Understanding the distribution of interfacial separations between contacting rough surfaces is integral for providing quantitative estimates for adhesive forces between them. Assuming non-adhesive, frictionless contact of self-affine surfaces, we derive the distribution of separations between surfaces near the contact edge. The distribution exhibits a power-law divergence for small gaps, and we use numerical simulations with fine resolution to confirm the scaling. The characteristic length scale over which the power-law regime persists is given by the product of the rms surface slope and the mean diameter of contacting regions. We show that these results remain valid for weakly adhesive contacts and connect these observations to recent theories for adhesion between rough surfaces.

理解接触的粗糙表面之间的界面间距的分布对于提供对它们之间的粘合力的定量估计是必不可少的。假定自仿射表面的非粘合，无摩擦接触，我们得出接触边缘附近的表面之间的间距分布。该分布在小间隙处表现出幂律散度，并且我们使用具有精细分辨率的数值模拟来确定缩放比例。幂律状态持续存在的特征长度尺度由均方根表面斜率与接触区域的平均直径的乘积给出。我们表明，这些结果对于弱粘合接触仍然有效，并将这些观察结果与粗糙表面之间粘合的最新理论联系起来。