It has been discussed how the Reynold's number can be considered as the ratio of two types of forces and two types of time scales (i.e. inertia & viscous). The goal of this problem is to do a similar dimensionless analysis for the Bond number, which describes interfacial dynamics and deformation owing to external flow and gravity.

The Bond number is defined as Ba = Apg L/, where Ap is the density difference between the droplet fluid and the surrounding fluid, g the gravitational acceleration, and the length scale of the drop. (C) Show that the Bond number is the ratio of two types of forces; in particular, the net gravitational forces and surface tension forces. Identify the scaling of these two forces as well as their units. Note that I refer to the net gravitational forces to show that the interfacial dynamics is affected by both gravity and buoyancy, this is also reflected in the definition of the Bond number which contains Ap and not the density itself. (d) Show that the Bond number is the ratio of two types of time scales; in particular, the (net) gravitational time scale and the surface tension time scale, and thus identify the (net) gravitational time scale