It is shown Aris’ general solution method for the asymptotic axial dispersion in nested two-layer systems with a radial distribution of the axial velocity and with different diffusion and sorption properties in each layer can be generalized to nested and distributed N-zone systems and systems with continuously varying sorption strength by introducing a generalized flux expression J = −D.K.∇(C/K). In this expression, the local diffusion coefficient D and the local sorption constant K can be either piecewise constant (N-zone system) or continuous functions of the radial space coordinates (continuous system). After a mathematically sound derivation of the general solution, it is validated by comparing the resulting expressions for D_ax with either existing literature expressions or with the dispersion coefficient found by numerically solving the complete, time-dependent advection–diffusion mass balance for a number of selected examples. Applications can be found in continuous flow membrane separations, chromatography, and flows through extruded mesoporous ceramic beds.

证明了 Aris 对轴向速度径向分布且每层具有不同扩散和吸附特性的嵌套两层系统中渐近轴向色散的一般求解方法可以推广到嵌套和分布式 N 区系统和系统通过引入广义通量表达式 J = -DK∇(C/K)，具有连续变化的吸附强度。在这个表达式中，局部扩散系数 D 和局部吸附常数 K 可以是分段常数（N 区系统）或径向空间坐标的连续函数（连续系统）。在对一般解进行数学上合理的推导后，通过比较 D _ax的结果表达式来验证它使用现有文献表达式或通过对一些选定示例的完整的、与时间相关的对流-扩散质量平衡进行数值求解得到的色散系数。应用可以在连续流膜分离、色谱法和流过挤出介孔陶瓷床中找到。