This appears to have been entirely possible previously but in the latest Character Animator Preview build (4) I can not get particles to flow upwards.
I apply the Particles behaviour to the (in this case) Bubble layer, choose Cannon, Continuous Mode, and point the dial up, but still in live mode the bubbles sink to the bottom of the screen.
What am I doing wrong?
Try increasing the velocity.
FWIW, in response to some similar requests we've experimented with some additional options to control the direction and force of gravity. If those pan out, it may provide a better answer for certain kinds of particles that one would want to drift upward (bubbles, for example) instead of needing to boost velocity to outrun the (in Preview 4) fixed downward gravity.