Continuity equation of the electric field

[speaknow]

According to the continuity equation of the electric field (i.e., ▽·Ε = 0) a decrease in cross-section area will increase the electric field strength, Why is that?

 

[Vanadium 50]

You're going to have to be more specific. Ddecrease the cross-section area of what exactly?

 

[speaknow]

Thanks for your reply, in previous studies on electroporation reducing the cross-section area of microchannels (microfluidics)used for cell trapping will have an amplification on the electric field strength. I want to understand the equations behind this phenomena.

 

[Vanadium 50]

You're going to make us slowly squeeze this out of you bit by bit, aren't you.

OK, for some reason that you won't tell us, possible related to the U's in the picture that you won't define, all the electric field lines from one region go into the other. Since for some other reason you won't tell us, they are excluded from the central region except for the joining channel, since the number is constamt and the area is smaller, the density has to go up.

 

[speaknow]

UEK and UDEP are the electrokinetic and dielectrophoretic velocities, respectively. UDEP,s and UDEP,n represent the dielectrophoretic velocity components tangential and normal to a streamline, respectively. The background shows the electric field contour (the darker the higher) and the electric field lines around the constriction region in the absence of cells.