What happens if two parallel square plates approach each other in a gas?

Imagine two solid massive parallel square plates, each with side length $l$ and mass $m$, approaching each other along the line that connects their centers of mass. At the moment we look at them they are separated by a distance $s_{in}gt l$ and have a velocity $v_{in}$. They are submerged in a gas. At any moment they have the same velocity wrt to the gas. Both plates are subjected to a friction force that opposes their velocity. Considered apart, they will decelerate until their velocity is zero. Is it possible that the velocity of the plates is reversed without the plates actually touching each other before coming in contact (because of the increase in pressure between them)? Or will they always collide (touch each other)?