Dispersing Powders in Liquids, Part 1, by Ralph D. Nelson, Jr.
Listed below are some equations defining the conversion between
several common methods of expressing slurry concentration. The
equations are written with the variables arranged to solve
starting from known values of the density of the liquid 
l,
the density of the solid s, and the mass of solids per
unit volume of slurry Ls. They may, of course, be rearranged
to start from other sets of known values.
DENSITY OF A SLURRY
l = density of the liquid [kg/m3]
s = density of the (nonporous) particle [kg/m3]
sl = Ll + Ls
= density of the slurry [kg/m3]
sed,clump = s
- 
void (s
- l)
= sedimentation density of a clump of particles
[kg/m3]
The void fraction, void, is the volume fraction
of space (within the boundary of a clump) that is not filled by solid.
The boundary may be imagined as a skin that has been shrunk to fit
about the outside of a clump without distorting the clump's structure.
Any liquid within this boundary moves about with the particle.
The void fraction is sometimes called the "occluded-liquid volume
fraction", and the sedimentation density of the clump equals
the mass of this occluded liquid plus the mass of the solid in
the clump divided by their net volume.
MASS LOADING IN A SLURRY
Ls = ms / Vsl
= mass of solids per unit volume of slurry (NOT liquid)
[kgs/msl3]
Ll = (s - Ls)
(l / s)
= mass of liquid per unit volume of slurry (NOT liquid)
[kgl/msl3]
VOLUME FRACTION IN A SLURRY
s = Ls /
s = volume fraction of solids in the slurry
l = 1 - s
= volume fraction of liquid in the slurry
void = fraction of liquid within a clump of particles
MASS PERCENT IN A SLURRY
ps = 100% Ls / (Ls
+ Ll) = mass percent of solids in the slurry [%]
pl = 100% - ps = mass percent of liquid in the slurry [%]
SINGLE PARTICLE VALUES
Vone = fVshape dp3
= volume of a particle [m3]
fVshape = volume shape factor = 
/ 6 for spheres; 1 for cubes
mone = s Vone
= mass of a particle [kg]
Aone = fAshape dp2
= area of a particle [m2]
fAshape = area shape factor = for spheres; 6 for cubes
AREA AND NUMBER OF SPHERES PER UNIT MASS OF PARTICLES
These are called the specific surface area and
specific particle number.
These formulas below are for a set of spheres with identical diameters
but a series of these could be weighted by the mass fractions in the channels
of a particle size analysis and summed to compute a value for a real
sample of spheres.
For nonspherical particles adsorption experiments can be used
to determine Asp and the specific particle number
can be determined by counting the particles in a known volume
of suspension with a known mass loading.
Asp = 6 / ( d)
Nsp = 6 / ( d3)
AREA AND NUMBER OF SPHERES PER UNIT VOLUME OF SLURRY
These formulas are general and not size dependent.
As / Vsl = Asp Ls
Nsp = Nsp Ls
EQUAL-THICKNESS COATING ON EQUAL-DIAMETER SPHERES
The volume of coating can be computed from the mass used and its density:
Vcoat = mcoat / coat
Remember that the total diameter of a coated particle is sum of
the diameter of the core plus twice the coating thickness, t.
The ratio of volume of coating to volume of core can be computed
from the core diameter and coating thickness. This can be helpful
in determining how much coating material must be added to attain
a given coating thickness.
Alternately the coating thickness can be computed from the diameter of the core,
the toal mass of core particles, and the total mass of coating addded.
