Electrohydrodynamic pump and equations

[hanson]

Hi all. I am reading a paper about electrohydrodynamic pump and I encounter the following equation. Can anyone explain me the physicl meaning of these two equations? I find no clue in understanding them.

The first equation is from the manipulation of Maxwell's equation in an electroquasistatic system (BTW, what i an electroquasistatic system?)

The author says that from the drive term on the right hand side of the first equation, it can be concluded that a requirement for the existence of free charge is the presence of a spatial gradient in conductivity or permittivity. Free charge injected into a region without such a gradient would relax in a time characterized by the charge relaxation time epsion/sigma.

Can anyone provide me some of the background knowldege and explain me why the author says so?

 

[Achy47]

Hello! As a scientist with knowledge in electrohydrodynamics, I can help explain the physical meaning of the equations and the concept of an electroquasistatic system.

First, let's define an electroquasistatic system. This refers to a system where the electric field changes slowly with respect to time, meaning that the displacement current (the term on the right hand side of the first equation) can be neglected. This assumption simplifies the equations and is often used in electrostatics and electromagnetism problems.

Now, let's look at the first equation, which is derived from Maxwell's equations. It relates the electric field (E) to the conductivity (sigma) and permittivity (epsilon) of the material. The drive term on the right hand side represents the source of the electric field, which could be a voltage or charge distribution.

The author is saying that in order for there to be free charge (Q) in a region, there must be a spatial gradient in either the conductivity or permittivity. This means that the material must have a non-uniform distribution of these properties. If there is no gradient, the free charge injected into the region will quickly relax (disappear) due to the material's properties.

The time it takes for the free charge to relax is characterized by the charge relaxation time (epsilon/sigma). This is because the permittivity and conductivity determine how quickly the electric field can be established and how easily charges can move through the material.

I hope this helps clarify the physical meaning of the equations and the concept of an electroquasistatic system. Let me know if you have any further questions.

 

[ravenprp]

The second equation is a simplified form of the conservation of mass equation for an incompressible fluid flow. It describes the relationship between the velocity of the fluid and the pressure gradient, with the addition of an electric field term. This term represents the contribution of electrostatic forces on the fluid particles, which can be used to manipulate and control the flow of the fluid.

In an electroquasistatic system, the electric field and the fluid flow are both in quasi-equilibrium, meaning that they do not change significantly over time. This allows for the use of simplified equations, such as the one mentioned above, to describe the behavior of the system.

The drive term in the first equation represents the force that is driving the fluid flow, which in this case is the electric field. The author is stating that for there to be a presence of free charge, there must also be a gradient in either the conductivity or permittivity of the medium. This gradient is necessary for the electric field to have an effect on the fluid particles and cause them to move.

The charge relaxation time, epsilon/sigma, refers to the time it takes for the charge to dissipate in the medium. If there is no gradient in conductivity or permittivity, the charge will quickly relax and there will be no significant effect on the fluid flow.

Overall, the equations describe the relationship between electric fields and fluid flow in an electroquasistatic system, and highlight the importance of gradients in the medium for the manipulation of fluid flow using electrohydrodynamic pumps. I hope this helps to clarify the physical meaning of the equations.