# Sessile drop fluid oscillations and frequencies

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In summary, sessile drop fluid oscillations and frequencies refer to the behavior and vibrations of a liquid droplet that is resting on a solid surface. These oscillations occur due to the surface tension and other factors, and their frequencies can be affected by various parameters such as droplet size, viscosity, and surface tension. Understanding and controlling these oscillations is important in various applications, such as in printing technologies and droplet-based microfluidics.
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)?

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!

## 1. What are sessile drop fluid oscillations and frequencies?

Sessile drop fluid oscillations and frequencies refer to the small, rapid movements of a liquid droplet that is resting on a solid surface. These oscillations occur due to the surface tension of the liquid and can be measured by the frequency of the droplet's movements.

## 2. What factors affect the oscillations and frequencies of sessile drops?

The oscillations and frequencies of sessile drops can be affected by various factors such as the surface tension of the liquid, the viscosity of the liquid, the size and shape of the droplet, and the properties of the solid surface it is resting on.

## 3. How are sessile drop fluid oscillations and frequencies measured?

Sessile drop fluid oscillations and frequencies can be measured using high-speed cameras or laser interferometry techniques. These methods allow for precise measurements of the droplet's movements and frequency.

## 4. What applications do sessile drop fluid oscillations and frequencies have?

Sessile drop fluid oscillations and frequencies have various applications in fields such as surface science, material science, and biotechnology. They can provide insights into the properties of liquids and surfaces, and can also be used in the development of new materials and technologies.

## 5. How can understanding sessile drop fluid oscillations and frequencies benefit society?

Understanding sessile drop fluid oscillations and frequencies can lead to advancements in various industries, such as the development of new materials with improved properties, more efficient drug delivery systems, and better understanding of natural phenomena such as raindrop formation. It can also contribute to the improvement of everyday products and technologies.

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