We derive a very simple and effective stickiness criterion for solids having random roughness using a new asymptotic theory, which we validate with that of Persson and Scaraggi and independent numerical experiments. Previous claims that stickiness may depend on small scale quantities such as rms slopes and/or curvatures, obtained by making oversimplified assumptions on the contact area geometry, are largely incorrect, as the truncation of the PSD spectrum of roughness at short wavelengths is irrelevant. We find stickiness is destroyed typically at roughness amplitudes up to three orders of magnitude larger than the range of attractive forces. With typical nanometer values of the latter, the criterion gives justification to the qualitative well known empirical Dalhquist criterion for stickiness which demands adhesives to have elastic modulus lower than about 1MPa. The results clarifies a much debated question in both the scientific and technological world of adhesion, and may serve as benchmark for better comprehension of the role of roughness.

中文翻译：

---

多尺度随机粗糙表面的粘性研究

我们使用新的渐近理论为具有随机粗糙度的固体推导出了一个非常简单且有效的粘性标准，我们通过 Persson 和 Scaraggi 以及独立的数值实验验证了该标准。先前声称粘性可能取决于小尺度量，例如均方根斜率和/或曲率，通过对接触区域几何形状进行过度简化的假设而获得，这在很大程度上是不正确的，因为在短波长处截断粗糙度的 PSD 光谱是无关紧要的。我们发现粘性通常在粗糙度幅度比吸引力范围大三个数量级时被破坏。对于后者的典型纳米值，该标准为粘性的定性众所周知的经验 Dalhquist 标准提供了理由，该标准要求粘合剂具有低于约 1MPa 的弹性模量。结果澄清了粘附科学和技术领域中一个备受争议的问题，并可作为更好地理解粗糙度作用的基准。