Department of Mathematics
Harvey Mudd College
Modeling moving droplets: A precursor film approach
Laminar flow wings are sometimes used on light aircraft because of
their increased efficiency, as compared to traditional wings where the
boundary layer becomes turbulent relatively early along the wing.
Their use is limited by the problem that small surface disturbances,
particularly raindrops and the associated film that forms as they
coalesce, induce turbulence in the boundary layer. This drastically
reduces the lifting capability of the wing, sometimes by as much as 50
percent, making it dangerous for aircraft with such wings to fly in
conditions with any possibility of precipitation developing, and thus
limiting their more widespread use. A possible method for overcoming
this issue is to attempt to eliminate or minimize the length of the
film that forms by guiding the droplets appropriately prior to their
Some color pictures from our simulations can be found below. When looking at them, note that the height and lengths have been scaled out, so the drops would in reality look much flatter.
A standard initial condition for a drop.
A drop after a short period of being subjected to shear.
It is roughly tetrahedral shaped at this stage.
A drop after shearing motion has caused the formation of a crescent depression on the back face.
The same qualitative feature can be seen when blowing on a droplet on a glass surface.
A feature of our model is that as the drop flattens out, shear forces will dominate over gravity forces. In this figure of a droplet profile changing in time, gravity intially sends the droplet to the right, and as it gets spread out surface shear sends it in the opposite direction.
We hope to eventually model the coalescence of many drops. While we have not yet done so, an example of two-drop coalescence is shown here.