The structure and transport properties of drying water clusters in porous media have been studied with a site-bond invasion percolation (IP) model. In this model an invader (air) enters a lattice (porous network) filled with defender (water) via a sequence of invasion steps. The decision to invade a site (pore) is made on the basis of the resistance of the bonds (throats). A simulation run is terminated the water cluster breaks up in isolated clusters (the fragmentation point). At this point the structure and conductivity (diffusivity) of the water network have been analysed.

Figure 1 – The defender fluid at the fragmentation point in an L=70 system: all sites filled with defender fluid (top), the spanning network (middle) and its backbone (bottom).

It is found that the backbone of the defender network and its transport properties are the same as in ordinary percolation (OP). In  particular the strength exponent of the backbone Db=0.99, the correlation length exponent n =0.88 and the conductivity exponent m=1.99 are the same as in OP. The total network deviates from networks generated with OP: on short length scales the formation of branches is suppressed, because pores with many empty neighbours are preferentially invaded. The differences between our IP results and the outcomes of OP are a consequence of the invasion mechanism. This makes clear that the details of the air invasion process are important for understanding the transport properties in a drying network.