Capillary Action

Unit 4 Micro Cohesion

Capillary Action

Juan Juan
13 min read
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Capillary Action is the spontaneous, rotational climbing or depression of liquid within narrow spaces, arising from the interplay of adhesion, cohesion, and surface tension. It is the Micro Cohesion force in Superphysics’ Liquid Relationalities — the rotational, structure-forming action of the liquid medium as it organizes itself through aetherspace and the outer intraaetherspace.

Unlike interfacial tension (linear/displacement), capillary action is rotational and cohesive — liquid curls into concave or convex menisci and draws itself along narrow channels in a self-sustaining loop.

The Equation: Capillary Fundamentals

Young–Laplace Equation (Pressure Across Curved Meniscus)

ΔP=γ(1R1+1R2) \Delta P = \gamma \left( \frac{1}{R_1} + \frac{1}{R_2} \right)

Where:

Symbol Meaning Unit
ΔP \Delta P Pressure difference across meniscus Pa \text{Pa}
γ \gamma Surface tension N/m \text{N}/\text{m}
R1,R2 R_1, R_2 Principal radii of curvature m \text{m}

Capillary Rise Height (Jurins Law)

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

Where:

Symbol Meaning Unit
( h ) Capillary rise (or depression) height ( \text{m} )
( \gamma ) Surface tension ( \text{N}/\text{m} )
( \theta ) Contact angle between liquid and tube ( \text{rad} ) or ( \degree )
( \rho ) Liquid density ( \text{kg}/\text{m}^3 )
( g ) Gravitational acceleration ( \text{m}/\text{s}^2 )
( r ) Capillary radius ( \text{m} )

Washburn Equation (Time-Dependent Capillary Flow)

L2=γrcos⁡θ2μt L^2 = \frac{\gamma r \cos\theta}{2\mu} t

Where:

Symbol Meaning Unit
( L ) Penetration distance ( \text{m} )
( \mu ) Dynamic viscosity ( \text{Pa} \cdot \text{s} )
( t ) Time ( \text{s} )

Laplace Pressure (Curvature-Induced Cohesion)

PLaplace=2γr P_{\text{Laplace}} = \frac{2\gamma}{r}

This pressure pulls liquid into the capillary, sustaining the rotational cohesive draw.

Key Properties of Capillary Action

Property Explanation
Rotational Liquid curls into meniscus, forming a curved interface
Cohesive Self-sustaining draw through narrow channels
Adhesion-dependent Liquid must wet the tube θ<90° \theta < 90\degree for rise
Cohesion-dependent Strong cohesive forces → depression θ>90° \theta > 90\degree
Radius-dependent Smaller r → greater capillary rise
Temperature-dependent Higher T → lower γ \gamma → less rise
Self-reinforcing Curvature creates pressure that draws more liquid

Contact Angle (Wetting Condition)

cos⁡θ=γsg−γslγlg \cos\theta = \frac{\gamma_{sg} - \gamma_{sl}}{\gamma_{lg}}

Where

γsg \gamma_{sg}

,

γsl \gamma_{sl}

, and

γlg \gamma_{lg}

are solid–gas, solid–liquid, and liquid–gas interfacial tensions. This determines whether capillary action rises or depresses.

Real-Life Examples

Example How Capillary Action Works
1. Water rising in a straw Narrow tube draws water up against gravity
2. Plant water transport Xylem vessels pull water from roots to leaves
3. Paper towel absorbing spills Cellulose fibers wick liquid through narrow pores
4. Ink in a fountain pen Capillary channels feed ink to the nib
5. Tear film in eyes Lacrimal fluid spreads across cornea via capillaries
6. Soil water retention Small soil pores hold water against gravity
7. Chromatography Solvent climbs paper, separating chemical compounds
8. Candle wick Melted wax rises through the wick to feed the flame
9. Concrete moisture Water migrates through microscopic pores
10. Microfluidic chips Capillary action drives liquid through tiny channels without pumps

Summary

Question Answer
What is capillary action? Rotational climbing of liquid in narrow spaces via cohesion and adhesion
What law describes it? Jurins Law: ( h = \frac{2\gamma \cos\theta}{\rho g r} ); Washburn: ( L^2 = \frac{\gamma r \cos\theta}{2\mu} t )
What type of force? Micro Cohesion (rotational, Rule 2 + 4)
What drives it? Surface tension, adhesion, and meniscus curvature
Real examples? Plant xylem, paper towels, ink pens, chromatography, candle wicks
What’s its displacement counterpart? Interfacial Tension (Micro Displacement)

Bottom line: Capillary action is the rotational, self-sustaining draw of liquid through narrow channels — the Micro Cohesion force that pairs with interfacial tension’s linear area-minimizing pull in Superphysics’ Liquid Relationalities.

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