Dynamic scaling behavior of a growing self-affine fractal interface in a paper-towel-wetting experiment.

Abstract

The dynamic scaling behavior of a growing self-affine fractal interface is examined in a simple paper-towel-wetting experiment. A sheet of plain white paper towel is wetted with red food dye solution, and the evolution of the interface is photographed with a 35-mm camera as a function of time. Each snapshot is scanned and digitized to obtain the interface height h(x,t) as a function of time and position. From these the interface width w(L,t) is determined as a function of time t and system size L. It is found that the interface width scales with system size L as w(L,t)\ensuremath{\sim}${\mathit{L}}^{\mathrm{\ensuremath{\alpha}}}$ with \ensuremath{\alpha}=0.67\ifmmode\pm\else\textpm\fi{}0.04 and scales with time as w(L,t)\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{\beta}}}$ with \ensuremath{\beta}=0.24\ifmmode\pm\else\textpm\fi{}0.02. It is also found that average height of the interface scales with time as 〈h〉\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{\delta}}}$ with \ensuremath{\delta}=0.33\ifmmode\pm\else\textpm\fi{}0.02. These results are assessed in comparison with the predictions of theoretical models and the results of other relevant experiments. \textcopyright{} 1996 The American Physical Society.