Usage Of Static Electricity To Remove Dust?
Calculation of what you will require will involve, as one of my fellow members has commented, trial and error to achieve, but it is certainly possible to achieve something along the lines of what you hope, though I recommend it as a continual process rather than a periodic one.

First I would recommend calculating the surface area of your respective meshes, that way you will have an indication of charge density of the mesh. I would do this because that will allow you to find a suitable value and have a point of comparison when varying different parameters - i.e. applied voltage and / or distance between meshes.

I gather from your description that your two meshes are aimed at preventing dust from passing through the finer mesh. Personally I would suggest that rather than allowing dust to deposit on this mesh, and then periodically attempting to purge it with a HVDC application, that you instead charged both plates with opposing polarities as a continual process, thereby attracting dust to the coarse mesh (easier to clean), and repelling it from the finer mesh. This should in fact reduce the quantity of dust passing through the fine mesh. Letting deposit build on the fine mesh may present issues in addition to airflow, including greater quantity of particulate passing through the fine mesh, as well as an inability to purge the deposit once it has been deposited due to adhesion and the cancelling of charge when it is deposited. A static field applied to the inner or both meshes (even better) would be more effective.

Additionally, by using a polymer mesh pre-filter (or other suitable material). Through friction, the dust particles that come into contact with the pre-filter should possess greater charge and similarly, any un-charged particles that contact the pre-filer should also become charged - which should increase the effectiveness of your setup, whatever it may be for.

This is actually a rather big issue for sensors in space (an area I used to work in), and among other publications, and although it is aimed at clearing a flat area rather than a filter, this one from NASA may be useful to you: NASA Paper

There also exist a number of patents for multi-layer options, one of which appears to include my suggestion for a polymer pre-filter: US5336299 

All the best.