Two surfaces are “sticky” if breaking their mutual contact requires a finite tensile force. At low fractal dimensions D, there is consensus stickiness does not depend on the upper truncation frequency of roughness spectrum (or “magnification”). As debate is still open for the case at high D, we exploit BAM theory of Ciavarella and Persson-Tosatti theory, to derive criteria for all fractal dimensions. For high D, we show that stickiness is more influenced by short wavelength roughness with respect to the low D case. BAM converges at high magnifications to a simple criterion which depends only on D, in agreement with theories that includes Lennard-Jones traction-gap law, while Persson-Tosatti disagrees because of its simplifying approximations.

如果断开两个表面的相互接触需要有限的拉力，则它们是“粘性”的。在低分形维D处，共有的粘性不取决于粗糙度谱（或“放大倍数”）的上截断频率。由于高D情况下的争论仍在进行中，我们利用Ciavarella的BAM理论和Persson-Tosatti理论来推导所有分形维数的标准。对于高D值，我们表明相对于低D值情况，粘性受短波长粗糙度的影响更大。BAM在高放大倍率下会聚到一个仅取决于D的简单标准，与包括Lennard-Jones牵引间隙定律在内的理论相一致，而Persson-Tosatti则因简化近似而不同意。