Cohesive Adhesive

Unit 5 Cohesion

Cohesive Adhesive

Juan Juan
14 min read
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Cohesive-Adhesive Forces are the rotational, binding interactions that hold liquid molecules together (cohesion) and attach them to surrounding surfaces (adhesion), forming stable structures at interfaces. They are the Mid 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 buoyant force (linear/displacement), cohesive-adhesive forces are rotational and self-reinforcing — molecules curl around each other and around surfaces, creating stable bonds that resist separation.

The Equation: Cohesion and Adhesion Fundamentals

Work of Cohesion (Energy to Separate Like Molecules)

Wc=2γL W_c = 2\gamma_L

Where:

SymbolMeaningUnit
Wc W_c Work of cohesionJ/m2 \text{J}/\text{m}^2
γL \gamma_L Surface tension of the liquidN/m \text{N}/\text{m}
2Factor for creating two new surfaces—

Work of Adhesion (Energy to Separate Unlike Phases)

Wa=γS+γL−γSL W_a = \gamma_S + \gamma_L - \gamma_{SL}

Where:

SymbolMeaningUnit
Wa W_a Work of adhesionJ/m2 \text{J}/\text{m}^2
γS \gamma_S Surface energy of the solidN/m \text{N}/\text{m}
γL \gamma_L Surface tension of the liquidN/m \text{N}/\text{m}
γSL \gamma_{SL} Solid–liquid interfacial tensionN/m \text{N}/\text{m}

Young–Dupré Equation (Contact Angle Relation)

γS=γSL+γLcos⁡θ \gamma_S = \gamma_{SL} + \gamma_L \cos\theta

Where:

SymbolMeaningUnit
θ \theta Equilibrium contact anglerad \text{rad} or ° \degree
γS \gamma_S Solid surface energy( \text{N}/\text{m} )
( \gamma_{SL} )Solid–liquid interfacial tension( \text{N}/\text{m} )
( \gamma_L )Liquid surface tension( \text{N}/\text{m} )

Cohesive Pressure (Laplace Pressure at Curved Interfaces)

Pc=2γLr P_c = \frac{2\gamma_L}{r}

Where ( r ) is the radius of curvature. This pressure binds liquid structures together.

Hamaker Constant (Van der Waals Cohesion)

AH=π2Cρ1ρ2 A_H = \pi^2 C \rho_1 \rho_2

Where ( A_H ) is the Hamaker constant, ( C ) is the London dispersion coefficient, and ( \rho_1, \rho_2 ) are number densities. This governs van der Waals cohesive-adhesive interactions.

Key Properties of Cohesive-Adhesive Forces

PropertyExplanation
RotationalMolecules curl around each other and surfaces, forming bonds
CohesiveLike molecules attract, holding the liquid together
AdhesiveUnlike molecules attract, binding liquid to surfaces
Self-reinforcingBonds strengthen as molecules align
Contact-angle-dependent( \theta < 90\degree ) → wetting (adhesion dominates); ( \theta > 90\degree ) → non-wetting (cohesion dominates)
Temperature-dependentHigher ( T ) → weaker bonds → lower ( \gamma )
Scale-dependentDominant at micro and nano scales

Wettability Condition (Adhesion vs. Cohesion)

S=γS−γL−γSL S = \gamma_S - \gamma_L - \gamma_{SL}

Where ( S ) is the spreading coefficient. If ( S > 0 ), the liquid spreads (adhesion wins). If ( S < 0 ), the liquid beads (cohesion wins).

Capillary Number (Viscous vs. Cohesive Forces)

Ca=μvγ Ca = \frac{\mu v}{\gamma}

When ( Ca \ll 1 ), cohesive forces dominate. When ( Ca \gg 1 ), viscous displacement dominates.

Real-Life Examples

ExampleHow Cohesive-Adhesive Forces Work
1. Water droplets on leavesCohesion pulls water into beads; adhesion determines contact angle
2. Meniscus in a glassAdhesion to glass pulls water up; cohesion holds it together
3. Mercury in a tubeStrong cohesion → convex meniscus (depression)
4. Adhesive tapeVan der Waals adhesion binds tape to surfaces
5. Gecko feetMillions of microscopic hairs create cohesive-adhesive van der Waals bonds
6. SolderingMolten solder adheres to metal via adhesive forces
7. Water stridersCohesion of water surface supports insect weight
8. Paint on wallsAdhesion binds paint to surface; cohesion holds film together
9. EmulsionsSurfactants balance cohesive-adhesive forces to stabilize droplets
10. Cell membrane fusionCohesive-adhesive forces drive lipid bilayer merging

Summary

QuestionAnswer
What are cohesive-adhesive forces?Rotational binding forces holding like molecules together and attaching them to surfaces
What law describes them?Young–Dupré: ( \gamma_S = \gamma_{SL} + \gamma_L \cos\theta ); Work of Adhesion: ( W_a = \gamma_S + \gamma_L - \gamma_{SL} )
What type of force?Mid Cohesion (rotational, Rule 2 + 4)
What drives them?Intermolecular attraction (van der Waals, hydrogen bonding, electrostatic)
Real examples?Water droplets, meniscus, adhesive tape, gecko feet, soldering
What’s its displacement counterpart?Buoyant Force (Mid Displacement)

Bottom line: Cohesive-adhesive forces are the rotational, self-reinforcing bonds that hold liquids together and attach them to surfaces — the Mid Cohesion force that pairs with buoyant force’s linear upward push in Superphysics’ Liquid Relationalities.

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