Transport Processes in Two-Phase Systems; An Effective Continuum Theory

本研究计划的目标是：1）将PI最近发展的有效连续介质方法应用于两相介质的大量传质和传热过程，从而获得有关有效参数的理论表达式; 2）将目前仅是临时性的有效连续介质方法置于更坚实的理论基础上;（3）发展确定流动系统中的成对概率函数的理论，从而计算这些有效参数对外加流的强度和结构的依赖关系;和4）推导了流动悬浮液中剪切诱导颗粒扩散系数和流动液体中传质速率增强的理论表达式，添加惰性固体颗粒。这两种效应在各种物理和生物操作中起着重要作用，目前只能定性地模拟。有效参数目前通过变分技术（通常不准确）、精确计算（非常耗时或非常专业）或包含通常不可靠的可调整因子的近似特设模型来计算。相比之下，PI开发的有效连续介质方法相对简单和直接，具有很大的通用性和通用性，并已成功地对实验结果进行了测试。这种方法还扩展了连续表示的适用性，系统的微观和宏观长度尺度是可比的幅度。

The objectives of this research program are: 1) To apply the effective continuum method recently developed by the PI to a host of mass and heat transport processes involving two-phase media, and, thereby, obtain theoretical expressions for the relevant effective parameters; 2) To place this method, which is presently only ad hoc, on a firmer theoretical foundation; 3) To develop a theory for determining the pair probability function in flowing systems and thereby compute the dependence of these effective parameters on the strength and structure of the impressed flow; and 4) To derive theoretical expressions for the shear induced particle diffusion coefficient in flowing suspensions and for the enhancement of the mass transfer rate in flowing liquids by the addition of inert solid particles. These two effects, which play an important role in a wide variety of physical and biological operations, can at present be modeled only qualitatively. Effective parameters are currently computed either via variational techniques (which are generally inaccurate), exact calculations (which are either very time consuming or very specialized), or approximate ad hoc models containing adjustable factors which are often unreliable. In contrast, the effective continuum method developed by the PI is relatively simple and straightforward, is of great generality and versatility, and, has been successfully tested against experimental results. This method also extends the applicability of the continuum representation to systems where the micro and macro length scales are of comparable magnitude.