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Surface Tension Calculator

Calculate capillary rise, surface tension effects, and liquid interface phenomena

Parameters

N/mⓘ
°ⓘ
mⓘ
kg/m³ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Capillary Rise:
0.01;m0.01;m
Capillary Force:
0.00;N0.00;N
Laplace Pressure:
144.00;Pa144.00;Pa
Bond Number:
0.55;0.55;

Examples

Example 1: Water in Glass Capillary

Water rising in a clean glass capillary tube.

  • Capillary Rise: 0.010.01
  • Capillary Force: 0.000.00
  • Laplace Pressure: 144.00144.00
  • Bond Number: 0.270.27

Example 2: Mercury in Glass

Mercury in a glass capillary tube.

  • Capillary Rise: −0.01-0.01
  • Capillary Force: −0.00-0.00
  • Laplace Pressure: 1940.001940.00
  • Bond Number: 0.140.14

Example 3: Oil in Capillary

Oil with moderate surface tension.

  • Capillary Rise: 0.000.00
  • Capillary Force: 0.000.00
  • Laplace Pressure: 25.0025.00
  • Bond Number: 1.331.33

Visualization

Surface Tension and Capillary Action

Surface tension is the property of liquid surfaces that allows them to resist external forces. It arises from the cohesive forces between liquid molecules, creating a 'skin' effect at the liquid-air interface. Surface tension is measured in N/m (Newtons per meter).

Capillary action is the ability of a liquid to flow in narrow spaces without external forces, such as against gravity. It occurs due to the combination of surface tension and adhesive forces between the liquid and the container walls.

The capillary rise height is given by: h = (2γcosθ)/(ρgr), where γ is surface tension, θ is contact angle, ρ is liquid density, g is gravitational acceleration, and r is tube radius. This equation shows that capillary rise increases with surface tension and decreases with tube radius.

The contact angle (θ) determines whether a liquid wets a surface. For θ < 90°, the liquid wets the surface (hydrophilic); for θ > 90°, it doesn't wet the surface (hydrophobic). Water on clean glass has θ ≈ 0°, while mercury on glass has θ ≈ 140°.

Surface tension has numerous applications including: capillary action in plants, inkjet printing, medical diagnostics, microfluidics, and the formation of droplets and bubbles.

Key Concepts

  • Surface Tension: γ (N/m) - force per unit length
  • Capillary Rise: h = (2γcosθ)/(ρgr)
  • Contact Angle: θ - determines wetting behavior
  • Cohesive Forces: Between liquid molecules
  • Adhesive Forces: Between liquid and solid
  • Laplace Pressure: ΔP = 2γ/R for spherical surfaces

Real-World Applications

  • Plant Water Transport: Capillary action in xylem
  • Inkjet Printing: Droplet formation control
  • Medical Diagnostics: Capillary blood tests
  • Microfluidics: Lab-on-a-chip devices
  • Bubble Formation: Soap bubbles and foams

Explore Further

More fluid mechanics tools

Physics Equations

Capillary Rise:
h=2γcos⁡θρgrh = \frac{2\gamma \cos\theta}{\rho g r}
Laplace Pressure:
ΔP=2γR\Delta P = \frac{2\gamma}{R}
Surface Energy:
E=γAE = \gamma A
Capillary Force:
F=2πrγcos⁡θF = 2\pi r \gamma \cos\theta
Bond Number:
Bo=ρgL2γBo = \frac{\rho g L^2}{\gamma}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Parameters

First, we identify the parameters needed for capillary rise calculation:

Equation:

h=2γcos⁡θρgrh = \frac{2\gamma \cos\theta}{\rho g r}

Calculation:

γ=0.072 N/m,θ=0°,r=0.001 m,ρ=1000 kg/m3\gamma = 0.072 \text{ N/m}, \theta = 0°, r = 0.001 \text{ m}, \rho = 1000 \text{ kg/m}^3

Explanation:

These are the surface tension, contact angle, tube radius, and liquid density.

2

Step 2: Convert Contact Angle to Radians

Convert contact angle from degrees to radians:

Equation:

θrad=θdegπ180\theta_{rad} = \frac{\theta_{deg} \pi}{180}

Calculation:

θrad=0×π180=0.0000 rad\theta_{rad} = \frac{0 \times \pi}{180} = 0.0000 \text{ rad}

Explanation:

Trigonometric functions require angles in radians.

3

Step 3: Calculate Capillary Rise

Using the capillary rise equation:

Equation:

h=2γcos⁡θρgrh = \frac{2\gamma \cos\theta}{\rho g r}

Calculation:

h=2(0.072)cos⁡(0.0000)1000×9.81×0.001=0.014679 mh = \frac{2(0.072)\cos(0.0000)}{1000 \times 9.81 \times 0.001} = 0.014679 \text{ m}

Explanation:

This gives the height to which the liquid rises (or falls) in the capillary tube.

4

Step 4: Calculate Capillary Force

Calculate the force due to surface tension:

Equation:

F=2πrγcos⁡θF = 2\pi r \gamma \cos\theta

Calculation:

F=2π(0.001)(0.072)cos⁡(0.0000)=0.000452 NF = 2\pi(0.001)(0.072)\cos(0.0000) = 0.000452 \text{ N}

Explanation:

This is the force exerted by surface tension around the circumference of the tube.

5

Step 5: Calculate Laplace Pressure

Calculate the pressure difference across the curved surface:

Equation:

ΔP=2γr\Delta P = \frac{2\gamma}{r}

Calculation:

ΔP=2(0.072)0.001=144.0 Pa\Delta P = \frac{2(0.072)}{0.001} = 144.0 \text{ Pa}

Explanation:

This is the pressure difference due to the curvature of the liquid surface.

Frequently Asked Questions (FAQ)

What is surface tension?

Surface tension is the property of liquid surfaces that allows them to resist external forces. It's caused by cohesive forces between liquid molecules and is measured in N/m.

What is capillary action?

Capillary action is the ability of a liquid to flow in narrow spaces against gravity due to surface tension and adhesive forces between the liquid and container walls.

How does contact angle affect capillary rise?

The contact angle determines whether a liquid wets a surface. For θ < 90°, the liquid rises (hydrophilic); for θ > 90°, it falls (hydrophobic). The rise height is proportional to cos(θ).

What is the Laplace pressure?

Laplace pressure is the pressure difference across a curved liquid surface due to surface tension. For a spherical surface, ΔP = 2γ/R, where γ is surface tension and R is radius of curvature.

How does tube radius affect capillary rise?

Capillary rise is inversely proportional to tube radius. Smaller tubes result in higher capillary rise, which is why capillary action is more pronounced in very narrow spaces.

Practice MCQs

  1. Capillary rise is given by:
  2. For a hydrophilic surface, contact angle is:
  3. Surface tension has units of:
  4. Laplace pressure for a spherical surface is:
  5. Capillary rise increases with:

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