Getting energy from kinetic motion of air particles

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ZawL
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I am proposing a piece of equipment a bit similar to Crooke's radiometer with the aim of using kinetic motion of air particles to rotate the mill, without need for an external source of EM radiation.

Instead of flat vanes as in Crooke's radiometer, I propose 3-dimensional vanes in the shape of a pyramid, cone or frustrum. The idea is for one side of the vane to have a larger surface area than the other side so that more of the air particles will hit the larger side and create a net force that causes the mill to rotate.

I would like to know whether this setup would theoretically produce rotation of the mill, however tiny. And if not, then why not? I realize there is some complication with the direction at which molecules hit the different surfaces which could cancel out any factor due to larger surface area. Does this always produce a net force of zero regardless of what shapes the two surfaces are? My setup obviously does not work as well under a partial vacuum as in Crooke's radiometer and could actually work better under higher air pressure.
 
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A picture would really help. But yes, if it presents a different surface area on one side than the other, it will rotate.

The thing below (used to scare away birds) has movable vanes, but it depends on the same principle.