The Contact Angle Calculator is a tool used to measure the wettability of a surface by a liquid. It determines the angle formed at the interface of liquid, solid, and vapor phases. This contact angle helps assess the interaction between the liquid and the solid surface, providing valuable insights in fields such as material science, surface engineering, and fluid dynamics. A smaller contact angle indicates better wettability, while a larger angle signifies poorer wettability.
Formula of Contact Angle Calculator
The contact angle is calculated using the following formula:
Contact Angle (θ) = arccos((γ_sv – γ_sl) / γ_lv)
Detailed Formula Components
- γ_sv (Surface Tension between Solid and Vapor): The surface energy at the interface of the solid and the surrounding vapor.
- γ_sl (Surface Tension between Solid and Liquid): The surface energy at the interface of the solid and liquid.
- γ_lv (Surface Tension between Liquid and Vapor): The surface energy at the interface of the liquid and the surrounding vapor.
- θ (Contact Angle): The angle formed at the interface of the liquid, solid, and vapor phases, typically expressed in degrees.
Assumptions
- The system is in thermodynamic equilibrium.
- The surface is homogeneous and isotropic.
- No external forces, such as gravity, significantly distort the liquid droplet.
General Terms Table
Here’s a reference table showing typical surface tension values for common substances:
| Substance | γ_lv (mN/m) | Typical Contact Angle on Solid Surface (°) |
|---|---|---|
| Water | 72.8 | ~0 (superhydrophilic) to 150 (superhydrophobic) |
| Ethanol | 22.1 | 10–30 |
| Glycerol | 63.4 | 30–60 |
| Mercury | 485 | ~140 |
This table provides a quick overview of surface tension values and expected contact angles, aiding in the interpretation of results.
Example of Contact Angle Calculator
Let’s calculate the contact angle for a liquid droplet on a solid surface. The following parameters are given:
- γ_sv (Surface Tension between Solid and Vapor): 40 mN/m
- γ_sl (Surface Tension between Solid and Liquid): 30 mN/m
- γ_lv (Surface Tension between Liquid and Vapor): 50 mN/m
Calculation:
Substitute the values into the formula: Contact Angle (θ) = arccos((γ_sv – γ_sl) / γ_lv)
Contact Angle (θ) = arccos((40 – 30) / 50)
Contact Angle (θ) = arccos(10 / 50) = arccos(0.2).
Using a scientific calculator: Contact Angle (θ) ≈ 78.46°.
Interpretation:
The calculated contact angle of approximately 78.46° indicates moderate wettability of the solid surface by the liquid.
Most Common FAQs
The contact angle provides information about the wettability of a surface. Smaller angles indicate better wettability (hydrophilic surfaces), while larger angles indicate poorer wettability (hydrophobic surfaces).
Contact angle measurements are used in various industries to assess coatings, cleanliness, adhesion properties, and material compatibility in applications like waterproofing, painting, and electronics manufacturing.
Yes, contact angles greater than 90° indicate that the liquid does not spread well on the surface, which is characteristic of hydrophobic surfaces.