See 2D fluid dynamics for explanations.

Yang Chenglin sent my kindly this remark
"I think when you advect something on staggered grid, different velocities should be used for different values. The velocity used in your code is just suitable for the density. To advect ux or uy, different velocity is needed. This can explain why your droplet simulation does not perform symmetrically enough (it flows right slightly)."

Karl Fredrickson made more accurate Droplet demo.