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Membrane filtration of feed containing multiple species of particles is a common process in the industrial setting. In this work, we propose a model for filtration of a suspension containing multiple particle species (concrete examples of our model are shown in two and three species), each with different affinities for the material of the porous filter membrane. Using the pore shape within the membrane as a design objective, we formulate a number of optimization problems pertaining to effective separation of desired and undesired particles in the special case of two-particle species and we present results showing how properties such as feed composition affect the optimal filter design. In addition, we propose a novel multi-stage filtration strategy, which provides a significant mass yield improvement for the desired particles, and, surprisingly, higher purity of the product as well.

 

We consider a free-surface thin film placed on a thermally conductive substrate and exposed to an external heat source in a set-up where the heat absorption depends on the local film thickness. Our focus is on modelling film evolution while the film is molten. The evolution of the film modifies local heat flow, which in turn may influence the film surface evolution through thermal variation of the film's material properties. Thermal conductivity of the substrate plays an important role in determining the heat flow and the temperature field in the evolving film and in the substrate itself. In order to reach a tractable formulation, we use asymptotic analysis to develop a novel thermal model that is accurate, computationally efficient, and that accounts for the heat flow in both the in-plane and out-of-plane directions. We apply this model to metal films of nanoscale thickness exposed to heating and melting by laser pulses, a set-up commonly used for self and directed assembly of various metal geometries via dewetting while the films are in the liquid phase. We find that thermal effects play an important role, and in particular that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. On the other hand, in the considered set-up the Marangoni (thermocapillary) effect turns out to be insignificant. 

Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destabilizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie–Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, such as emerging wavelengths, may not be influenced by the imposed substrate anchoring. Going further into the nonlinear regime, considered via large-scale GPU-based simulations, shows however that nonlinear effects may play an important role, in particular in the case of strong substrate anchoring anisotropy. Our simulations show that instability of the film develops in two stages: the first stage involves formation of ridges that are perpendicular to the local anchoring direction; and the second involves breakup of these ridges and formation of drops, whose final distribution is influenced by the anisotropy imposed by the substrate. Finally, we show that imposing more complex substrate anisotropy patterns allows us to reach basic understanding of the influence of substrate-imposed defects in director orientation on the instability evolution. 

Research on colloids is motivated by several factors. They can be used to answer fundamental questions related to the assembly of materials, and they have many potential applications in electronics, photonics, and life sciences. However, the rich variety of colloidal structures observed on the Earth can be influenced by the effects of gravity, which leads to particles settling and the motion of the surrounding fluid. To suppress the gravity effects, experiments on concentrated colloids of spherical and ellipsoidal fluorescent particles were carried out aboard the International Space Station. The particles were suspended in a decalin/tetralin mixture to match the particle refractive index. Confocal microscopy was used to visualize the particle behavior. The work was supported by the NSF CBET grants 1832260 and 1832291 and the NASA grant 80NSSC19K1655. 

Research on colloids is motivated by several factors. They can be used to answer fundamental questions related to the assembly of materials, and they have many potential applications in electronics, photonics, and life sciences. However, the rich variety of colloidal structures observed on the Earth can be influenced by the effects of gravity, which leads to particles settling and the motion of the surrounding fluid. To suppress the gravity effects, experiments on concentrated colloids of spherical and ellipsoidal fluorescent particles were carried out aboard the International Space Station. The particles were suspended in a decalin/tetralin mixture to match the particle refractive index. Confocal microscopy was used to visualize the particle behavior. The work was supported by the NSF CBET grants 1832260 and 1832291 and the NASA grant 80NSSC19K1655.