The first part of the description for Blink reads:
Roll a d20 at the end of each of your turns for the duration of the spell. On a roll of 11 or higher, you vanish from your current plane of existence and appear in the Ethereal Plane (the spell fails and the casting is wasted if you were already on that plane)....
If our wizard cast Blink at the start of an encounter and was then knocked unconscious, would she still go to the ethereal plane as part of the effect of the Blink spell?