PHASE-SPACE DIFFUSION EQUATIONS FOR SINGLE BROWNIAN PARTICLE MOTION NEAR SURFACES

In numerous physical processes involving the motion of micron and submicron sized particles near surfaces, such as the filtration of hydrosols and aerosols, the particle motion is the net result of the combined effects of fluid convection, external forces, particle inertia, Brownian particle motion, and particle-surface fluid dynamic interactions. The most general method of describing particle motion under the combined action of these effects is through the so-called Fokker-Planck equation. In the absence of particle-surface fluid dynamic interactions, the Fokker-Planck equation is well-known, and it has been applied in a general way to problems involving the adsorption or deposition of Brownian particles onto surfaces through a solution technique known as the Brownian dynamics simulation method.

In this study, the Fokker-Planck equation for Brownian particle motion near surfaces is generalized to include particle-surface fluid dynamic interactions. The Fokker-Planck equation is shown to follow from the Liouville equation for the Brownian particle and n-fluid molecules present in the system, thus, establishing a firm theoretical foundation for the Fokker-Planck equation and the various other phase-space diffusion equations that follow from it.

Based on diagonalization of the Fokker-Planck equation, its short-time behavior is also derived here which enables a generalization of the Brownian dynamics method for the study of particle motion near surfaces including fluid dynamic interactions. Additionally, a perturbation solution of the Fokker-Planck equation under the conditions of small, but finite particle Stokes number is also derived. These solutions are shown to agree with previously given representations of the Smoluchowski or convective-diffusion equation for Brownian particle motion near surfaces, as well as with inertial corrections to the Smoluchowski equation available in the literature. This latter equation is also generalized here to include particle-surface fluid dynamic interactions.     

Low-temperature methanol synthesis in a circulating slurry bubble reactor

A circulating slurry bubble reactor was developed to synthesise methanol via methyl formate from the gas mixture of carbon monoxide and hydrogen at low temperature. The strategy for designing and scaling up the bubble reactor involved a preliminary understanding of fluid dynamics in a cold model, continuous operations under industrial conditions and a parallel experiment in an autoclave. Per-pass syngas conversion was investigated during 100-h operations. The axial profile of solid catalyst concentration was measured just before the shutdown and the composition of liquid product was analysed after the shutdown. These results show that the circulating slurry bubble column will become a potential reactor for the commercial process of low-temperature methanol synthesis after the catalyst system has been improved.     

鼓泡床内气泡-液体两相湍流代数应力模型的数值模拟

现有的气泡 -液体两相流动的数值模拟中 ,或者不考虑湍流 ,或者仅仅考虑液体湍流 ,但是直接模拟和PIV测量结果都表明气泡由于尾迹的作用有强烈的湍流脉动 .本文首次推导和封闭了同时模拟气泡湍流脉动和液体湍流脉动的二阶矩输运方程两相湍流模型 ,并在此基础上建立了代数应力气泡 -液体两相湍流模型 .用代数应力模型模拟了二维矩形断面鼓泡床内气泡 -液体两相流动 .预报结果给出了气泡和液体两相速度场、两相Reynolds应力及湍动能分布和气泡体积分数分布 .模拟结果与PIV测量结果符合很好 ,表明了模型的合理性 .研究结果表明 ,原先静止的液体在气泡因浮力而产生的上升运动的作用下产生回流流动 ,而气泡则只有上升运动 .气泡速度始终大于液体速度 .在床内气泡湍流脉动确实始终很强烈 .液体则由于气泡的作用以及自身速度梯度产生的双重作用而发生湍流脉动 .气泡的脉动显著地大于液体的脉动 .两相湍流脉动都是各向异性的 ,而且气泡湍流脉动的各向异性比液体的更强烈     

Settling velocities of particles in bubbly gas-liquid mixtures

The axial dispersion-sedimentation model is commonly used to describe the axial concentrations of solids in three phase bubble columns at low liquid velocities. When the two parameters of this model, the particle settling velocity and the solids axial dispersion coefficient, are uncoupled by the use of various assumptions, physically unrealistic values of these parameters often result. Direct experimental measurements of solids settling rates in bubbly gas-liquid mixtures were carried out. The measured mean settling velocities decreased slightly with gas flow rate and were equal to or slightly less than the single particle free settling velocity in the liquid alone. Solids axial dispersion coefficients were also obtained from the solids settling rate distribution data, and gave values considerably less than the experimental liquid axial dispersion coefficient.     

用CCD摄像法测量下喷环流反应器内的气泡行为

本文开发了一种集高速视频分析系统和计算机数字图像处理技术于一体的具有普适性的动态高速ＣＣＤ摄像系统，并利用该系统测定了两相三维下喷环流反应气内的环境气泡行为，考察了不同喷咀和操作条件对气泡行为及平均传质比表面积的影响。     

考虑空气阻力的抛体最大射程和最佳抛射角研究

为了研究抛体在什么抛射角抛出时具有最大射程,利用拉格朗日乘子法,推导出存在空气阻力并且起点和终点不在同一高度时,在某一斜面上抛出的抛体的最大射程和最佳抛射角.通过计算机编程,以计算投掷手榴弹时的最大射程和最佳抛射角为例进行验证,并对物理教学中抛体运动的动力学过程进行了进一步的分析和讨论,有利于提高教学效果.     

分数跳-扩散下外汇期权定价

用保险精算方法,在股票价格服从分数跳-扩散过程,且无风险利率、波动率和期望收益率为时间的非随机函数,给出了外汇期权定价公式.     

气液两相流中气泡形态及运动特征参数提取

对气泡发生装置中竖直向上气泡的形态及运动特征提取方法进行了研究。采集原始气泡图像,进行图像灰度化、差影和中值滤波等图像预处理,针对气泡图像的特点,提出动态阈值压缩大津法进行阈值分割,并结合扫描线种子填充算法与图像形态学运算进行孔洞填充,同时基于边缘面积属性对气泡特征区域进行自动识别。实验结果表明,该方法简单有效,鲁棒性强,可以很好地将目标气泡从背景中分离出来,有效提取气泡周长、面积、圆形度和质心坐标等形态特征参数,并实现气泡运动速度的测量。     

液体温度对空泡生长和溃灭过程的影响

采用光偏转测试系统研究了不同温度纯净水中激光空泡脉动过程,通过实验获得了激光空泡在靶表面膨胀和收缩全过程,确定了空泡的最大、最小泡半径、脉动周期和泡壁运动速度。实验采用0℃到70℃的纯净水,测量了空泡的泡半径和脉动周期等特征参量变化情况。实验结果表明,液体温度是影响空泡脉动的一个非常重要的因素,随着液体温度的增加空泡的最大泡半径和溃灭周期均呈增加趋势。给出了相应的理论解释。