Surface Tension Given Contact Angle Calculator

Surface Tension Formula:

\[ \gamma = \frac{2 \times R_{curvature} \times \rho_{fluid} \times g \times h_c}{\cos(\theta)} \]

Radius of Curvature:

Density of Fluid:

kg/m³

Height of Capillary Rise/Fall:

Contact Angle:

degrees

Surface Tension of Fluid:

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1. What is Surface Tension?

Surface tension is the property of a liquid that allows it to resist an external force, due to the cohesive nature of its molecules. It is measured as the energy required to increase the surface area of a liquid by a unit amount.

2. How Does the Calculator Work?

The calculator uses the capillary rise formula:

\[ \gamma = \frac{2 \times R_{curvature} \times \rho_{fluid} \times g \times h_c}{\cos(\theta)} \]

Where:

\( \gamma \) — Surface tension (N/m)
\( R_{curvature} \) — Radius of curvature (m)
\( \rho_{fluid} \) — Density of fluid (kg/m³)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( h_c \) — Height of capillary rise/fall (m)
\( \theta \) — Contact angle (degrees)

Explanation: This formula relates the surface tension to the capillary rise phenomenon, where liquids rise or fall in narrow tubes due to surface tension effects.

3. Importance of Surface Tension Calculation

Details: Surface tension calculations are crucial in various fields including fluid mechanics, materials science, biomedical engineering, and industrial processes where wetting and capillary action are important.

4. Using the Calculator

Tips: Enter all values in appropriate units. Radius of curvature and height should be in meters, density in kg/m³, and contact angle in degrees (0-180°). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of contact angle?
A: Contact angle measures the wettability of a surface. A small contact angle indicates good wetting, while a large contact angle indicates poor wetting.

Q2: Why does capillary rise occur?
A: Capillary rise occurs due to the interplay between adhesive forces (liquid-solid) and cohesive forces (liquid-liquid), resulting in surface tension pulling the liquid up the tube.

Q3: What are typical surface tension values for common liquids?
A: Water at 20°C: ~72 mN/m, Mercury: ~465 mN/m, Ethanol: ~22 mN/m, Soap solution: ~25 mN/m.

Q4: How does temperature affect surface tension?
A: Surface tension generally decreases with increasing temperature as molecular kinetic energy increases and intermolecular forces weaken.

Q5: What are practical applications of surface tension calculations?
A: Applications include inkjet printing, medical diagnostics, coating processes, microfluidics, and understanding biological processes like lung function.