Numerical experiments on the efficiency of local grid refinement based on truncation error estimates

Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each control volume. Often the grid refinement criterion is based on an estimate of the truncation error in each control volume, because the truncation error is a natural measure of the discrepancy between the algebraic finite-volume equations and the original differential equations. However, it is not a straightforward task to associate the truncation error with the optimum grid density because of the complexity of the relationship between truncation and discretisation errors. In the present work several criteria based on a truncation error estimate are tested and compared on a regularised lid-driven cavity case at various Reynolds numbers. It is shown that criteria where the truncation error is weighted by the volume of the grid cells perform better than using just the truncation error as the criterion. Also it is observed that the efficiency of local refinement increases with the Reynolds number. The truncation error is estimated by restricting the solution to a coarser grid and applying the coarse grid discrete operator. The complication that high truncation error develops at grid level interfaces is also investigated and several treatments are tested.     

Measuring Bismuth Oxide Particle Size and Morphology in Film-Coated Tablets

The assessment of active pharmaceutical ingredient (API) particle size and morphology is of great importance for the pharmaceutical industry since it is expected to significantly affect physicochemical properties. However, very few methods are published for the determination of API morphology and particle size of film-coated (FC) tablets. In the current study we provide a methodology for the measurement of API particle size and morphology which could be applied in several final products. Bismuth Oxide 120 mg FC Tabs were used for our method development, which contain bismuth oxide (as tripotassium dicitratobismuthate (bismuth subcitrate)) as the active substance. The sample preparation consists of partial excipient dissolution in different solvents. Following this procedure, the API particles were successfully extracted from the granules. Particle size and morphology identification in Bismuth Oxide 120 mg FC Tabs was conducted using micro-Raman mapping spectroscopy and ImageJ software. The proposed methodology was repeated for the raw API material and against a reference listed drug (RLD) for comparative purposes. The API particle size was found to have decreased compared to the raw API, while the API morphology was also affected from the formulation manufacturing process. Comparison with the RLD product also revealed differences, mainly in the API particle size and secondarily in the crystal morphology.     

Highly Efficient Production of Nanoporous Block Copolymers with Arbitrary Structural Characteristics for Advanced Membranes

The great significance of boosting the design of percolating nanopore structures in block copolymers (BCPs) for various cases has been widely demonstrated in the past several decades. However, it still remains challenging to prepare the desired porous structures in a rapid, facile, and universal manner. Here we have developed an unconventional and benchtop strategy to rapidly generate the nanoporous polystyrene-based BCPs with arbitrary structural characteristics regardless of the BCP bulk morphology. This universal pore-forming strategy enables the sustainable CO₂-based BCPs to form advanced membranes after 1 s soaking for efficiently rejecting 94.2 % brilliant blue R (826 g mol⁻¹). Meanwhile, the water permeance retains around 1020 L (m² h bar)⁻¹, which is 1–3 orders of magnitude higher than that of other membranes. This strategy may offer an excellent opportunity to introduce percolating pore structures in those newly developed BCPs with which the previously reported pore-forming methods may not deal.     

Use of a solid-state nanopore for profiling the transferrin receptor protein and distinguishing between transferrin receptor and its ligand protein

A nanopore device is capable of providing single-molecule level information of an analyte as they translocate through the sensing aperture—a nanometer-sized through-hole—under the influence of an applied electric field. In this study, a silicon nitride (Si_xN_y)-based nanopore was used to characterize the human serum transferrin receptor protein (TfR) under various applied voltages. The presence of dimeric forms of TfR was found to decrease exponentially as the applied electric field increased. Further analysis of monomeric TfR also revealed that its unfolding behaviors were positively dependent on the applied voltage. Furthermore, a comparison between the data of monomeric TfR and its ligand protein, human serum transferrin (hSTf), showed that these two protein populations, despite their nearly identical molecular weights, could be distinguished from each other by means of a solid-state nanopore (SSN). Lastly, the excluded volumes of TfR were experimentally determined at each voltage and were found to be within error of their theoretical values. The results herein demonstrate the successful application of an SSN for accurately classifying monomeric and dimeric molecules while the two populations coexist in a heterogeneous mixture.