Drag force on a porous, non-homogeneous spheroidal floc in a uniform flow field

The force acting on a porous spheroidal floc having a nonhomogeneous structure in a uniform flow field is evaluated theoretically. Here, the floc is simulated by an entity having a two-layer type of structure, and its porous nature is mimicked by varying the relative magnitudes of the permeabilities of its inner and outer layers. The results of numerical simulation reveal that, for the same volume-averaged permeability, the drag coefficient of a spheroidal floc with a nonhomogeneous structure is much larger than that of a floc with a homogeneous structure for both prolate and oblate spheroids. This is true regardless of the relative magnitudes of the permeability of the inner layer and that of the outer layer. While the drag coefficient of a homogeneous prolate is the same as that of a homogeneous oblate the drag coefficient of a nonhomogeneous prolate is larger than that of a nonhomogeneous oblate. For the same volume-averaged size, the more nonhomogeneous the structure of a spheroidal floc the easier for the relation between the drag coefficient and the Reynolds number to deviate from a Stokes-law-like relation. For a fixed volume-averaged permeability, the effective drag coefficient increases with the increase in the ratio (polar radius of inner layer/polar radius of floc), regardless of whether its inner layer is less permeable than its outer layer or not.