Receptivity of unbounded granular shear flow to periodic external forces

The formation of clusters in rapid flow of particulate media is a ubiquitous feature and the active control of these clusters by external forces is of primary interest in a variety of industrial and technological applications, such as pneumatic transport, sediment dynamics or combustion in circulating fluidized beds. In this present work, we will investigate the receptivity characteristics of unbounded granular shear flows to periodic external forces. Based on the linearized initial-value problem for the evolution of three-dimensional, infinitesimal disturbances, a general receptivity measure involving the solution operator is introduced. The maximum receptivity to periodic external forces is assessed with special emphasis on the effects of three-dimensionality, mean solid fraction and coefficient of restitution.