Soriano Jordi, Ortín Jordi, Hernández-Machado A
Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Avenida Diagonal 647, E-08028 Barcelona, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 2):056308. doi: 10.1103/PhysRevE.67.056308. Epub 2003 May 21.
We report experimental evidence of anomalous kinetic roughening in the stable displacement of an oil-air interface in a Hele-Shaw cell with strong quenched disorder. The disorder consists of a random modulation of the gap spacing that is transverse to the growth direction (tracks). Experiments were performed by varying the average interface velocity and the gap spacing, and measuring the scaling exponents. The following values of the scaling exponents were obtained; beta approximately 0.50, beta* approximately 0.25, alpha approximately 1.0, alpha(loc) approximately 0.5, and z approximately 2. When there is no fluid injection, the interface is driven solely by capillary forces, and a higher value of beta of approximately beta=0.65 is measured. The presence of multiscaling and the particular morphology of the interfaces, characterized by large height differences that follow a Lévy distribution, confirms the existence of anomalous scaling. From a detailed study of the motion of the oil-air interface, we show that the anomaly is a consequence of different local velocities on the tracks plus the coupling in the motion between neighboring tracks. The anomaly disappears at high interface velocities, weak capillary forces, or when the disorder is not sufficiently persistent in the growth direction. We have also observed the absence of scaling when the disorder is very strong or when a regular modulation of the gap spacing is introduced.
我们报告了在具有强淬火无序的Hele-Shaw盒中油-气界面稳定位移时反常动力学粗糙化的实验证据。这种无序由垂直于生长方向（轨迹）的间隙间距的随机调制组成。通过改变平均界面速度和间隙间距并测量标度指数来进行实验。获得了以下标度指数值：β约为0.50，β*约为0.25，α约为1.0，α(loc)约为0.5，以及z约为2。当没有流体注入时，界面仅由毛细力驱动，并且测量到更高的β值，约为β = 0.65。多标度的存在以及界面的特殊形态，其特征是高度差异大且遵循Lévy分布，证实了反常标度的存在。通过对油-气界面运动的详细研究，我们表明这种反常是轨迹上不同局部速度加上相邻轨迹之间运动耦合的结果。当界面速度高、毛细力弱或无序在生长方向上不够持久时，反常现象消失。我们还观察到当无序非常强或引入间隙间距的规则调制时不存在标度。
