JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II MINERAL PROCESSING Previous Question Paper (November/December - 2020 - R16)

Liberation is the physical process of breaking an ore into smaller particles such that each particle consists of only one mineral phase. It is the fundamental prerequisite for effective mineral separation, as physical separation methods (like flotation or magnetic separation) rely on the distinct physical properties of individual minerals.

Consider an ore consisting of two minerals, A and B, present in equal quantities (50% each). The degree of liberation depends on the texture and grain size of these minerals within the host rock:

• Coarse-grained ore: If minerals A and B exist as large, distinct patches, liberation is achieved at a relatively coarse particle size. Crushing the ore to a size slightly smaller than the average grain size will produce a high percentage of 'free' particles of A and 'free' particles of B.
• Fine-grained or disseminated ore: If mineral A is finely dispersed within a matrix of mineral B, liberation requires much finer grinding. If the particle size produced by grinding is larger than the grain size of the inclusions, the resulting particles will be middlings (composite particles containing both A and B).

The degree of liberation (L) for a component is defined as the ratio of the amount of the mineral occurring as free particles to the total amount of that mineral in the ore. Ideally, for an ore with 50% A and 50% B, the goal is to reach the liberation size, where the number of composite particles is minimized.

As the particle size decreases, the percentage of free particles increases, eventually approaching 100%. However, excessive grinding leads to over-grinding or sliming, which wastes energy and complicates downstream separation. Therefore, the theory of liberation dictates that the ore should be ground only to the size necessary to achieve sufficient liberation for the chosen separation process, balancing the grade of the concentrate against the recovery of the valuable mineral.

The three laws of comminution relate the energy input required for size reduction to the change in particle size. They are based on the premise that energy consumption is a function of the change in surface area or volume of the material.

1. Rittinger's Law: Proposed by Rittinger in 1867, this law states that the energy required for size reduction is directly proportional to the new surface area produced. It is expressed as:

where E is energy, K_R is Rittinger's constant, and d₁ and d₂ are initial and final particle sizes. This law is most applicable to fine grinding where surface area generation is the dominant energy consumer.

2. Kick's Law: Proposed by Kick in 1885, this law states that the energy required is proportional to the reduction ratio (the ratio of initial size to final size). It is expressed as:

where K_K is Kick's constant. This law is generally considered more accurate for coarse crushing where the energy is primarily used for elastic deformation of the particles.

3. Bond's Law: Proposed by Fred C. Bond in 1952, this law serves as a compromise between Rittinger's and Kick's laws. It states that the energy input is proportional to the square root of the surface-to-volume ratio. The formula is:

where W_i is the Work Index (the energy required to reduce a material from infinite size to 100 microns). This is the most widely used law for industrial ball mill and rod mill sizing.

Comparison and Contrast:

• Applicability: Kick's law is best for coarse crushing, Bond's law for intermediate crushing and grinding, and Rittinger's law for fine grinding.
• Theoretical Basis: Kick's law assumes energy is proportional to volume reduction, Rittinger's to surface area creation, and Bond's to the length of crack tips formed.
• Practical Utility: Bond's law is the standard in mineral processing because it accounts for the material's resistance to breakage via the Work Index, whereas the constants in Kick's and Rittinger's laws are less consistent across different materials.