There is no such thing as a collisionally modified Bohm criterion

The conventional equations describing plasma and sheath are examined over a full range of collisionality to determine the influence of collisionality on the ion equation of motion-that is, when the ion motion is essentially inertial and when it is collisional. When it is inertial in the sheath the Bohm criterion has been satisfied, while when the sheath is collisional the ions remain in equilibrium with the field all the way to the wall.