## Effect of Particle Shape and Density in the Gravitational SPLITT

The SPLITT cell has been largely applied for the separation of environmental samples. Since the natural matter particles have different properties (porosity, density, shape), the basic SPLITT equations have to be revised to fit the relevant particle properties.

The basic relationship for the SPLITT cell, previously derived (see eqn [6]) can be written as:

The 11 accounts for positive or negative mass values in eqn [25] corresponding, respectively, to a falling or a floating particle. The friction coefficient f can be expressed by Stokes law f = 3nyd, where y is the viscosity of the suspension fluid, which can be approximated by the carrier viscosity, y0. By combining eqns [23], [24] and [25] one obtains the classical expression (see eqn [13]):

bLgd2\Ap\

In the case of porous particles, porosity is defined as:

where Vp is the volume of the pore, Vs the volume of the solid and Vtpot the total volume of the particle. Then eqn [25] changes into:

meff = i1 nd3(1 -s)\Ap\ and the correspondent eqn [26] into:

18^o

The porosity can be expressed also in terms of 'apparent density':

from which the differential apparent density is defined as:

By combining Ap = ps — pl with eqns [31] and [32] one has:

which can be substituted in eqn [30]. When the 'mass porosity' is available:

m where m is the real mass of the particle, i.e. m = Vsps and by using eqn [27] one can show that:

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