The second case:  the wetness of the pile is greater but remains below the saturation threshold. This situation is called funicular. There still exist liquid bridges between the grains but in addition certain pores (spaces between grains) are filled with liquid. The cohesion between the grains is greater because it is assured by the bridges and the liquid contained in the pores. The third case, called capillary: this time the pile of sand onto which the grains fall is saturated in liquid. There are no longer any bridges between grains but all the pores are filled with liquid. A liquid which is spread throughout the whole pile and whose pressure is lower than air pressure, which ensures that cohesion is present. Finally, in the fourth case, called slurry, the pile of sand is totally submerged in the liquid. In this case, the pressure of the liquid is equal to or greater than that of the air and there is no cohesion between the heap’s grains. If the extreme situations had already been studied, the intermediary cases have remained widely unexplored. 

The GRASP researchers thus established the conditions for these famous towers appearing – and falling – according to various parameters.

‘The first finding,’ explains Felipe Pacheco-Vazquez, ‘is that the towers only appear in funicular and capillary systems. In other words, it is necessary that a proportion at least of the pores situated between the grains are filled with liquid. That corresponds to a precise interval of the pile’s wetness threshold coefficient W. Below this value, it is too dry, whilst above it the system is saturated.’ The researchers also observed that the speed at which a tower grows diminishes exponentially as its height increases, up until the point when the structure collapses dramatically. And that the final height of the tower increases when the quantity of liquid at its base is reduced. To put it differently, for a tower to be high the wetness threshold coefficient of its base must not be too large, but closer to the phenomenon’s activation coefficient. From these findings it turns out that the phenomenon of self-building towers only occurs in funicular and capillary systems if three conditions are met:
-    It must be possible that the dry grains which fall on the pile can be captured by capillary bridges;
-    It must be possible for the liquid to be sucked up to the top of the structure;
-    The weight of the tower must be smaller than the cohesion forces at its base, which themselves depend on the base’s degree of wetness.