The propagation and roughening of a fluid-gas interface through a disorderedmedium in the case of capillary driven spontaneous imbibition is considered.The system is described by a conserved (model B) phase-field model, with thestructure of the disordered medium appearing as a quenched random field$\alpha({\bf x})$. The flow of liquid into the medium is obtained by imposing anon-equilibrium boundary condition on the chemical potential, which reproducesWashburn's equation $H \sim t^{1/2}$ for the slowing down motion of the averageinterface position $H$. The interface is found to be superrough, with globalroughness exponent $\chi \approx 1.25$, indicating anomalous scaling. Thespatial extent of the roughness is determined by a length scale $\xi_{\times}\sim H^{1/2}$ arising from the conservation law. The interface advances byavalanche motion, which causes temporal multiscaling and qualitativelyreproduces the experimental results of Horv\a'ath and Stanley [Phys. Rev. E{\bf 52} 5166 (1995)] on the temporal scaling of the interface.
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机译：考虑了毛细管驱动的自吸过程中流体-气体界面通过无序介质的传播和粗糙化。该系统用守恒（模型B）相场模型描述，无序介质的结构表现为淬灭随机字段$ \ alpha（{\ bf x}）$。通过在化学势上施加非平衡边界条件来获得液体流入介质的能力，该条件重现了Washburn方程$ H \ sim t ^ {1/2} $，用于减慢平均界面位置$ H $的运动。发现该接口超级粗糙，全局粗糙度指数为$ \ chi \ approx 1.25 $，表明缩放异常。粗糙度的空间范围由由守恒定律引起的长度尺度$ \ xi _ {\ times} \ sim H ^ {1/2} $确定。界面通过雪崩运动前进，这导致时间多尺度化，并且定性地再现了Horv \ a'ath和Stanley的实验结果。 Rev. E {\ bf 52} 5166（1995）]。
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