Incipient motion of individual particles in horizontal particle–fluid systems: B. Theoretical analysis

This paper presents a theoretical analysis of the force and moment balance during incipient motion of a single particle. The analysis showed that large particles start their motion by rolling for spherical particles and by sliding for non-spherical particles. It also showed that fine spherical or near spherical powders start their motion by rolling. The theoretical analysis shown that the incipient motion velocity of individual particles for all fluid, system and particle properties might be presented as power relationships between the Reynolds and Archimedes numbers.

Graphical abstractThis paper presents a theoretical analysis of the force and moment balance during incipient motion of a single particle. The forces acting on a single particle resting on the bottom of a pipe/tunnel while fluid is flowing above were divided into two groups. The first group includes forces encouraging particle movement (drag and lift forces) and the second group includes forces resisting the movement (gravity, adhesion and friction forces). Fig. 1 presents the ratio between encouraging and resisting forces acting on large non-spherical particle in horizontal and vertical directions and the ratio between the encouraging and resisting moments. According to this figure large non-spherical particles start their motion by sliding, since the horizontal force ratio is equal to unit at the lowest fluid velocity.Figure optionsDownload full-size imageDownload as PowerPoint slideFig. 1: Force or moment ratios as a function of superficial velocity for large non-spherical particles.Fig. 2 presents the ratio between encouraging and resisting forces acting on fine particle in vertical directions and the ratio between the encouraging and resisting moments. According to this figure fine particles start their motion by rolling, since the moment ratio is equal to unit at the lowest fluid velocity.Figure optionsDownload full-size imageDownload as PowerPoint slideFig. 2: Force or moment ratios as a function of superficial velocity for fine particles in air.