Contact angle

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Edited by Pichet Adstamongkonkul, AP225, Fall 2011


Contact angle.png

The contact angle is a quantitative measure of the wettability of the surface, represented by the angle at which a liquid or vapor interface makes with a solid surface.[1] The angle is specific and determined by the interactions across the three interfaces. Typically, the contact angle is illustrated by a drop of liquid on the surface. The shape of the drop is governed by the Young-Laplace equation (contact angle is incorporated as a boundary condition of the equation.) Normally, the contact angle can be measured using the so-calledgoniometer.[2]

 The contact angle is independent of geometry and hence a material property. Recent publications on contact angles on deformable surfaces can be included.

Connection to Capillarity/Wettability

The figure (from the lecture) illustrated different contact angles corresponding to different wettability of the surface, which depends on the relative hydrophobicity/ hydrophilicity of the surface compared to the liquid. Conventionally, the contact angle is measured as the angle between the solid surface and the liquid drop surface. In other words, the contact angle is the angle between the solid-liquid interfacial (surface) force (denoted as gamma_SL) and the surface tension or the liquid-vapor interfacial force (denoted as gamma_LG). The larger the angle, the more the drop is repelled from the surface, indicating a relatively higher hydrophobicity of the surface, in the case of water drop.

Surface tension.pngContact angle.jpg

If the liquid strongly attracts to the surface, the drop of the liquid would spread out on the solid surface. On highly hydrophobic surfaces, the contact angle can be as big as <math>-120^o</math>. However, materials with high degree of roughness on the surface can increase the angle up to <math>-150^o</math>; the materials in this group are called superhydrophobic surfaces.[2]

From the surface tensions at all three interfaces, we can explicitly write the Young equation that the system must satisfy at equilibrium:

<math>0=\gamma_{SG}-\gamma_{SL}-\gamma_{LG}cos(\theta_c)</math> where <math>\theta_c</math> is the contact angle.[3]

In the capillary effect, the driving force that causes water to go up the capillary is the net surface tension, balancing between the solid-vapor interfacial tension that pulls in the upward direction , and the solid-liquid interfacial tension that pulls downward.

 This is commonly stated but is incorrect. The Young-Dupre equation resolves all the inbalances in energy - no unresolved force is left to cause a lift. Capillary rise is due to Laplace pressures.

Examples of surfaces where the contact angles play an important role:

  • Lotus leaf: superhydrophobic surface that causes the water droplet to roll over the surface without “wetting” the surface.[4]

Lotus leaf.jpg

  • Human cornea: an extremely hydrophobic surface and, together with hydrophilic tears, maintain the lachrymal layer.
  • Modified surfaces with enhanced hydrophilicity, via plasma treatment
This entry needs references to advancing and receding contact angles.

Connection to Natural Systems

Aphids Figure1.jpg

Whether or not a surface wets when it makes contact with water is important in many natural systems. One reason that it is important is that small insects can drown in small amount of water if the surface on which they live gets wet. This is especially important in insects that live in confined spaces such as aphids that live inside plant galls. These insects have had to develop adaptations that allow them to live in a small, enclosed space without drowning or becoming sick from the wate that they produce. In order to protect themselves they coat the interior of the gall with a waxy substance that makes the surface very hydrophobic and allows the waste drops to become coated in this same substance and form into enclosed marbles. [5]

The picture to the right shows:

a) a droplet of aphid waste (honeydew) on a smooth surface of aphid wax
b) The rough texture of the waxy surface that adds to the hydrophobicity
c) We see the waxy crystals coating the surface of one of these droplets
d) A view of the same droplet from above


[1] Lecture on Capillarity and Wetting, AP225 Fall 2011

[2] Wikipedia contributors. “Contact angle.” Wikipedia, The Free Encyclopedia. 27 Nov 2011.

[3] Robert J. Good. “Contact angle, wetting, and adhesion: a critical review.” Journal of Adhesion Science and Technology. 6.12 (1992): 1269-302.

[4] Wikipedia contributors. “Lotus Leaf.” Wikipedia, The Free Encyclopedia. 27 Nov 2011.

[5] How aphids lose their marbles

Keyword in references:

Contact angle associated with thin liquid films in emulsions

Dewetting-Induced Membrane Formation by Adhesion of Amphiphile-Laden Interface

Surface-Tension-Induced Synthesis of Complex Particles Using Confined Polymeric Fluids

Substrate Curvature Resulting from the Capillary Forces of a Liquid Drop

Enriching libraries of high-aspect-ratio micro- or nanostructures by rapid, low-cost, benchtop nanofabrication

Steering nanofibers: An integrative approach to bio-inspired fiber fabrication and assembly

Screening Conditions for Rationally Engineered Electrodeposition of Nanostructures (SCREEN): Electrodeposition and Applications of Polypyrrole Nanofibers using Microfluidic Gradients

Liquid-infused structured surfaces with exceptional anti-biofouling performance

Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance

Wetting in Color: Colorimetric Differentiation of Organic Liquids with High Selectivity

Elastic Instability in Growing Yeast Colonies

Functionalized glass coating for PDMS microfluidic devices

Electric-field-induced capillary attraction between like-charged particles at liquid interfaces

Dynamic mechanisms for apparent slip on hydrophobic surfaces

The Optimal Faucet

Linear stability and transient growth in driven contact lines

Evaporation-Driven Assembly of Colloidal Particles

Thermal bending of liquid sheets and jets

Self-Assembly of Spherical Particles on an Evaporating Sessile Droplet

Non-stick water

How aphids lose their marbles

Kinks, rings, and rackets in filamentous structures

The wall-induced motion of a floating flexible train

Confined developable elastic surfaces: cylinders, cones and the Elastica

The ‘‘Cheerios effect’’

Capillary rise between elastic sheets

Equilibrium of an elastically confined liquid drop

Control of Shape and Size of Nanopillar Assembly by Adhesion-Mediated Elastocapillary Interaction

Hydrodynamics of Writing with Ink

Minimal surfaces bounded by elastic lines

Frequency distribution of mechanically stable disk packings

A new device for the generation of microbubbles

Controlled Buckling and Crumpling of Nanoparticle-Coated Droplets

Surface-Tension-Induced Synthesis of Complex Particles Using Confined Polymeric Fluids

Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids

Photoreactive coating for high-contrast spatial patterning of microfluidic device wettability

Patterning microfluidic device wettability using flow confinement

Impact of inlet channel geometry on microfluidic drop formation

Bacillus subtilis spreads by surfing on waves of surfactant

Structure of adhesive emulsions

Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature

Dewetting Instability during the Formation of Polymersomes from Block-Copolymer-Stabilized Double Emulsions

Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids

Viscoelastic properties of oxide-coated liquid metals

Electric-field-induced capillary attraction between like-charged particles at liquid interfaces

Short-time self-diffusion of nearly hard spheres at an oil–water interface

Drop formation in non-planar microfluidic devices

Dewetting-Induced Membrane Formation by Adhesion of Amphiphile-Laden Interfaces

Multicompartment Polymersomes from Double Emulsions

Hierarchical Porous Materials Made by Drying Complex Suspensions

Microfluidic Fabrication of Monodisperse Biocompatible and Biodegradable Polymersomes with Controlled Permeability

Dynamics of Drying in 3D Porous Media

Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature

Fabrication and Wetting Properties of Metallic Half-Shells with Submicron Diameters

Chemical Force Spectroscopy in Heterogeneous Systems: Intermolecular Interactions Involving Epoxy Polymer, Mixed Monolayers, and Polar Solvents

Surface Tension-Powered Self-Assembly of Microstructures—The State-of-the-Art

Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology