If low voltage is applied between two electrodes in dielectric medium (like air), they act like a normal condenser – store some little + and - charge at corresponding electrodes. Then current stops. Nothing else happens, no matter what
shape (including highly asymmetrical) electrodes have.

Fig 1

The only current flowing is a very small current due to few free ions always present in air due to ionizing radiation. When voltage is gradually increased, this little free ions become more and more accelerated when they fly between electrodes, because their speed can be roughly considered as v=E*k where E is field strength. The energy of collision with neutral molecules become greater. Finally at certain voltage their collision energy becomes enough to kick out more electrons from neutral molecules, so instead of one ion we get two.

Fig 2

These two are again accelerated and produce another two, and so we get an avalanche of ions. All the air between electrodes becomes conductive, we have a mix of + and – ions there.

To achieve  such avalanche everywhere between electrodes, we need a huge voltage V. However, if one of the electrodes is very thin or sharp, field near its surface is much higher then at the surface of other, wider, electrode (see red line showing relative E). That means that “E” sufficient to cause the ion avalanche near this electrode (starting with the distance where E>E0, see yelow area in the picture) can be achieved at much less voltage between electrodes. Such localized ionization is called corona discharge.

What happens if all air become ionized near one electrode (say for example +)?  Inside the small layer near electrode (yellow in the picture) we have a mix of + and – ions. Negative ions become neutralized very fast by nearby + electrode. What happens with positive once? They have no other way but to fly to the opposite (-) electrode, as they are attracted to it, and their (+) counterparts are gone. This way we get a continuous stream of (+) ions in the area between electrodes, as in Fig. 3. Now we have a current I flowing, called "corona discharge".

Fig 3

 Now  we have two regions:
 1) thin neutral plasma region with both ion signs present (corona) and
 2) mono-polar region, with single sign ions present - having sign of corona electrode

 One important result is that in mono-polar region all ions are moving  from corona wire to collector. But this ions are not only things which live in this area. There are huge number of neutral molecules there. Ions are colliding with them about 10^7 times a second. Energy of collision is not enough to blow the electron out of the molecule, as above. But something does happen. As ions bump their way between zillions of neutral molecules, it causes all molecules it collides with to gain a little speed in direction of wide electrode (See Fig 4). Momentum from flying ions is transmitted to outside air molecules.

Fig 4

But momentum is never lost, because of momentum conservation law. If ions give momentum to air, air gives momentum (opposite direction) to the ions. But ions are not free – they are driven by the “hand” of electric field, which itself is fixed in the frame of the electrodes. So, giving momentum to ions means in effect giving momentum to electrode frame.

To visualize this, try to imaging yourself in a boat placed in a water full of balls (ball-pull :-). This balls are the air-molecules. You have an oar in your hand (electric field), which at the end has another ball (that is the ion). You pull this ball forcefully through the bunch of balls,
just like field is puling the ion through the bunch of air molecules. What will happen with the boat? Right, it will move in direction opposite to that where you pull the ball-oar.

This is a simple logic, and it shows how directed flow of ions causes both electrodes to move together in direction opposite to ion flow, which means from wide to thin electrode.
Note that polarity of electrodes does not matter, as same logic can be used when “thin” electrode is (-) instead of (+). Another question is - how much movement will we get exactly, e.g. how much force will be applied to our “boat” at given current? This relation is derived here. More sofisticated question, like how much thrust you can achieve at given voltage, distance between electrodes, etc are treated in Lifter Articles Collection. If you are interested to make Life calculations for your particular Lifter configuration, or want to use lifter-equations for something else, see summary of lifter equations - Lifter Modeling Toolbox.