Contact conductance of rough surfaces composed of modified RMD patches

The dependence of the contact conductance of self-affine rough surfaces on the applied pressure is studied using the electric-mechanical analogy which relates the contact conductance to the normal stiffness. According to dimensional analysis arguments, an efficient dimensionless formulation is proposed which minimizes the number of dimensionless variables governing the phenomenon. Assuming incomplete similarity in the dimensionless pressure, a power-law dependence between contact conductance and mean pressure is proposed. This is confirmed by earlier semi-empirical correlations that are recovered as special cases of the proposed formulation. To compute the exponent β of the power-law, and relate it to the morphological properties of the surfaces, we numerically test self-affine rough surfaces composed of random midpoint displacement (RMD) patches. Such patches are generated using a modified RMD algorithm in order to decouple the effect of the long wavelength cut-off from that due to microscale roughness. Numerical results show that the long wavelength cut-off has an important effect on the contact conductance, whereas the sampling interval and the fractal dimension are less important. The effect of elastic interaction between asperities has also been quantified and it significantly influences the predicted power-law exponent β.