Structure and transport properties of liquid clusters in a drying porous medium

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). 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 beta(B)=0.99+/-0.03, the correlation length exponent nu=0.88, and the conductivity exponent mu=1.99+/-0.04 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 neighbors 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 invasion process are important for understanding the transport properties in a drying network.