How to Calculate and Solve for Work of Adhesion between Solid and Liquid | Young-Dupre Equation I Mineral Processing

Last Updated on December 10, 2021

The image above represents work of adhesion between solid and liquid.

To compute for work of adhesion between solid and liquid, two essential parameters are needed and these parameters are Interfacial Tension between Liquid and Air (γ_LA) and Angle Interface (θ).

The formula for calculating the work of adhesion between solid and liquid:

W_SL = γ_LA(cosθ + 1)

Where:

W_SL = Work of Adhesion between Solid and Liquid | Young-Dupre Equation
γ_LA = Interfacial Tension between Liquid and Air
θ = Angle Interface

Let’s solve an example;
Find the work of adhesion between solid and liquid when the interfacial tension between liquid and air is 44 and the angle interface is 11.

This implies that;

γ_LA = Interfacial Tension between Liquid and Air = 44
θ = Angle Interface = 11

W_SL = γ_LA(cosθ + 1)
W_SL = 44(cos(11°) + 1)
W_SL = 44(0.98 + 1)
W_SL = 44(1.98)
W_SL = 87.19

Therefore, the work of adhesion between solid and liquid is 87.19 J.

Calculating the Interfacial Tension between Liquid and Air when the Work of Adhesion between Solid and Liquid and the Angle Interface is Given.

γ_LA = ^W_SL / _{(cosθ + 1)}

Where:

γ_LA = Interfacial Tension between Liquid and Air
W_SL = Work of Adhesion between Solid and Liquid | Young-Dupre Equation
θ = Angle Interface

Let’s solve an example;
Find the interfacial tension between liquid and air when the work of adhesion between solid and liquid is 44 and the angle interface is 11.

This implies that;

W_SL = Work of Adhesion between Solid and Liquid | Young-Dupre Equation = 44
θ = Angle Interface = 11

γ_LA = ^W_SL / _{(cosθ + 1)}
γ_LA = ⁴⁴ / _{(cos11 + 1)}
γ_LA = ⁴⁴ / _1.98
γ_LA = 22.2

Therefore, the interfacial tension between liquid and air is 22.2.

Calculating the Angle Interface when the Work of Adhesion between Solid and Liquid and the Interfacial Tension between Liquid and Air is Given.

θ = cos^-1(^W_SL / _γLA – 1)

Where:

θ = Angle Interface
W_SL = Work of Adhesion between Solid and Liquid | Young-Dupre Equation
γ_LA = Interfacial Tension between Liquid

Let’s solve an example;
Find the angle interface when the work of adhesion between solid and liquid is 8 and the interfacial tension between liquid is 4.

This implies that;

W_SL = Work of Adhesion between Solid and Liquid | Young-Dupre Equation = 8
γ_LA = Interfacial Tension between Liquid = 4

θ = cos^-1(^W_SL / _γLA – 1)
θ = cos^-1(⁸ / ₄ – 1)
θ = cos^-1(2 – 1)
θ = cos^-11
θ = 0

Therefore, the angle interface is 0.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the work of adhesion between solid and liquid.

Now, Click on Mineral Processing under Materials and Metallurgical

Now, Click on Work of Adhesion between Solid and Liquid under Mineral Processing

The screenshot below displays the page or activity to enter your values, to get the answer for the work of adhesion between solid and liquid according to the respective parameter which is the Interfacial Tension between Liquid and Air (γ_LA) and Angle Interface (θ).

Now, enter the values appropriately and accordingly for the parameters as required by the Interfacial Tension between Liquid and Air (γ_LA) is 44 and Angle Interface (θ) is 11.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the work of adhesion between solid and liquid and presents the formula, workings and steps too.