Consider the rising motion of a buoyant droplet in an otherwise quiescent fluid. For example, imagine that in a motionless fluid you place a droplet with smaller density than that of the surrounding fluid; due to the density difference the droplet will start moving upwards. Observe that the droplet motion is caused by the density difference only (and not by an external flow such as a shearing or pressure-driven flow.)

(e) Determine the scale for the droplets velocity.

(f) The rising motion of a buoyant droplet in an otherwise quiescent fluid creates flow in the surrounding fluid, especially near the droplet. Identify clearly the condition so that the fluid flow near the droplet is dominated by viscous effects (and not by inertia effects). Your answer should contain the density difference . Also identify a realistic situation where this condition is valid (e.g. for which fluids this condition is valid?)