Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM-D Inferred from the Adsorption Kinetics and a Frequency-Domain Lattice Boltzmann Simulation

Abstract

A simulation based on the frequency-domain lattice Boltzmann method (FreqD-LBM) is employed to predict the shifts of resonance frequency, Δf, and half bandwidth, ΔΓ, of a quartz crystal microbalance with dissipation monitoring (QCM-D) induced by the adsorption of rigid spheres to the resonator surface. The comparison with the experimental values of Δf and ΔΓ allows to estimate the stiffness of the contacts between the spheres and the resonator surface. The contact stiffness is of interest in contact mechanics, but also in sensing because it depends on the properties of thin films situated between the resonator surface and the sphere. The simulation differs from previous implementations of FreqD-LBM insofar, as the material inside the particles is not included in the FreqD-LBM algorithm. Rather, the particle surface is configured to be an oscillating boundary. The amplitude of the particles' motions (displacement and rotation) is governed by the force balance at the surface of the particle. Because the contact stiffness enters this balance, it can be derived from experimental values of Δf and ΔΓ. The simulation reproduces experiments by the Krakow group. For sufficiently small spheres, a contact stiffness can be derived from the comparison of the simulation with the experiment.