10. What happens to a gas when it is changed from moving in a straight path to a curved path?

            When a gas is flowing the velocity of each particle can be decomposed into a flow velocity and a thermal velocity. For example, consider two particles with a flow velocity  and with a thermal velocity magnitude of  (the rms speed) where the particles have their thermal velocity parallel to the flow velocity with one particle thermal velocity in the same direction and the other particle thermal velocity in the opposite direction of the flow velocity as shown below for particle A and particle B.

This particle A has a much larger absolute velocity than particle B. If the gas with flow velocity   is forced to go in a curved path of radius R then the force required to make A take the curved path is  while for particle B it is . What occurs is that particles with thermal velocity components in the flow direction will migrate outward and the particles with thermal velocity components opposite the flow velocity will migrate inward toward the center of curvature.

            As a result of this outward migration the flow velocity of the outer gas will increase while the flow velocity of the inner gas will decrease for this new mix of particles. The net result of the outer increase and the inner decrease produces additional curvature in the path. This mechanism is believed to be a fundamental part of the phenomenon of hurricanes, tornadoes, dust devils, gas turbulence (in general), and in vortex tubes.

       After a constant radius of curvature is achieved it is not clear what the distribution is. For example, in a volume fixed to a frame rotating with the gas the distribution may still be Maxwell-Boltzmann except with the proviso that the particle paths between collisions will be curved instead of straight. Further, after a steady state curved flow is obtained and the gas is in an equilibrium state one could ask why the particles with forward thermal components do not continue migrating outward and those with aft thermal components continue to move inward. They, of course, do not continue the migration and the probable reason is that the faster (forward moving) particles have more collisions than the apt moving ones. This differs from when curvature was initiated when nothing was different except that a transient curved path began.

            In this theory it is assumed that statistical perturbations occur in the background with the end result of forming stable assemblages of particles which are not homogenous. Further, for practically all of these inhomogeneous assemblies we assume the local distribution of particles is Maxwell-Boltzmann.