This small droplet moves against gravity. How to calculate its initial upward velocity exactly after pinch-off?
First you have to look closely at the video and realize that there is not one pinch-off, but two. The first event occurs at the bottom of the neck, near the droplet. After this point, surface tension causes the still-connected neck to begin to assume a spherical form, which pulls the center of the neck upwards. By computing the vertical velocities of every component of the neck, you can determine the overall velocity.
As the neck begins to contract, the overall force pulls the area around the connection point downwards, and eventually the second pinch-off occurs. At this point, knowing the vertical velocities of every part of the resulting blob you can calculate the velocity of the blob.