非牛顿流体中溶质分散的一种近似理论

AN APPROXIMATE THEORY ON DISPERSION OF SOLUTE MATTER IN NON-NEWTONIAN FLUIDS

本文对溶质在作圆管流动的非牛顿流体中非定常分散过程进行了理论研究。讨论了三种微观结构的非牛顿流体模型——微极流体、等温双极流体和偶应力流体。利用奇异摄动方法(多重尺度法),取三个时间尺度:t_0=t,t_1=εt,t_2=ε~2t(ε<<1),导出等效扩散系数、分散方程的近似形式及其一致有效的解析解。等效扩散系数D'=D+U^2a^2/48DK由分子扩散系数和表现扩散之和组成。在牛顿流体情况,本方法得到的等效扩散系数和Aris的结果完全相同。本方法适用于研究已知圆管流速分布的任意流体模型中溶质的分散问题。本文结果同样可以直接推广于其它非牛顿流体模型,例如三阶Rivlin-Erickson流体,Reiner-Philippoff流体等,只要其流速分布可以表达为 V={0,0,1-r^2-f(r)}的形式。

The nonsteady dispersion of solute matter in three types of micro-structure non-Newtonian flow models—micropolar, dipolar and couple-stresses fluids through a circular tube are theoretically studied. Using singular perturbation methods (methods of multiple scales) and introducing three time scales, t_0 = t, t_1=εt, t_2 =ε~2t, the author derived, the effective diffusion coefficient, an approximate form of diffusion equation and its uniform asymptotic analytical solution. Effective diffusion coefficient D' =D + U^2a^2K/48D consists of the molecular diffusion coefficient and the apparent diffusion coefficient. In case of Newtonian flow, the effective diffusion coefficient obtained by this method is perfectly in agreement with the result by Aris. This method is suitable for studying the problem on the dispersion of solute matter in arbitrary fluid models where velocity distributions through a circular tube are known. The present results can be directly applied to other non-Newtonian fluid models, so long as the velocity distribution can be expressed as: V={0, 0, 1-r^2-f(r)}.