性产生影响的临界条件. 比较了黑腔不同布置朝向时的流场和温度分布, 结果显示黑腔水平布置时自然对流更加强烈, 造成的靶丸温度不均匀性也更大. 在此基础上, 讨论了消除自然对流影响的可能性, 结果发现仅当黑腔垂直布置时利用黑腔分区方法能够消除对流效应对靶丸温度不均匀性的影响而黑腔水平布置时不能消除. 研究结论对于实验中冷冻靶结构的设计、改进和实验的开展等具有指导意义.     

Microparticle collection for water purification based on laser-induced convection

Water purification is required for environmental protection. In this paper, we propose and demonstrate a rapid, effective and low-cost approach to collect numerous impurities(microparticles) in water on the basis of laser-induced thermal convection. We introduce a heat source by using a fiber tip, which is fabricated into a non-adiabatic-tapered shape. In order to improve the laser power absorption efficiency, we coat a gold film with a thickness of 300 nm on the fiber tip. Due to absorption, the laser power transferred from the fiber to the water results in thermal convection. The forces generated from the thermal convection drive the microparticles to move towards the fiber tip, thereby performing microparticle collection and achieving water purification. Laser-induced thermal convection provides a simple, high-efficiency and low-cost method of collecting microparticles, which is a suitable and convenient for local water purification.     

Vibration-induced granular segregation: a phenomenon driven by three mechanisms

The segregation of large spheres in a granular bed under vertical vibrations is studied. In our experiments, we systematically measure rise times as a function of density, diameter, and depth, for two different sinusoidal excitations. The measurements reveal that, at low frequencies, inertia and convection are the only mechanisms behind segregation. Inertia (convection) dominates when the relative density is greater (less) than one. At high frequencies, where convection is suppressed, fluidization of the granular bed causes either buoyancy or sinkage and segregation occurs.     

液封液桥内振荡热毛细对流的三维数值模拟

为了了解微重力下液封液桥内热毛细对流的基本特性,利用有限差分法进行了非稳态三维数值模拟,液桥高为(1-3)mm,直径为2mm和3 mm,液封外直径为(4-7)mm。模拟结果表明,当Marangoni数较小时,液封液桥内的热毛细对流为稳定的轴对称运动,当Marangoni数超过某一临界值后,流动将转化为三维振荡流动;为此,确定了发生振荡的临界Marangoni数,分析了各种条件下热毛细对流的振荡特性,计算了相应的振荡频率。     

Semi-Lagrangian multistep exponential integrators for index 2 differential–algebraic systems

Implicit-explicit (IMEX) multistep methods are very useful for the time discretization of convection diffusion PDE problems such as the Burgers equations and the incompressible Navier–Stokes equations. In the latter as well as in PDE models of plasma physics and of electromechanical systems, semi-discretization in space gives rise to differential–algebraic (DAE) system of equations often of index higher than 1. In this paper we propose a new class of exponential integrators for index 2 DAEs arising from the semi-discretization of PDEs with a dominating and typically nonlinear convection term. This class of problems includes the incompressible Navier–Stokes equations. The integration methods are based on the backward differentiation formulae (BDF) and they can be applied without modifications in the semi-Lagrangian integration of convection diffusion problems. The approach gives improved performance at low viscosity regimes.     

Convection in a rotating binary ferrofluid

In this work we report theoretical and numerical results on convection for a binary magnetic mixture under rotation. We obtain explicit expressions of convective thresholds in terms of the control parameters of the system for stationary convection. Finally, we analyze the stabilizing effect of rotation on instability thresholds for aqueous suspensions.     

Instabilities and spatio-temporal chaos of long-wave hexagon patterns in rotating Marangoni convection

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study the stability of the steady hexagonal patterns with respect to general side band instabilities. In the presence of rotation, steady and oscillatory instabilities are identified. One of them leads to stable, homogeneously oscillating hexagons. For sufficiently large rotation rates the stability balloon closes, rendering all steady hexagons unstable and leading to spatio-temporal chaos. (c) 2002 American Institute of Physics.     

Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods

In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.     

Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.     

Studying anomalous scaling and heat transport of turbulent thermal convection using a dynamical model

Turbulent thermal convection is a well-studied problem with various issues of interest. In this paper, we review our work which shows the nature and origin of anomalous scaling and heat transport in the limit of very strong thermal forcing, can be gained by studying a dynamical model, known as shell model, of homogeneous turbulent thermal convection in which buoyancy acts directly at most scales. Specifically, we have obtained two results. The first result is that when buoyancy acts directly at most scales such that the dynamics are governed by a cascade of entropy, the scaling behavior is described by Bolgiano and Obukhov scaling plus corrections that are due to the variations of the local entropy transfer rate. This result indicates the validity of the extension of refined similarity hypothesis to turbulent thermal convection. The second result is that when buoyancy is acting directly at most scales, a damping term acting on the largest scale, which has to be added for the system to achieve stationarity, plays a crucial role in heat transport, and that the heat transport depends on the strength of thermal forcing in the same manner as that predicted for the ultimate state of very strong thermal forcing. With our interpretation of the damping term representing the effect of the boundaries, this result indicates that in the ultimate state of turbulent thermal convection, when buoyancy is acting at most scales, boundaries would play a significant role in heat transport.     

