Particulate matter in air is generally bad for your lungs, and it can be a problem under some other circumstances, like in hospital operating rooms, biology labs, or semiconductor or hard disk clean rooms.
One way to remove particulates from air is to filter it by passing the air through a thin sheet with a lot of small holes in it. Particulates that are bigger than the holes won’t pass at all; some fraction of smaller particulates will stick to the filter. Ideally, all the holes would be the same size, because if there are a fair number of really big holes, most of the air will go through them.
The particulates that are of most concern for health are in the categories PM10, which is 2.5–10 μm in diameter, and PM2.5, which is 1–2.5 μm in diameter. So it would be useful to have a sheet of material that was full of holes under 1 μm in diameter.
A spark of a well-controlled energy applied to a thin sheet of metal,
such as gold leaf or the metallization layer on a sheet of Mylar,
should vaporize a well-controlled amount of metal in a pretty round
hole, requiring about 14 kJ/g to vaporize aluminum (((2470 - 20) K
24.20 J/mol/K + 10.71 kJ/mol + 284 kJ/mol) * 27.0 g/mol). A
cylindrical hole of 1 μm radius through an 0.5 μm layer of aluminum
metallization would amount to about 400 attoliters or about a picogram
of aluminum, requiring about 15 nJ of spark energy.
Gold leaf is probably more practical, since it can be free-standing at as little as 0.1 microns thick. I’m going to assume that the energy needed to vaporize an area of gold leaf is close to the energy to vaporize the same area of aluminum metallization, because gold is thinner, but denser, and with higher specific heat and heat of fusion.
Getting a spark that’s only 15 nJ in air may be actually kind of tricky, because Paschen’s Law has a minimal voltage of about 300 volts to start an arc in air. It’s tough to get parasitic capacitances below about 10 pF, and at 300 V, that holds about 450 nanojoules. So the hole you’re going to blow in the metal with just the parasitic capacitance, if you go around charging things up to 300 volts and then touching an electrode to the sheet, that hole will be about six microns across.
As an alternative, you could maybe use an inductor and strike a spark like you were using a stick welder: first bring the electrode into contact with the workpiece, allowing current to flow through an inductive load, then move it away, striking an arc which continues until the inductor’s energy is dissipated.
How much current can you have flowing without heating things up? A 34-gauge wire is 160 microns across (thus a cross-sectional area of 20 000 square microns) and can handle 300 mA. If your area of contact is, say, 100 square microns, then the same current density would be 0.5% of that, or 1.5 mA. Let’s say 1 mA to be sure it’ll work. ½LI² = 15 nJ at I = 1 mA if L = 2·15 nJ/(1 mA)², which comes out to a very conveniently large 30 millihenries. It’s easy to build a circuit with less than that amount of parasitic inductance.
The most popular off-the-shelf inductor in this range at Digi-Key is the Murata 13R336C inductor: "33mH Unshielded Wirewound Inductor 60mA 68 Ohm Max Radial". It costs 59¢. It’s ferrite-cored, and craps out at a couple hundred kilohertz; I’m not sure what would happen if you try to break the contact faster than ten microseconds, but I suspect that you lose most of the energy to core losses. If that happens, that’s a problem.
An air-core coil with 10 mm diameter and 20 mm length has 25 mH once it gets to 2500 turns, which is totally feasible to wind with magnet wire. But I suspect you’ll have enough parasitic capacitance to prevent it from responding within less than a few microseconds.
So you can build a power supply circuit that provides up to 1 mA at some low voltage (say 1–10 V), run it through a 30 mH air-core inductor, hook that up to your graphite electrode, and you’re in business. Then you just have to move the electrode away from the metal sheet fast enough that the inductor’s energy is mostly dissipated in the arc and not in the resistances of the rest of the circuit.
(Will 1–10 V be enough to drive a milliamp through such a small point contact? I think so.)
By peppering a sheet of metal with sparks of well-controlled energy, you should be able to get the sheet up to 1% hole even without controlling the hole position without a significant number of “hole collisions” producing oversized holes. Even up to about 10% hole, almost all the “hole collisions” will produce holes that are only oversized in one dimension. If you can control the hole position closely, then with hexagonal close-packing you can get arbitrarily close to 3√3/2π ≈ 82.7% hole; if you reach that limit, the sheet falls apart into tiny triangles.
You can use the same spark approach to blow holes up to nearly a millimeter in diameter in the metal sheet, with fairly precise control of hole size (under 1% error, say). This provides a way to produce very fine-grained “mesh” sieves with precisely controlled hole sizes, which in theory could separate particles up to a particular size with very high precision, at least if they don’t stick to the filter.
Separating particles into precisely graded size groups is the first step to being able to separate them by density and morphology with an air updraft.