The influence of temperature gradients on the drying of water-saturated porous networks has been studied. We have focussed on the influence of the temperature on the drying process via the equilibrium vapour density r0, because this is the most sensitive parameter with respect to variations of the temperature T. We have used a 2D model, which accounts for both capillary and buoyancy forces. Invasion events by air or water are handled by standard rules of invasion percolation in a gradient (IPG). Vapour fluxes are calculated by solving a discretized version of the Laplace equation. In the model the temperature T varies linearly from the open side T0 to the closed side TL. The temperature gradients strongly influence the cluster evolution during the process, because they facilitate vapour transport through wet regions, see figure 1.
  




Figure 1  The influence of temperature gradients on the drying process when gravity is of little importance. For three different temperature gradients (from left to right: T0> TL, T0= TL and T0< TL the water distributions at three different saturation stages (from top to bottom: S=0.91, 0.65 and 0.26) are shown. The open side (x=0) of the system is always at the bottom.

When T0< TL the movement of the front is inhibited and dry patches develop after a certain time at the closed side. When T0> TL the front movement is enhanced and the air ingress in the wet region behind the front is inhibited. The corresponding drying curves are shown in figure 2.
  

Figure 2 – The drying curves (saturation S versus time t) of systems with different temperature gradients: T0> TL, T0= TL and T0< TL. The initial parts of the curves are also plotted in the insert, but now the time is rescaled with the equilibrium vapour density at the open side of the system.

The behaviour of 3D systems differs from that of 2D systems, because the point where air percolates the system and the point where the water network breaks up in isolated clusters do not coincide. Before the latter fragmentation point the temperature will mainly influence the drying rates. After this point also the water distribution becomes sensitive to the temperature profile.