The motion of thin drops under the effects of surfactants and gravity is studied. First, the effects of surfactant and temperature on the spreading of a viscous droplet are considered. Lubrication theory is used to develop a two-dimensional model for the evolution of the droplet. The surfactant is assumed to be insoluble, and it may transport onto and off of the droplet interface at the contact line. A linear temperature gradient and a gradient in the surface energy along the substrate are examined. We find that these effects together can increase the speed of the translation of the droplet. When contact-angle hysteresis is included, surfactant transport along the interface can cause the droplet to stop moving. These results are compared with a three-dimensional axisymmetric lubrication model and are found to be in good agreement. A fully three-dimensional lubrication model is formed that allows the droplet to translate down an inclined plane. Critical Bond numbers and angles of inclination are calculated for when the droplet remains pinned to the plane. A larger hysteresis window is found to require a higher Bond number to force the droplet to begin moving. These results compare favorably with other published studies. We construct a stability diagram that details the Bond numbers for which the droplet will remain pinned to the surface, when it will translate at a steady speed, and when it will begin to deform. The formation of cusps and pearling behavior of droplets is discussed

Last modified

• 05/22/2018

Creator

• Matthew Allen Clay

DOI

• https://doi.org/10.21985/N2112X

Subject

• Applied Mathematics

Keyword

• contact line
• Marangoni
• capillary

Date created

• 2007-05-10

Resource type

• Dissertation

Rights statement

• In Copyright