Soft, Structured Layers on the Surface of a Quartz Crystal Microbalance (QCM): A Computational Model to Predict Shifts of Frequency and Bandwidth Based on the Lattice-Boltzmann Method
Analytical Chemistry
Fluid Mechanics
Final Report Abstract
The project was concerned with the prediction of changes in frequency and resonance bandwidth of acoustic shear wave resonators induced by structured samples - for example, consisting of adsorbed particles, vesicles, or biological cells. Resonators of this type are widely used in the form of the quartz crystal microbalance (QCM). In principle, the QCM can make statements about the mechanical properties of the sample (in addition to the gravimetrically determined layer thickness). For structured samples, the link between the mechanical properties and the QCM response requires numerical calculations, though. Such calculations were performed in this project, based on the frequency-domain lattice-Boltzmann method (FD- LBM). Beyond this specific project, this novel method opens up LBM for modeling viscoelasticity, which is not accessible with ordinary LBM. FD-LBM is characterized by simplicity and transparency of the procedure. The core of the program comprises about 200 lines. Two different variants (for hard and for soft particles) have been implemented. In the former variant, the surface of the particle represents a wall, from which the populations constituting the fluid are reflected ("bounce back"). In doing so, they transfer a momentum to the particle. The periodic motion of the particle is adjusted by the algorithm in such a way that a stress balance is achieved at the surface. The dynamics of the particle is modeled analytically. The motion consists of translation and rotation. Shear deformation can be included as long as it follows analytically from the stresses at the surface. In addition to the momentum transfer from the fluid, the stiffness of the contact with the resonator surface is included in the force balance. This is of much practical importance because the contact stiffness is used for sensing. Building on particles and their contact with a sample (consisting of, for example, DNA), the QCM signal can be amplified. The simulations provide a link between the QCM signal and the contact stiffness. Soft particles, in contrast, are explicitly modeled as part of the simulation volume. The algorithm is compatible with a complex viscosity. In contrast to the ordinary Lattice-Boltzmann method, elastic samples are accessible to modeling. The maximum viscosity is about 20 times the viscosity of the surrounding liquid. Soft particles to be modeled with this method are, for example, biological cells. In a first part of the work, the ∆Γ-∆f-extrapolation scheme was tested for its applicability. The scheme is a conjectured rule by which one infers the thickness of a particulate sample from the ratios of the shifts in bandwidth and frequency. This recipe is very well confirmed by the simulation. A second simulation reproduces a result from experiments on fouling in emulsion polymerization. A transient maximum in the bandwidth is interpreted - underpinned by the simulations - as evidence for particle fouling (to be distinguished from reaction fouling). Furthermore, experiments from other groups on adsorption of spherical particles are replicated with FD-LBM simulation. From these simulations, the contact stiffness can be derived. Finally, a vertical drift velocity was calculated for particles floating above the surface. The particles drift downwards. The effect thus promotes adsorption.
Publications
- Soft Viscoelastic Particles in Contact with a Quartz Crystal Microbalance (QCM): A Frequency-Domain Lattice Boltzmann Simulation. Analytical Chemistry 2021, 93, (29), 10229-10235
Gopalakrishna, S.; Langhoff, A.; Brenner, G.; Johannsmann, D.
(See online at https://doi.org/10.1021/acs.analchem.1c01612)
