# Difference between revisions of "Profile of a large drop"

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<center><math>2\kappa\approx 3.5 \text{mm}</math></center> | <center><math>2\kappa\approx 3.5 \text{mm}</math></center> | ||

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+ | Nevertheless, the bottom left corner of the 179 degree profile does resemble a quarter-circle. |

## Revision as of 18:06, 18 February 2009

In class we derived the profile <math>z(x)</math> of a large drop as being:

where we had defined <math>e</math> as being the maximum height of the drop:

and <math>\kappa=\sqrt{\frac{\rho g}{\sigma_{lv}}}</math> was the inverse capillary length.

To visualize what the edge of a large drop then looks like, you can use the following two MATLAB programs, which will solve and plot the above differential equation. Figure 1 also shows what some of these plots look like.

In class we had a brief discussion as to the nature of the drop's periphery on superhydrophobic surfaces. In the superhydrophobic limit (i.e., as <math>\theta_e</math> approaches 180 degrees), will the edge of the drop have a semicircular shape? The shape is apparently not semicircular at 179 degrees, since the horizontal range of the drop is only 1 mm, while it vertically extends to a height of

Nevertheless, the bottom left corner of the 179 degree profile does resemble a quarter-circle.