Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Brownian dynamics simulation of the crystallization dynamics of charged colloidal particles

Crystal formation process of charged colloidal particles is investigated using Brownian dynamics (BD) simulations. The particles are assumed to interact with the pair-additive repulsive Yukawa potential. The time evolution of crystallization process and the crystal structure during the simulation are characterized by means of the radial distribution functions (RDF) and mean square displacement (MSD). The simulations show that when the interaction is featured with long-range, particles can spontaneously assemble into body-centered-cubic (BCC) arrays at relatively low particle number density. When the interaction is short-ranged, with increasing the number density particles become trapped into a stagnant disordered configuration before the crystallization could be actualized. The simulations further show that as long as the trapped configurations are bypassed, the face-centered-cubic (FCC) structures can be achieved and are actually more stable than BCC structures. (C) 2010 Elsevier Inc. All rights reserved.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

Thermal effects on Rayleigh-Marangoni-Benard instability in a system of superposed fluid and porous layers

Thermal effects of the heat transfer at free surface (represented by Biot number) on the Rayleigh-Marangoni-Benard instability in a system of liquid-porous layers with top free surface are investigated numerically. The results indicate that this thermal effect can evidently lead to the mode transition of convection, which is overlooked in previous works. (C) 2010 Elsevier Ltd. All rights reserved.

Coupling of thermocapillary convection and evaporation effect in a liquid layer when the evaporating interface is open to air

The coupling mechanism of thermocapillary convection and evaporation effect in evaporating liquids was studied experimentally. The experiments were carried out to study a thin evaporating liquid layer in a rectangular test cell when the upper surface was open to air. By altering the imposed horizontal temperature differences and heights of liquid layers, the average evaporating rate and interfacial temperature profiles were measured. The flow fields were also visualized by PIV method. For comparison, the experiments were repeated by use of another two non-evaporating liquids to study the influence of evaporation effect. The results reveal evidently the role that evaporation effect plays in the coupling with thermocapillary convection.

Three-Dimensional Linear Instability Analysis of Thermocapillary Return Flow on a Porous Plane

A three-dimensional linear instability analysis of thermocapillary convection in a fluid-porous double layer system, imposed by a horizontal temperature gradient, is performed. The basic motion of fluid is the surface-tension-driven return flow, and the movement of fluid in the porous layer is governed by Darcy's law. The slippery effect of velocity at the fluid-porous interface has been taken into account, and the influence of this velocity slippage on the instability characteristic of the system is emphasized. The new behavior of the thermocapillary convection instability has been found and discussed through the figures of the spectrum.

2010年环境力学夏季讲习班简介

<正>2010年环境力学夏季讲习班于8月21日～25日在南京河海大学举办.本次讲习班由国家自然科学基金委员会数理科学部主办,河海大学承办,中国力学学会环境力学专业委员会、美国工程力学学会、江苏省力学学会、海岸灾害及防护教育

大肠杆菌的mRNA翻译效率决定于Shine-Dalgarno的局部结构(英文)

在大肠杆菌中,多胺对mRNA翻译的影响程度决定于Shine-Dalgarno(SD)序列局部结构.与信使RNA其他区域松散配对的SD序列的局部结构受多胺的扰动较大,其局部解链的概率也较大,因而SD序列结合到核糖体RNA上并启动蛋白质翻译的概率也较大,相反,则启动mRNA翻译的概率就会较小.基于此,建立一个简单数学模型来描述这一现象,即蛋白质的表达水平是与由多胺刺激而引起mRNA的SD序列局部暴露的概率相关的.结果显示,模型与实验结果相符的很好.