There are many forces and factors that affect whether or not a drop of water will adhere when it contacts a solid substance or coalesce when it contacts another droplet of water. These factors include the time of contact, the geometry of the surface and the drop, as well as the drop’s viscosity, pressure, velocity and surface tension. The equation that helps us to predict exactly how a drop of water will act in a given situation is so complex that it is not very useful. However, certain relationships have been developed that give us a good idea of how a drop of water will behave.

The first of these relationships is known as the Bond number. This number looks only at the effects of gravity and pressure on a drop. This number is defined as:

where is the density of water, g is the local acceleration due to gravity, R is the radius of the drop and is the surface tension of water. If the Bond number is much greater than 1, then gravity will dominate whether or not the drop will coalesces or adhere. This means that time of contact against a surface/drop will be so long that the squeeze film will be pushed out and coalescence will occur. If the Bond number is much smaller than 1, surface tension will dominate the system and coalescence/adherence will not be guaranteed.

This is why our experiment must be tested in zero gravity or near to it…with the local acceleration due to gravity on earth being a fairly constant and surface tension of water being relatively small coalescence/adherence will always occur.

Another important relationship is known as Weber number. This number considers the effect of inertia and pressure on coalescence/adherence of a drop. This number is defined as:

where u is the normal velocity of the drop. If this number is much greater or much less than one then adherence/coalescence is almost guaranteed…according to the affects of velocity and surface tension. However, right around one it is not certain whether or not a drop will coalesce or adhere.

It is important to remember that this value is a normal velocity…thus if a drop is traveling at u 0 as shown below,

It is also important to realize that the effect of the squeeze film is assumed unimportant in the derivation of the Weber number. Thus if a significant squeeze film exists coalescence may not occur even though the Weber number indicates it should.

To take into account the squeeze film, another number is needed, one that looks at the effects of viscous forces and pressure on the drop. This number is called the Capillary Number and is defined as:

where u is the tangential velocity ( in the example above) of the drop and is the distance between the drop and the surface it is to contact. If the Capillary Number is much greater than one, coalescence will not occur. If it is much smaller than one then coalescence is favored. If the drop is rotating, an even more substantial squeeze film develops that shows up in the equation by increasing the overall tangential velocity by R ω where ω is the angular velocity of the drop…making coalescence even less likely.

The greatness of this number could be what prevents the skipping rain drop from joining the puddle, until gravity dominates the system and coalescence occurs anyway. However in space, gravity will never dominate the system…and the drop could continue to slide along a surface without adhering!

*****Team members! Ok, the important thing to take from this is that we can focus on any one area we want to test….we could simply set it up so viscous effects are minimal (by making sure the Capillary Number is always much less than one) and just test the surface tension affects by playing with the Weber number or vice versa. We could also set it up (choosing our velocity and such) so that it is in the close to one “grey area” where coalescence is neither guaranteed nor impossible and try and make something that will catch drops anyway…which from the video clips Mark showed me is quiet a challenge gravity dominating the system. So think about that…when we tell Mark what it is we really want to test, he will give us the range of Weber/Capillary numbers that we need to be within in order for our test to really do that. With that range, we can design the specifics.