Magnetic field assisted fluidization—Dimensional analysis addressing the physical basis

Abstract

This paper originates a discussion on dimensional analysis and scaling in magnetically assisted fluidized beds. Basic examination of process variables, merging mechanical and magnetic units, allows the conversion of mixed sets of variables into unified terms representing surface forces as effects of the fields contributing to the assisted fluidization behaviour. This transformation is termed “pressure transform” since the new variables are all characteristic pressures generated by three basic fields: gravity, magnetic and fluid flow. This approach addresses the physical basis in terms of dimensionless groups rather than formal algebraic manipulations pertinent to classical dimensional analysis. Basic dimensionless group termed granular magnetic Bond number is introduced as the ratio of characteristic pressures of gravity and of magnetic field. This analysis also provides a set of named dimensionless numbers characterizing magnetic field assisted fluidization such as Filippov number, Rosensweig number, Kwauk number and Siegell number, derived as ratios of characteristic pressures.