In the field of minerals processing the concentration of valuable minerals normally takes place in suspensions of ore particles in liquids. The fluid resistance offered by Newtonian liquids to the movement of free settling spheres for the limiting cases of creep flow and turbulent flow is well described by Stokes’ and Newton’s Laws. However, these equations are not applicable to non-Newtonian fluids, since the relationship between applied shearing stress and resulting rate of shear is a non-linear function, and more than one viscosity parameter is necessary to describe their rheological properties.
The apparatus for this investigation consists of a transparent column fitted with an electronic sensing device which determines the velocity of metallic balls passing through a solid-liquid opaque suspension. A suspension was formed by allowing water of constant head to flow through a bed of fine glass beads contained in the column. The degree of dilation of the suspension was accurately controlled. The suspension density was measured hydrostatically.
- The concentration of solids.
- The size of the glass beads.
- The density of the glass beads.
Suspensions are classified as
a) Static suspension, those composed of spherical solids of identical diameter and densities and which remain in fixed position with respect to a fixed coordinate system.
b) Dynamic suspension, those of similar solid phase but moving with respect to fixed coordinate system.
A crystallographic system in which the solids may be arranged in such a manner is the cubic structure. The stacking of spherical objects in nature takes place with its close packed planes perpendicular to the direction of gravity, and this orientation would be adopted by the solids of a suspension.
On the basis of these considerations it is suggested that the spherical particles of a static solid-liquid system arrange themselves in a face center cubic crystal-like structure with its plane oriented to the flow of water.
Assuming that the solids of a static suspension do arrange themselves in a FCC structure, the minimum size of glass bead necessary to avoid “through channeling” of the water. It is not possible to create a static suspension with a content of solids of less than 25% by volume. At these low concentrations the size of the unit cell is large in comparison to the size of the bead and “through channeling” occurs, thus preventing an appropriate balance of the forces acting on each bead.
In order for a glass bead to be maintained in suspension, it is necessary that a number of forces acting on it reach equilibrium. These are force of gravity, Fq, force of buoyancy, FB, and force of drag, Fd.
FG + FB + Fd = 0
FG and FB may be readily calculated. Fd may be further subdivided into two parts, FD, a drag force due only to the liquid, and FI due only to the action of the neighboring glass beads. Since the velocity of the liquid is very small, FD may be calculated directly from Stokes law.
An explanation for the stability of a static suspension, where through channeling of water does not occur, may be now proposed on the basis of the former development. Large Reynolds numbers for the suspension would produce less stable suspensions, since there would be a tendency towards a turbulent flow. This behavior is actually observed experimentally, since for suspensions of large glass beads the Reynolds number increases, and the suspension is less stable. Suspensions of high density have smaller Reynolds numbers and are more stable than diluted ones.