Difference between revisions of "Profile of a large drop"
Line 11: | Line 11: | ||
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. | 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. | ||
− | [[Image:Dropshape1.jpg| | + | [[Image:Dropshape1.jpg|300px|thumb|right|Figure 1: Drop profiles for various contact angles and using the physical constants given in class.]] |
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 | 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 |
Revision as of 18:14, 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.