Dynamical scaling of fragment distribution in drying paste

Crack patterns of drying paste and their statistical properties are investigated through smoothed particle hydrodynamics, which is one method for solving continuum equations in the Lagrangian description. In addition to reproducing a realistic crack pattern, we also find that the average area of a fragment decays inversely with time in the case of linearly increasing desiccation stress. We find that the distribution can be scaled with the average area of the fragment over the corresponding time, even though the distribution function of the fragment area changes the functional form during evolution.

Figure 1

The geometry of the paste under simulation is a square with dimensions of $L\times L$ and a thickness of $H$.

Figure 2

Snapshots of the time evolution of the stress of the paste in the simulation. The color shows the magnitude of the local average stress; the black region represents cracks.

Figure 3

Time evolution of the average area of fragments, ${\langle S\rangle }_t$. The reciprocal of ${\langle S\rangle }_t$ is plotted as a function of time, $t$.

Figure 4

Calculated areal distribution of fragments. Distributions from $t=90.0$ to $t=300.0$ are shown.

Figure 5

Area distributions scaled according to individual averages of the area. The horizontal axis represents the scaled area, $X=S{\langle S\rangle }_t$. The time range is the same as that shown in Fig. 4.

Figure 6

Area distributions scaled according to individual averages of the area. The same as Fig. 5, but for the initial relaxation of the distribution discarded.