The production of particles with shape-specific properties is reliant upon the separation of micro-/nanoparticles of particular shapes from particle mixtures of similar volumes. However, compared to a large number of size-based particle separation methods, shape-based separation methods have not been adequately explored. We review various up-to-date approaches to shape-based separation of rigid micro-/nanoparticles in liquid phases including size exclusion chromatography, field flow fractionation, deterministic lateral displacement, inertial focusing, electrophoresis, magnetophoresis, self-assembly precipitation, and centrifugation. We discuss separation mechanisms by classifying them as either changes in surface interactions or extensions of size-based separation. The latter includes geometric restrictions and shape-dependent transport properties.

A numerical model that incorporates temperature-dependent non-Newtonian viscosity was developed to simulate the extrusion process in extrusion-based additive manufacturing. Agreement with the experimental data was achieved by simulating a polylactic acid melt flow as a non-isothermal power law fluid using experimentally fitted parameters for polylactic acid. The model was used to investigate the temperature effect on the flow behavior, the cross-sectional area, and the uniformity of the extruded strand. OpenFOAM, an open source simulation tool based on the finite volume method, was used to perform the simulations. A computational module for solving the equations of non-isothermal multiphase flows was also developed to simulate the extrusion process under a small gap condition where the gap between the nozzle and the substrate surface is smaller than the nozzle diameter. Comparison of the strand shapes obtained from our model with isothermal Newtonian simulation, and experimental data confirms that our model improves the agreement with the experimental data. The result shows that the cross-sectional area of the extruded strand is sensitive to the temperature-dependent viscosity, especially in the small gap condition which has recently increased in popularity. Our numerical investigation was able to show nozzle temperature effects on the strand shape and surface topography which previously had been investigated and observed empirically only.

A new polydisperse “toy” constitutive model is derived and developed from fundamental principles and ideas governing the nonlinear rheology of linear flexible polymers [Mead et al., J. Rheol. 59, 335–363 (2015)]. Specifically, the new model is comprised of four fundamental pieces. First, the model contains a simple differential description of the entanglement dynamics of discrete entanglement pairs. Second, the model contains a differential description of the ij entanglement pair orientation tensor dynamics. Third, following a similar development by Mead and Mishler [J. Non-Newtonian Fluid Mech. 197, 61–79 and 80–90 (2013).], a diluted stretch tube is constructed to describe the relative stretch of each component in the molecular weight distribution (MWD). Fourth, a description of configuration dependent friction coefficients is generated by generalizing the monodisperse formulation of Ianniruberto et al. [Macromolecules 45, 8058–8066 (2012)]. The polydisperse stress calculator is developed from the orientation, stretch and entanglement density and is fundamentally different from other molecular models that assume a constant entanglement density. The resulting model is comprised of three differential evolution equations and is simple to code and fast to execute. The model can simulate arbitrary fast nonlinear flows of arbitrary MWD's. In the slow flow linear viscoelastic limit, the model collapses to the double reptation model. This welcome result has positive implications with respect to our model parameter determination [Ye et al., J. Rheol. 47, 443–468 (2003); Ye and Sridhar, Macromolecules 38, 3442–3449 (2005)] for making quantitative calculations.

We performed a numerical analysis to study the orientation distribution of a dilute suspension of thin, rigid, rod-like nanoparticles under shearing flow near a solid boundary of weak confinement. Brownian dynamics simulation of a rod was performed under various ratios of shear rate and rod diffusivity (Peclet number), as well as the center-of-mass position (wall confinement). We discuss the effects of Peclet number and wall confinement on the angle distributions, Jeffery orbit distribution and average orientation moments. The average orientation moments, obtained as a function of Peclet number and wall confinement, can be used to improve a previous shear-induced migration model. We demonstrate that the improved model can give excellent prediction of the orientation moment distributions in a microchannel flow.