3.4.2 The ratios of various time scales

Now we can look at several time ratios. The ratio of solidification time to filling time

(3.24)

where

   Reynolds number   


Stefan number 

Here we augment the discussion on the importance of equation (). The ratio is extremely important since it actually define the required filling time.

(3.25)

At the moment, the ``constant'', , is unknown and its value has to come out from experiments. Furthermore, the ``constant'' is not really a constant and is a very mild function of the geometry. discuss the geometry shape effects on this constant Note that this equation also different from all the previously proposed filling time equations, since it take into account solidification and filling process into account¹⁷.

The ratio of liquid metal conduction characteristic time to characteristic filling time is given by

(3.26)

The solidification characteristic time to conduction characteristic time is given by

(3.27)

The ratio of the filling time and atomization is

(3.28)

Note that , in this case, is the thickness of the gate and not of the die cavity.

(3.29)

which means that if atomization occurs, it will be very fast compared to the filling process.

The ratio of the dissipation time to solidification time is given by

(3.30)

this equation yields typical values for many situations in the range of indicating that the solidification process is as fast as the dissipation. It has to be noted that when the solidification progress, the die thickness decreases. The ratio, , reduced as well. As results the last stage of the solidification can be considered as a pure conduction problem as was done by the ``english'' group.