Porosity and pressure drop in packed beds of spheres between narrow parallel walls

This is a theoretical and experimental study on porosity and pressure losses in a packed bed of spheres between parallel walls. It is focused on small values of the ratio of the distance p between the walls to the average diameter dav of solid particles: p/dav <= 2. We report a semi-empirical formula for the prediction of porosity of monodisperse packings made by randomly pouring the spheres between narrow parallel walls. Concerning the more general case of polydisperse lattices, characterized by a statistical distribution of diameters in the range dmin-dmax, we show how to determine a range p = f(dmax)- f(dmin) which ensures that the maximum value of the solid volume fraction, and thus of pressure losses, is less than a specific target. Lastly we present a new semi-empirical formula for the prediction of pressure losses of an air flow through random packings of spheres between narrow parallel walls, by adapting the Ergun equation to the peculiar geometry at issue.