# The distance upon contact: Determination from roughness profile

## TL;DR

This paper investigates how the initial contact distance between rough surfaces depends on surface roughness and contact area, providing a scale-dependent model crucial for understanding dispersive forces.

## Contribution

It introduces a simple expression for the contact distance as a function of roughness and contact area, highlighting scale dependence in contact mechanics.

## Key findings

- Contact distance depends on surface roughness and contact area.
- Uncertainty in separation decreases with increasing contact scale.
- Model applies to gold films and similar rough surfaces.

## Abstract

The point at which two random rough surfaces make contact takes place at the contact of the highest asperities. The distance upon contact d_0 in the limit of zero load has crucial importance for determination of dispersive forces. Using gold films as an example we demonstrate that for two parallel plates d_0 is a function of the nominal size of the contact area L and give a simple expression for d_0(L) via the surface roughness characteristics. In the case of a sphere of fixed radius R and a plate the scale dependence manifests itself as an additional uncertainty \delta d(L) in the separation, where the scale L is related with the separation d via the effective area of interaction L^2\sim\pi Rd. This uncertainty depends on the roughness of interacting bodies and disappears in the limit L\to \infty.