Two sample applications of a classical isoperimetric problem of the calculus of variations to fluid mechanical problems in fluidization and spouting

This paper is devoted to outlining precisely the basic mathematics of a classical isoperimetric problem of the calculus of variations and showing how significant fluid mechanical problems in fluidization and spouting can be addressed using this approach.     

Flow regimes in wet conical spouted beds using glass bead mixtures

Using a high-viscosity Newtonian fluid, glycerol, an experimental investigation was carried out to evaluate the stable spouting regime in conical spouted beds using four particle mixtures： a reference （monoparticles）, a binary mixture, two ternary mixtures with flat and Gaussian distributions respectively. The mixtures were selected for particle diameters （dp） ranging from 1.09 to 4.98 mm and particle diameter ratios （dpL/dps） ranging from 1.98 to 4.0. Experimental data show that pressure fluctuation signals of the bed, as indicated by changes in their standard deviations, provide suitable information to identify the range of operational conditions for stable spouting. However, the analysis of skewness of curves of pressure fluctuation as a function of air velocity appears not sufficient to identify a particular flow regime. For glycerol in the spouting regime, the standard deviation is noted to increase with increasing glycerol concentration due to the growth of interparticle forces. The implications of these research findings on the drying of suspensions in conical spouted beds using glass bead mixtures are also discussed.     

Flow regimes in wet conical spouted beds using glass bead mixtures

Using a high-viscosity Newtonian fluid, glycerol, an experimental investigation was carried out to evaluate the stable spouting regime in conical spouted beds using four particle mixtures: a reference (monoparticles), a binary mixture, two ternary mixtures with flat and Gaussian distributions respectively. The mixtures were selected for particle diameters (dp) ranging from 1.09 to 4.98 mm and particle diameter ratios (dpL/dps) ranging from 1.98 to 4.0. Experimental data show that pressure fluctuation signals of the bed, as indicated by changes in their standard deviations, provide suitable information to identify the range of operational conditions for stable spouting. However, the analysis of skewness of curves of pressure fluctuation as a function of air velocity appears not sufficient to identify a particular flow regime. For glycerol in the spouting regime, the standard deviation is noted to increase with increasing glycerol concentration due to the growth of interparticle forces. The implications of these research findings on the drying of suspensions in conical spouted beds using glass bead mixtures are also discussed.