Insights from high-fidelity modeling of industrial rotary bell atomization.

The global automotive industry sprayed over 2.6 billion liters of paint in 2018, much of which through electrostatic rotary bell atomization, a highly complex process involving the fluid mechanics of rapidly rotating thin films tearing apart into micrometer-thin filaments and droplets. Coating operations account for 65% of the energy usage in a typical automotive assembly plant, representing 10,000s of gigawatt-hours each year in the United States alone. Optimization of these processes would allow for improved robustness, reduced material waste, increased throughput, and significantly reduced energy usage. Here, we introduce a high-fidelity mathematical and algorithmic framework to analyze rotary bell atomization dynamics at industrially relevant conditions. Our approach couples laboratory experiment with the development of robust non-Newtonian fluid models; devises high-order accurate numerical methods to compute the coupled bell, paint, and gas dynamics; and efficiently exploits high-performance supercomputing architectures. These advances have yielded insight into key dynamics, including i) parametric trends in film, sheeting, and filament characteristics as a function of fluid rheology, delivery rates, and bell speed; ii) the impact of nonuniform film thicknesses on atomization performance; and iii) an understanding of spray composition via primary and secondary atomization. These findings result in coating design principles that are poised to improve energy- and cost-efficiency in a wide array of industrial and manufacturing settings.

Three-Dimensional Sag Tracking in Falling Liquid Films.

Coating defects often arise during application in the flash stage, which constitutes the ∼10 min interval immediately following film application when the solvent evaporates. Understanding the transient rheology and kinematics of a coating system is necessary to avoid defects such as sag, which results in undesirable appearance. A new technique named variable angle inspection microscopy (VAIM) aimed at measuring these phenomena was developed and is summarized herein. The essence of this new, non-invasive, rheological technique is the measurement of a flow field in response to a known gravitational stress. VAIM was used to measure the flow profile through a volume of a liquid thin film at an arbitrary orientation. Flow kinematics of the falling thin film was inferred from particle tracking measurements. Initial benchmarking measurements in the absence of drying tracked the velocity of silica probe particles in ∼140 µm thick films of known viscosity, much greater than water, at incline angles of 5° and 10°. Probe particles were tracked through the entire thickness of the film and at speeds as high as ∼100 µm/s. The sag flow field was well resolved in ∼10 µm thick cross sections, and in general the VAIM measurements were highly reproducible. Complementary profilometer measurements of film thinning were utilized to predict sag velocities with a known model. The model predictions showed good agreement with measurements, which validated the effectiveness of this new method in relating material properties and flow kinematics.

Single and pairwise motion of particles near an ideally polarizable electrode.

Single-particle longitudinal motion and pairwise lateral motion was investigated while the particles were excited by an oscillating electric field directed normally to an electrode proximate to the particles. The electrode was polarized over a range of potential insufficient to drive electrochemical reactions, a range called the "ideally polarizable region". The particles' motion was qualitatively dependent on the choice of electrolyte despite the absence of electrochemical reactions. As when electrochemical reactions were not explicitly excluded, the phase angle θ between particle height and electric field correlated with the particles' separation or aggregation during excitation. A simple harmonic oscillator model of the particles' response, including colloidal and hydrodynamic forces and including the Basset force not previously cited in this context, showed how θ can increase from 0° at low frequencies, cross 90° at ∼100 Hz, and then increase to 180° as frequency was increased. The model captured the essence of experimental observations discussed here and in earlier works. This is the first a priori prediction of θ for this problem.

Ensemble average TIRM for imaging amperometry.

Colloidal particles can function as probes of local electrochemical current density if a functional relationship between the response of the particles and the electric field in the vicinity of the particles can be established. The nanometer scale movement of a single colloidal particle during cyclic voltammetry can be observed with the aid of total internal reflection microscopy. The intensity of scattered light can be related back to the current density local to that particle, and hence the method is called imaging amperometry. Data acquisition and optical constraints, however, make a single-particle method impractical for analysis of macro-scale (~1 cm(2)) surfaces covered by several hundred thousand particles. Subdivision of the electrode into small patches, each containing an ensemble of particles, solves this problem if the scattering from the ensembles can be related to the local electric field. For example, a 100×100 array of square 100 µm patches each containing approximately two dozen particles would form a mosaic of electrochemical activity with 0.01% area resolution on a 1cm(2) electrode having location-dependent electrocatalytic properties. The focus of this contribution, therefore, is adaptation of the method from single particles to particle ensembles. The algebraic relationship between current density and scattering intensity for single particles holds for ensembles if the mean scattering intensity is corrected to its mode. Currents calculated from particle light scattering at different locations on a single ITO/gold patterned electrode agree well with currents measured on these two electrode materials, which have quite different electrocatalytic properties.

The effect of electrode kinetics on electrophoretic forces.

Electric fields are commonly used to deposit colloidal particles on electrode surfaces and can even be used in directed assembly. The electric field beneath each particle changes as the particle approaches the wall; the proximity of the wall breaks the fore/aft symmetry and drives complicated flows that exert forces on the particle. While two limiting cases have been partially analyzed, constant electrode potential and uniform current density, the full problem has not been explored. Here, the electroosmotic flows in the region between the particle and the electrode are analyzed and the forces are computed for arbitrary electrode kinetic boundary conditions. Finite element analysis is employed to explore the effect of the current distribution beneath a particle on the net force acting on it. Previously established dimensionless kinetic parameters are used to scale between the two limiting cases. The forces on particles are an order of magnitude larger than the bulk electrophoretic force and are profoundly sensitive to the current distribution beneath the particle as it approaches the electrode.