Electrowetting simulation problem

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In summary, the conversation involves someone seeking help with solving an electrowetting problem using the finite element Galerkin method. The problem requires finding the shape of a liquid drop and the distribution of potential in an electrode and air. The person has calculated residuals and derivatives for potential and free surface, as well as a volume constraint residual for the liquid drop. They are specifically having trouble calculating derivatives for potential in air with respect to a certain variable. The person also includes equations and a question for clarification. They are asking for suggestions and have addressed the post to a specific person.
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HellRaiZer
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Hi,

I'm trying to solve an electrowetting problem, by using the finite element Galerkin method. The problem is to find simultaneously the shape of the liquid drop and the distribution of potential in electrode and air.
I've calculated the residuals for the potential u (Ru), in both air (Ru2) and electrode (Ru1) (as seen in the figure inside the attachement) as well as the derivatives with respect to uj (for the jacobian). I also have calculated the free surface (f(θ)) residuals (Rf), and their derivatives with respect to fj. Finally i have calculated the volume constraint residual (Rv) for the liquid drop, and its derivatives with respect to f.

I'm having a problem calculating the derivatives of Ru2 with respect to fj.

Ιn the attachment you can find all the equations i mentioned earlier. And the actual question (in the third page).

Do you have any suggestion on how this can be done ?

Thanks in advance.

HellRaiZer.

P.S. If this is the wrong forum please move it to the correct one.
 

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ping @BvU . Can you help with this spring cleaning post?
 

1. What is electrowetting simulation problem?

Electrowetting simulation problem is a computational challenge that involves predicting the behavior of liquids on a surface under an applied electric field. It is used to study the effects of electrowetting on different surfaces and to design new systems or devices that utilize this phenomenon.

2. Why is electrowetting simulation important?

Electrowetting simulation is important because it allows scientists and engineers to predict and understand the behavior of liquids on surfaces under an applied electric field. This information can be used to optimize the design of electrowetting-based systems and devices, such as digital microfluidic devices, lab-on-a-chip technologies, and electronic paper displays.

3. What are the challenges in electrowetting simulation?

One of the main challenges in electrowetting simulation is accurately modeling the complex interactions between the liquid, the surface, and the applied electric field. This requires sophisticated mathematical models and high-performance computing resources. Additionally, the properties of the liquid and the surface, such as surface tension and contact angle, can be difficult to measure and vary with different experimental conditions, making it challenging to accurately predict their behavior.

4. How is electrowetting simulation performed?

Electrowetting simulation is typically performed using computational fluid dynamics (CFD) software, which solves the Navier-Stokes equations to predict the behavior of fluids. The software takes into account the physical properties of the liquid, the surface, and the applied electric field to simulate the dynamics of the liquid droplets on the surface. It can also be combined with other simulation tools, such as molecular dynamics, to provide a more detailed understanding of the electrowetting phenomenon.

5. What are the applications of electrowetting simulation?

Electrowetting simulation has a wide range of applications in various fields, including microfluidics, optofluidics, and display technologies. It is used to design and optimize lab-on-a-chip devices for medical diagnostics, electronic paper displays for e-readers and smartphones, and microfluidic devices for chemical and biological analysis. It is also being explored for potential applications in energy and environmental technologies, such as energy harvesting and water treatment.

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