Weakly nonlinear theories in electrohydrodynamics

In summary, the conversation discusses a problem with a numerical solution for a Benjamin-Ono like equation that does not match an analytical solution when the nonlinear term is set to zero. Possible causes mentioned include issues with boundary conditions, numerical methods, data, and the derived equation itself. Suggestions for resolving the discrepancy include trying different boundary conditions, analyzing the numerical solution for errors, and further examination of the equation and its physical interpretations.
  • #1
hunt_mat
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I have been working on the problem of electrified fluid flow down a channel with a moving pressure distribution. I have derived an equation which describes the free surface of said fluid flow which is a Benjamin-Ono like equation. I have a numerical solution for this equation and it gives the sort of pictures that I expect.

I can ignore the nonlinear part of the equation and I can an equation which I can solve analytically via Fourier transforms. Here is what is winding me up: When I set the nonlinear term to zero in my numerical code and compare it to my analytical solution, they should match but they don't, it's almost a factor of 10 out.

Has anyone come across this sort of thing happening before? Is it something I've done wrong?

Any suggestions are always welcome.

Mat
 
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  • #2
hematically, it could be an issue with the boundary conditions. Maybe you need to impose a different set of boundary conditions for the linear case compared to the nonlinear case. It could also be a numerical problem, such as the method you are using to solve the equation numerically. Or it could be a problem with the data you're using, like the initial and boundary conditions. It could even be that the equation you derived is wrong. It might be useful to try running the numerical simulation with a few different sets of boundary conditions and seeing if the results change. If they do, then you can narrow down which boundary condition is causing the discrepancy. You can also look at the numerical solution and see if there are any irregularities or artifacts which suggest a numerical error in your solution. Finally, it might be worth doing some more analysis on the equation you derived. Are there any other terms which could be influencing the solution? Are there any simplifying assumptions which could be made? It might be useful to look at the physical interpretations of the equation as well, to see if any of them contradict the numerical solution.
 

Related to Weakly nonlinear theories in electrohydrodynamics

1. What is electrohydrodynamics?

Electrohydrodynamics (EHD) is a branch of physics that studies the effects of electric fields on the motion of fluids, such as liquids and gases. It is a combination of electromagnetics and fluid dynamics, and is used to understand and control the behavior of electrically charged fluids.

2. What is the significance of weakly nonlinear theories in electrohydrodynamics?

In electrohydrodynamics, weakly nonlinear theories are used to describe the behavior of fluids in which the effects of nonlinearity are small. This is important because many physical systems, such as biological membranes and microfluidic devices, exhibit weakly nonlinear behavior. Understanding and predicting these behaviors is crucial for designing and optimizing such systems.

3. How do weakly nonlinear theories differ from linear theories in electrohydrodynamics?

Linear theories assume that the response of a fluid to an electric field is directly proportional to the strength of the field. In contrast, weakly nonlinear theories take into account the nonlinear relationships between the electric field and the fluid's response. This allows for a more accurate description of the fluid's behavior in systems with strong electric fields.

4. What are some applications of weakly nonlinear theories in electrohydrodynamics?

Weakly nonlinear theories have a wide range of applications in various fields, including microfluidic devices, electrophoresis, and the study of biological membranes. They are also used in the development of new technologies, such as electrospinning for the production of nanofibers and electrospray for the formation of aerosols.

5. Can weakly nonlinear theories in electrohydrodynamics be experimentally verified?

Yes, weakly nonlinear theories can be experimentally verified through various techniques, such as particle image velocimetry, micro-particle tracking, and electrical impedance spectroscopy. These experiments help to validate the assumptions and predictions made by weakly nonlinear theories and provide a better understanding of the underlying physics.

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