How to Calculate and Solve for Work of Adhesion per Unit Area for Flotation | Mineral Processing

The image above represents work of adhesion per unit area for flotation. To calculate work of adhesion per unit area for flotation, three essential parameters are needed and these parameters are Surface Tension of Particle A, (γ_A), Surface Tension of Particle B, (γ_B) and Surface Tension Existing between A and B, (γ_AB).

The formula for calculating work of adhesion per unit area for flotation:

W_AB = (γ_A + γ_B) – γ_AB

Where:

W_AB = Work of Adhesion per Unit Area for Flotation
γ_A = Surface Tension of Particle A
γ_B = Surface Tension of Particle B
And then, γ_AB = Surface Tension Existing between A and B

Let’s solve an example;
Find the work of adhesion per unit area for flotation when the surface tension of particle is 9, the surface tension of particle is 4 and the surface tension existing between A and B is 2.

This implies that;

γ_A = Surface Tension of Particle A = 9
γ_B = Surface Tension of Particle B = 4
And then, γ_AB = Surface Tension Existing between A and B = 2

W_AB = (γ_A + γ_B) – γ_AB
That is, W_AB = (9 + 4) – 2
W_AB = (13) – 2
W_AB = 11

Therefore, the work of adhesion per unit area for flotation is 11 J.

Calculating the Surface Tension of Particle A when the Work of Adhesion per Unit Area for Flotation, the Surface Tension of Particle B and the Surface Tension Existing between A and B are Given.

γ_A = W_AB + γ_AB – γ_B

Where:

γ_A = Surface Tension of Particle A
W_AB = Work of Adhesion per Unit Area for Flotation
γ_B = Surface Tension of Particle B
γ_AB = Surface Tension Existing between A and B

Let’s solve an example;
Find the surface tension of particle A when the work of adhesion per unit area for flotation is 42, the surface tension of particle B is 10 and the surface tension existing between A and B is 8.

This implies that;

W_AB = Work of Adhesion per Unit Area for Flotation = 42
γ_B = Surface Tension of Particle B = 10
γ_AB = Surface Tension Existing between A and B = 8

That is, γ_A = W_AB + γ_AB – γ_B
γ_A = 42 + 8 – 10
γ_A = 40

Therefore, the surface tension of particle a is 40.

Read more: How to Calculate and Solve for Work of Cohesion Per Unit Area | Mineral Processing

Calculating the Surface Tension of Particle B when the Work of Adhesion per Unit Area for Flotation, the Surface Tension of Particle A and the Surface Tension Existing between A and B are Given

γ_B = W_AB + γ_AB – γ_A

Where:

γ_B = Surface Tension of Particle B
W_AB = Work of Adhesion per Unit Area for Flotation
γ_A = Surface Tension of Particle A
γ_AB = Surface Tension Existing between A and B

Let’s solve an example;
Find the surface tension of particle B when the work of adhesion per unit area for flotation is 25, the surface tension of particle A is 12 and the surface tension existing between A and B is 10.

This implies that;

W_AB = Work of Adhesion per Unit Area for Flotation = 25
γ_A = Surface Tension of Particle A = 12
γ_AB = Surface Tension Existing between A and B = 10

That is, γ_B = W_AB + γ_AB – γ_A
γ_B = 25 + 10 – 12
γ_B = 23

Therefore, the surface tension of particle B is 23.

Calculating the Surface Tension Existing between A and B when the Work of Adhesion per Unit Area for Flotation, the Surface Tension of Particle A and the Surface Tension of Particle B are Given

γ_AB = γ_A + γ_B – W_AB

Where:

γ_AB = Surface Tension Existing between A and B
W_AB = Work of Adhesion per Unit Area for Flotation
γ_A = Surface Tension of Particle A
γ_B = Surface Tension of Particle B

Let’s solve an example;
Find the surface tension existing between A and B when the work of adhesion per unit area for flotation is 10, the surface tension of particle A is 20 and the surface tension of particle B is 14.

This implies that;

W_AB = Work of Adhesion per Unit Area for Flotation = 10
γ_A = Surface Tension of Particle A = 20
γ_B = Surface Tension of Particle B = 14

So, γ_AB = γ_A + γ_B – W_AB
γ_AB = 20 + 14 – 10
γ_AB = 24

Therefore, the surface tension existing between A and B is 24.

Read more: How to Calculate and Solve for Infinitesimal Change in Surface Tension | Gas Absorption | Mineral Processing

How to Calculate Work of Adhesion per Unit Area for Flotation With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the work adhesion per unit area for flotation.

Now, Click on Mineral Processing under Materials and Metallurgical

Now, Click on Work Adhesion per Unit Area for Flotation under Mineral Processing

The screenshot below displays the page or activity to enter your values, to get the answer for the work adhesion per unit area for flotation according to the respective parameter which is the Surface Tension of Particle A, (γ_A), Surface Tension of Particle B, (γ_B) and Surface Tension Existing between A and B, (γ_AB).

Now, enter the values appropriately and accordingly for the parameters as required by the Surface Tension of Particle A, (γ_A) is 9, Surface Tension of Particle B, (γ_B) is 4 and Surface Tension Existing between A and B, (γ_AB) is 2.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the work adhesion per unit area for flotation and presents the formula, workings and steps too.