Sessile drop fluid oscillations and frequencies

[member 428835]

Hi PF!

I'm looking at a sessile drop of water in ambient air. The drop is plucked lightly, inducing surface oscillations. The fundamental frequencies $\lambda_i$ can be computed from spectral theory, and output complex values, say $\lambda_1 = 2+7i$.

Now, I simulate the experiment via CFD and find that the numerical frequency is $\lambda_{N1} = |2+7i| = \sqrt {53}$. Can anyone explain why the numerics output the magnitude of the fundamentals (eigenvalues)?

 

[eljose79]

Hi there,

Thanks for sharing your interesting research on sessile drops and surface oscillations. The difference between the fundamental frequency computed from spectral theory and the numerical frequency obtained from CFD can be attributed to the different methods used in each approach.

Spectral theory is a mathematical framework that deals with the properties of eigenvalues and eigenfunctions of linear operators. In this case, the fundamental frequencies $\lambda_i$ are the eigenvalues of the linear operator that describes the surface oscillations of the drop. These eigenvalues are complex numbers that contain both magnitude and phase information.

On the other hand, CFD is a numerical method that solves the Navier-Stokes equations to simulate fluid flow. In this approach, the fundamental frequency is obtained by solving for the roots of the characteristic equation of the linearized Navier-Stokes equations. This results in a purely real numerical frequency, which is the magnitude of the complex fundamental frequency obtained from spectral theory.

In summary, the difference between the two frequencies is due to the different approaches used in each method. While spectral theory provides a theoretical understanding of the fundamental frequencies, CFD gives a numerical approximation based on the fluid dynamics of the system.

I hope this helps to clarify the difference between the two frequencies. Good luck with your research!