DYNAMIC SCALING BEHAVIOR OF A GROWING SELF-AFFINE FRACTAL INTERFACE IN A PAPER-TOWEL-WETTING EXPERIMENT

The dynamic scaling behavior of a growing self-affine fractal interfac e is examined in a simple paper-towel wetting experiment. A sheet of p lain white paper towel is wetted with red food dye solution, and the e volution of the interface is photographed with a 35-mm camera as a fun ction of time. Each snapshot is scanned and digitized to obtain the in terface height h(x,t) as a function of time and position. From these t he interface width w(L,t) is determined as a function of time t and sy stem size L. It is found that the interface width scales with system s ize L as w(L,t)similar to L(alpha) with alpha=0.67+/-0.04 and scales w ith time as w(L,t)similar to t(beta) with beta=0.24+/-0.02. It is also found that average height of the interface scales with time as [h]sim ilar to t(delta) with delta=0.33+/-0.02. These results are assessed in comparison with the predictions of theoretical models and the results of other relevant experiments.