Measurement theory of a density profile of small spheres on a cylindrical surface: Conversion of force curve measured with surface force apparatus into pressure on its surface element

TL;DR

This paper develops a transform theory for converting force measurements from a surface force apparatus into the density distribution of small spheres on a cylindrical surface, enabling experimental analysis of particle arrangements.

Contribution

It introduces a novel transform theory specifically for cylindrical geometries, extending previous methods designed for spherical surfaces.

Findings

Derived a mathematical transform for cylindrical surfaces

Validated the transform with experimental force data

Enabled direct measurement of particle density profiles

Abstract

Recently, in an ensemble of small spheres, we proposed a method that converts the force between two large spheres into the pressure on the large sphere's surface element. Using it, the density distribution of the small spheres around the large sphere can be obtained experimentally. In a similar manner, in this letter, we propose a transform theory for surface force apparatus, which transforms the force acting on the cylinder into the density distribution of the small spheres on the cylindrical surface. The transform theory we derived is briefly explained in this letter.