On the Partial Regularity of a 3D Model of the Navier-Stokes Equations

We study the partial regularity of a 3D model of the incompressible Navier-Stokes equations which was recently introduced by the authors in [11]. This model is derived for axisymmetric flows with swirl using a set of new variables. It preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected in the model. If we add the convection term back to our model, we would recover the full Navier-Stokes equations. In [11], we presented numerical evidence which seems to support that the 3D model develops finite time singularities while the corresponding solution of the 3D Navier-Stokes equations remains smooth. This suggests that the convection term play an essential role in stabilizing the nonlinear vortex stretching term. In this paper, we prove that for any suitable weak solution of the 3D model in an open set in space-time, the one-dimensional Hausdorff measure of the associated singular set is zero. The partial regularity result of this paper is an analogue of the Caffarelli-Kohn-Nirenberg theory for the 3D Navier-Stokes equations.     

对流占优扩散问题的特征线法-差分法计算格式

本文用特征线目的和有限差分目的相结合的数值目的来求解对流问题和对流占优扩散问题,提出了两个计算格式,并给出了数值例子。     

Pinning and long-time-scale behavior in traveling-wave convection

We study nonlinear traveling-wave (TW) and stationary states of convection in experiments in ethanol-water mixtures. While the TW phase velocity as a function of Rayleigh number has been recently shown to be in agreement with the predictions of theory and numerical calculations, we find that this velocity is temporally modulated at frequencies corresponding to the travel time of a single convection roll and of a roll pair past a point stationary in the convection cell. This modulation could be due to the pinning of the convection pattern by experimental inhomogeneities. For large Rayleigh numbers where stationary overturning convection is expected, we sometimes observe extremely slow unidirectional TW states. For larger Rayleigh numbers, this slow TW state starts and stops intermittently on a characteristic time scale of several days. The possible origin of these phenomena and their potential utility are discussed.     

Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous Brinkman porous media

A model for double-diffusive convection in a heterogeneous porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source using the Brinkman model. In particular, we analyse the effect of slip boundary conditions on the stability of the model. Because of the many applications in micro-electro-mechanical systems (MEMS) and other microfluidic devices, a study of this problem is necessary. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient.     

Experimental Study on Liquid Free Surface in Buoyant-Thermocapillary Convection

We investigate the surface deformations of buoyant-thermocapillary convection in a rectangular cavity due to gravity and temperature gradient between the two sidewalls. The cavity is 52mm×42 mm in horizontal cross section, the thickness of liquid layer h is changed from 2.5 mm to 6.5 mm. Surface deformations of h = 3.5 mm and 6.0mm are discussed and compared. Temperature difference is increased gradually, and the flow in the liquid layer will change from stable convection to unstable convection. Two kinds of optical diagnostic system with image processor are developed for study of the kinetics of buoyant-thermocapillary convection, they give out the information of liquid free surface. The quantitative results are calculated by Fourier transform and correlation analysis, respectively. With the increasing temperature gradient, surface deformations calculated are more declining. It is interesting phenomenon that the inclining directions of the convections in thin and thick liquid layers are different. For a thin layer, the convection is mainly controlled by thermocapillary effect. However, for a thick layer, the convection is mainly controlled by buoyancy effect. The surface deformation theoretically analysed is consistent with our experimental results. The present experiment proves that surface deformation is related to temperature gradient and thickness of the liquid layer. In other words, surface deformation lies on capillary convection and buoyancy convection.     

Nonequilateral hexagonal patterns

Rotational symmetry of pattern formation problems is the origin of a variety of patterns (rolls, squares, hexagons etc.) in convection and reaction-diffusion systems. Traditionally, only the patterns based on equilateral lattices in the Fourier space were considered. In the present paper, we develop an analysis of the patterns with slightly different lengths of the basic wave vectors. The analysis applies as well to systems with a broken rotational symmetry (convection in an inclined layer, etc.). We find, in the framework of the amplitude equations, existence and stability conditions for periodic nonequilateral patterns based on two and three wave vectors. In the latter case, special attention is paid to the case when the three amplitudes are coupled by the resonant interaction.     

A PFG NMR experiment for translational diffusion measurements in low-viscosity solvents containing multiple resonances

Pulsed gradient simulated-echo (PGSE) NMR diffusion measurements provide a facile and accurate means for determining the self-diffusion coefficients for molecules over a wide range of sizes and conditions. The measurement of diffusion in solvents of low intrinsic viscosity is particularly challenging, due to the persistent presence of convection. Although convection can occur in most solvent systems at elevated temperatures, in lower viscosity solvents (e.g., short chain alkanes), convection may manifest itself even at ambient laboratory temperatures. In most circumstances, solvent suppression will also be required, and for solvents that have multiple resonances, effective suppression can likewise represent a substantial challenge. In this article, we report an NMR experiment that combines a double-stimulated echo PFG approach with a WET-based solvent suppression scheme that effectively and simultaneously address the issues of dynamic range and the deleterious effects of convection. The experiment described will be of general benefit to studies aimed at the characterization of diffusion of single molecules directly dissolved in low-viscosity solvents, and should also be of substantial utility in studies of supramolecular assemblies such as reverse-micelles dissolved in apolar solvents.