Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems

S. Dungan, M. Shapiro, H. Brenner
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引用次数: 19

Abstract

Convective-diffusive transport of a chemically reactive solute is studied analytically for a general model of a multiphase system composed of ordered or disordered particles of arbitrary shapes and sizes. Use of spatially periodic boundary conditions permits analysis of particulate multiphase systems of effectively infinite size. Solute transport occurs in both the continuous and discontinuous bulk phases, as well as within and across the interfacial phase boundaries separating them. Additionally, the solute is allowed to undergo generally inhomogeneous first-order irreversible chemical reactions occurring in both the continuous and discontinuous volumetric phases, as well as within the interfacial surface phase. Our object is that of globally describing the solute transport and reaction processes at a macro- or Darcy-scale level, wherein the resulting, coarse-grained particulate system is viewed as a continuum possessing homogeneous material transport and reactive properties. At this level the asymptotic long-time solute macrotransport process is shown to be governed by three Darcy-scale phenomenological coefficients: the mean solute velocity vector ͞U*, dispersivity dyadic ͞D*, and apparent volumetric reactivity coefficient ͞K*. A variant of a Taylor-Aris method-of-moments scheme (Brenner & Adler 1982), modified to include solute disappearance via chemical reactions, is used to express these three macroscale phenomenological coefficients in terms of the given microscale phenomenological data and geometry. The general solution technique, illustrated here for a simple, ordered geometrical realization of a two-phase system, reveals the competitive influences of the respective volumetric/surface-excess transport and reaction processes, as well as the solute adsorptivity, upon the three macroscale transport coefficients.
颗粒多相体系中的对流-扩散-反应泰勒分散过程
对由任意形状和大小的有序或无序粒子组成的多相体系的一般模型,对化学反应溶质的对流扩散输运进行了分析研究。使用空间周期性边界条件允许分析颗粒多相系统的有效无限大小。溶质输运既发生在连续体相和不连续体相中,也发生在分离它们的界面相边界内和边界上。此外,允许溶质在连续和不连续的体积相以及界面表面相中发生一般不均匀的一阶不可逆化学反应。我们的目标是在宏观或达西尺度上全面描述溶质输运和反应过程,其中产生的粗粒度颗粒系统被视为具有均匀物质输运和反应性质的连续体。在这个水平上,渐近长时间溶质宏观输运过程由三个达西尺度的现象系数控制:平均溶质速度矢量、色散二元矢量和表观体积反应性系数。泰勒-阿里斯矩法方案(Brenner & Adler 1982)的一种变体,经过修改,包括通过化学反应的溶质消失,用于根据给定的微观尺度现象学数据和几何来表达这三个宏观尺度现象学系数。通解技术,这里说明了一个简单的,有序的两相系统的几何实现,揭示了各自的体积/表面过剩传输和反应过程,以及溶质吸附性,对三个宏观尺度传输系数的竞争影响。
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