Tracer dispersion in axially periodic (non-turbulent)) flows proves determinant in defining the performance of a wide class of chemical processes, ranging from microreactor engineering to chromatographic analyses. A comprehensive theory, known as Brenner’s macrotransport approach, has been developed for incompressible flows, where fluid density, diffusion coefficients, average velocity, and large-scale pressure gradient are constant throughout the entire channel length. In Brenner’s approach, the effective dispersion coefficient of a generic solute entrained in the flow is obtained by solving of an elliptic (i.e., steady state) advection-diffusion equation defined on the minimal periodic cell of the flow, making it feasible to obtain accurate numerical predictions even in complex 3d periodic structures. In contrast, a general theory of axial dispersion in the compressible case is yet to be developed, the main shortcoming being the axial variation of fluid properties along the channel axis. Here, we show how Brenner’s theory can be extended and exploited to predict axial dispersion in axially periodic compressible flows exhibiting large variations of density and average gas velocity across the channel length channel. The extension of Brenner’s approach leverages on a multiscale formulation of the fluid-dynamic problem, which allows to derive the axially varying dispersion coefficient based on the solution of a standard dimensionless formulation of Brenner’s equation in the generic periodic cell of the flow. The compressible inertial flow of an ideal gas through a sinusoidal capillary and a capillary embedding a baffle under isothermal conditions are considered as a case study.
