Turbulent coagulation of colloidal particles
Turbulent coagulation of colloidal particles
复制标题
胶体颗粒的湍流凝聚
DOI：
10.1017/s0022112098001037
复制
发表时间：
1998
影响因子：
3.7
通讯作者：
L. W. Lion
中科院分区：
文献类型：
--
作者：
Brett K. Brunk;D. Koch;L. W. Lion
湍流剪切引起的凝结速率的理论预测通常基于这样的假设，即湍流速度梯度是持久的（Saffman & Turner 1956），胶体颗粒之间的流体动力学和颗粒间相互作用（货车德瓦尔斯吸引力和静电双层排斥力）可以忽略。在目前的工作中，我们考虑颗粒间力的湍流凝结率的影响，我们探讨的凝结率的变化的拉格朗日速度梯度相关时间（即在一个参考系中的速度梯度的特征演化时间以下的流体运动）的响应。斯托克斯运动方程适用于半径远小于湍流长度尺度（即小颗粒雷诺数）的颗粒的相对运动。我们表示的流体运动在附近的一对粒子作为一个局部线性流动的时间变化的速度梯度。脉动的速度梯度被假定为各向同性和高斯统计取自出版的直接数值模拟湍流（DNS）。颗粒轨迹的数值计算被用来确定在存在和不存在颗粒相互作用的湍流凝聚率。数值模拟的结果正确地再现了小总应变和大总应变的渐近极限的计算凝固速率，其中总应变是用于描述特征应变率及其相关时间的乘积的术语。最近的DNS表明，波动应变和旋转速率的相关时间与Kolmogorov时间具有相同的数量级（Pope 1990），这表明假设小或大的总应变的理论可能很难近似湍流凝结速率。事实上，各向同性随机流与中间总应变的模拟表明，在湍流中的凝结率是显着不同的分析限制大，小的总应变。用柯尔莫哥洛夫时间和颗粒半径标度的非相互作用单分散颗粒的湍流凝结速率常数为8.62±0.02，而Saffman和Turner（1956）的常用模型预测，在持续湍流速度梯度的极限下，非旋转流的数值为10.35。另外的模拟，结合流体动力学相互作用和货车范德华吸引力被用来估计颗粒凝聚的实际速率。对于这些参数的典型值，颗粒相互作用使凝结速率常数降低至少50%。在一般情况下，碰撞效率（与粒子相互作用的凝结的比率，没有）随粒径和Kolmogorov剪切速率的增加而降低。
Theoretical predictions for the coagulation rate induced by turbulent shear have often been based on the hypothesis that the turbulent velocity gradient is persistent (Saffman & Turner 1956) and that hydrodynamic and interparticle interactions (van der Waals attraction and electrostatic double-layer repulsion) between colloidal particles can be neglected. In the present work we consider the effects of interparticle forces on the turbulent coagulation rate, and we explore the response of the coagulation rate to changes in the Lagrangian velocity gradient correlation time (i.e. the characteristic evolution time for the velocity gradient in a reference frame following the fluid motion). Stokes equations of motion apply to the relative motion of the particles whose radii are much smaller than the lengthscales of turbulence (i.e. small particle Reynolds numbers). We express the fluid motion in the vicinity of a pair of particles as a locally linear flow with a temporally varying velocity gradient. The fluctuating velocity gradient is assumed to be isotropic and Gaussian with statistics taken from published direct numerical simulations of turbulence (DNS). Numerical calculations of particle trajectories are used to determine the rate of turbulent coagulation in the presence and absence of particle interactions. Results from the numerical simulations correctly reproduce calculated coagulation rates for the asymptotic limits of small and large total strain where total strain is a term used to describe the product of the characteristic strain rate and its correlation time. Recent DNS indicate that the correlation times for the fluctuating strain and rotation rate are of the same order as the Kolmogorov time (Pope 1990), suggesting theories that assume either small or large total strain may poorly approximate the turbulent coagulation rate. Indeed, simulations for isotropic random flows with intermediate total strain indicate that the coagulation rate in turbulence is significantly different from the analytical limits for large and small total strain. The turbulent coagulation rate constant for non-interacting monodisperse particles scaled with the Kolmogorov time and the particle radius is 8.62±0.02, whereas the commonly used model of Saffman & Turner (1956) predicts a value of 10.35 for non-rotational flows in the limit of persistent turbulent velocity gradients. Additional simulations incorporating hydrodynamic interactions and van der Waals attraction were used to estimate the actual rate of particle coagulation. For typical values of these parameters, particle interactions reduced the coagulation rate constant by at least 50%. In general, the collision efficiency (the ratio of coagulation with particle interactions to that without) decreased with increasing particle size and Kolmogorov shear rate.