Contact Angle Relaxation during Droplet Spreading

In this Demonstration, the macroscopic behavior of the contact line during spontaneous spreading of a nonvolatile droplet on a substrate is studied. A droplet is placed on a substrate and initially makes contact with the substrate at some nonequilibrium contact angle . The drop then begins to spread until it reaches its equilibrium contact angle . The dynamics of this process are simulated in this Demonstration.
The molecular-kinetic theory of viscous spreading [1] is used to describe the dependence of the contact angle on the speed of the wetting line, where is the base radius of the drop:
In this model, is the frequency of molecular displacements at the wetting line, the average length of displacements, is the surface tension of the liquid, is the number of adsorption sites per unit area, is Boltzmann's constant, and is the temperature. In this Demonstration, these parameters are consolidated into two parameters called and . The equilibrium contact angle is denoted by .
Noting that , the expression for the time rate of change of the contact angle can be derived:
where is dimensionless time.
Using the sliders, you can vary the initial contact angle when the drop is placed on the substrate, the dimensionless wetting parameter , the maximum time for spreading , and the equilibrium contact angle . The Demonstration shows how and vary with time and the dependence of on the speed of the contact line . You can see the 3D shape of the spreading drop at different spreading times by clicking the spherical drop tab in the drop-down menu and then varying the time slider .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


[1] T. D. Blake, A. Clarke, J. De Coninck, and M. J. de Ruijter, "Contact Angle Relaxation during Droplet Spreading: Comparison between Molecular Kinetic Theory and Molecular Dynamics," Langmuir, 13(7), 1997 pp. 2164–2166. doi:10.1021/la962004g.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+