Generalized master curve for threshold superficial velocities in particle–fluid systems

This paper presents our previous analyses of pickup gas velocity from a layer of particles in pipes and big wind tunnels, pickup liquid velocity, boundary saltation and minimum pressure velocities, and a new analysis of the minimum fluidization velocity and the terminal velocity. All these threshold velocities are defined as simple relations between the Reynolds and Archimedes numbers as modified by various effects. The Reynolds number is modified by taking into account the pipe diameter while the Archimedes number is modified by taking into account various properties that affect each threshold mechanism. Since all threshold velocities could be defined successfully by the same non-dimensional groups it was possible, at the first time, to present a Generalized Master Curve, which provides an overview of all the threshold velocities. This overview enabled, for example, to find quantitatively the relationships between all the threshold velocities to the terminal velocity and to compare the pickup and saltation velocities.

Graphical abstractPreviously we analyzed pickup gas velocity from a layer of particles in pipes and big wind tunnels, pickup liquid velocity and boundary saltation velocity. All these threshold velocities together with new ones (minimum fluidization velocity and the terminal velocity) are defined as simple and reasonably accurate relations between the Reynolds and Archimedes numbers modified by various effects. Consequently, a Generalized Master Curve can be presented, that provides, at the first time, an overview of all the threshold velocities. This overview enabled us to find the relationships between all the threshold velocities.Figure optionsDownload full-size imageDownload as PowerPoint slide