We investigate the two-dimensional dynamic motion of magnetic particles of ellipsoidal shapes in shear flow under the influence of a uniform magnetic field. In the first part, we present a theoretical analysis of the rotational dynamics of the particles in simple shear flow. By considering paramagnetic and ferromagnetic particles, we study the effects of the direction and strength of the magnetic field on the particle rotation. The critical magnetic-field strength, at which particle rotation is impeded, is determined. In a weak-field regime (i.e., below the critical strength) where the particles execute complete rotations, the symmetry property of the rotational velocity is shown to depend on the direction of the magnetic field. In a strong-field regime (i.e., above the critical strength), the particles are impeded at steady angles and the stability of these angles is examined. Under a uniform field, paramagnetic and ferromagnetic particles behave differently, in terms of the critical strength, symmetry property of the rotational velocity, and steady angles. In the second part, we use two-dimensional numerical simulations to study the implications of rotational dynamics for lateral migration of the particles in wall-bound shear flows. In the weak-field regime, the paramagnetic prolate particles migrate away when the field is applied perpendicular to the flow and towards the bounded wall when the field is applied parallel to the flow. Ferromagnetic particles exhibit negligible migration under fields that are parallel or perpendicular to the flow. The different lateral migration behaviors are due to the difference in the symmetry property of particle rotational velocity. In the strong-field regime, the particles are impeded at different stable steady angles, which result in different lateral migration behaviors as well. The fundamental insights from our work demonstrate various feasible strategies for manipulating paramagnetic and ferromagnetic particles.

We numerically investigate the dynamics of a pair of circular Janus microparticles immersed in a Newtonian fluid under a simple shear flow and a uniform magnetic field by direct numerical simulation. Using the COMSOL software, we applied the finite element method, based on an arbitrary Lagrangian-Eulerian approach, and analyzed the dynamics of two anisotropic particles (i.e., one-half is paramagnetic, and the other is non-magnetic) due to the center-to-center distance, magnetic field strength, initial particle orientation, and configuration. This article considers two configurations: the LR-configuration (magnetic material is on the left side of the first particle and on the right side of the second particle) and the RL-configuration (magnetic material is on the right side of the first particle and on the left side of the second particle). For both configurations, a critical orientation determines if the particles either attract (below the critical) or repel (above the critical) under a uniform magnetic field. How well the particles form a chain depends on the comparison between the viscous and magnetic forces. For long particle distances, the viscous force separates the particles, and the magnetic force causes them to repel as the particle orientation increases above the configuration’s critical value. As the initial distance decreases, a chain formation is possible at a steady orientation, but is more feasible for the RL-configuration than the LR-configuration under the same circumstances.

We numerically investigated the dynamics of a paramagnetic elliptical particle immersed in a low Reynolds number Poiseuille flow in a curved channel and under a uniform magnetic field by direct numerical simulation. A finite element method, based on an arbitrary Lagrangian-Eulerian approach, analyzed how the channel geometry, the strength and direction of the magnetic field, and the particle shape affected the rotation and radial migration of the particle. The net radial migration of the particle was analyzed after executing a $\pi$ rotation and at the exit of the curved channel with and without a magnetic field. In the absence of a magnetic field, the rotation is symmetric, but the particle-wall distance remains the same. When a magnetic field is applied, the rotation of symmetry is broken, and the particle-wall distance increases as the magnetic field strength increases. The causation of the radial migration is due to the magnetic angular velocity caused by the magnetic torque that constantly changes directions during particle transportation. This research provides a method of magnetically manipulating non-spherical particles on lab-on-a-chip devices for industrial and biological applications.

Using a one-dimensional code, we computed the power (enthalpy discharge rate) of a twelve-cell mechanical draft cooling tower (MDCT) using over two hundred visible condensed water vapor plume volume measurements derived from images, weather data, and tower operating conditions. The plume images were simultaneously captured by multiple stationary digital cameras surrounding the cooling tower. An analysis technique combining structure from motion (SfM), a neural-network-based image segmentation algorithm, and space carving was used to quantify the volumes. Afterwards, the power output was computed using novel techniques in the one-dimensional code that included cooling tower exhaust plume adjacency effects implemented with a modified version of the entrainment function, weather data averaged from eleven stations, and fan operations at the times when plume volumes were measured. The model was then compared with the averaged observed power output, and it validated well with an average error ranging from 6 to 12%, depending on the meteorological data used in the simulations. This methodology can possibly determine power plant fuel consumption rates by applying visible imagery.

We examine a time-dependent, three-dimensional rotation of magnetic ellipsoidal particles in a two-dimensional, simple shear flow and a uniform magnetic field. We consider that the particles have paramagnetic and ferromagnetic properties, and we compare their rotational dynamics due to the strengths and directions of the applied uniform magnetic field. We determine the critical magnetic field strength that can pin the particles’ rotations. Above the critical field strength, the particles’ stable steady angles were determined. In a weak magnetic regime (below the critical field strength), a paramagnetic particle’s polar angle will oscillate toward the magnetic field plane while its azimuthal angle will execute periodic rotations. A ferromagnetic particle’s rotation depends on its initial angles and the magnetic field strength and direction. Even when it is exposed to a critical magnetic field strength, its rotational dynamics will either be pinned in or out of the magnetic field plane. In a weak magnetic regime, a ferromagnetic particle will either execute out-of-plane rotations or will oscillate toward the magnetic field plane and perform periodic rotations. For both particles, we analytically determine the peaks and troughs of their oscillations and study their time-dependent rotations through analytical and numerical analyses.

Interactions between gold metallic nanoparticles and molecular dyes have been well described by the nanometal surface energy transfer (NSET) mechanism. However, the expansion and testing of this model for nanoparticles of different metal composition is needed to develop a greater variety of nanosensors for medical and commercial applications. In this study, the NSET formula was slightly modified in the size-dependent dampening constant and skin depth terms to allow for modeling of different metals as well as testing the quenching effects created by variously sized gold, silver, copper, and platinum nanoparticles. Overall, the metal nanoparticles followed more closely the NSET prediction than for Förster resonance energy transfer, though scattering effects began to occur at 20 nm in the nanoparticle diameter. To further improve the NSET theoretical equation, an attempt was made to set a best-fit line of the NSET theoretical equation curve onto the Au and Ag data points. An exhaustive grid search optimizer was applied in the ranges for two variables, $0.1\le C\le 2.0$ and $0\le \alpha \le 4$, representing the metal dampening constant and the orientation of donor to the metal surface, respectively. Three different grid searches, starting from coarse (entire range) to finer (narrower range), resulted in more than one million total calculations with values $C=2.0$ and $\alpha =0.0736$. The results improved the calculation, but further analysis needed to be conducted in order to find any additional missing physics. With that motivation, two artificial intelligence/machine learning (AI/ML) algorithms, multilayer perception and least absolute shrinkage and selection operator regression, gave a correlation coefficient, $R^2$, greater than $0.97$, indicating that the small dataset was not overfitting and was method-independent. This analysis indicates that an investigation is warranted to focus on deeper physics informed machine learning for the NSET equations.