I have a simple fluid statics problem of a liquid drop, resting on a stationary flat solid surface with a static gas of constant pressure above. The density in both the gas and liquid are constant. To solve this system we drop it into solving the 2d system (in the z-r plane) and using axisymmetry to give us the full solution
Given static we can assume that the velocity vector u is symmetrically zero. Which gives the system to be given by
$$p= \rho_{l} gz$$ $$\sigma H = p_{g} -\rho_{l} gz$$
With subscripts l and g referring to liquid/gas perameters respectively and H being the mean curvature, the standard expression for a body of rotation being
$$\frac{1}{R\sqrt{1+R'^{2}}} - \frac{R''}{\sqrt{1+R'^{2}}}$$
In order to advance to numerically solve this problem I first need to normalize it. But I have no real idea how to go about doing so, there is no characteristic velocity scale and I don't really know how to deal with the mean curvature.
Any help, or being pointed to somewhere I can find help, is appreciated.
Mike,
This is not an equation without an equals sign:
$$ \frac{1}{R\sqrt{1+R'^2}} - \frac{R''}{\sqrt{1+R'^2}} $$ What are you trying to solve for? Curvature of drop? How is the 'equation' in R related to the previous two?
Thanks,
Paul Safier