Archimedes Screw Design: An Analytical Model for Rapid Estimation of Archimedes Screw Geometry

In designing Archimedes screws, determination of the geometry is among the fundamental questions that may affect many aspects of the Archimedes screw powerplant. Most plants are run-of-river and highly depend on local flow duration curves that vary from river to river. An ability to rapidly produce realistic estimations for the initial design of a site-specific Archimedes screw plant helps to facilitate and accelerate the optimization of the powerplant design. An analytical method in the form of a single equation was developed to rapidly and easily estimate the Archimedes screw geometry for a specific site. This analytical equation was developed based on the accepted, proved or reported common designs characteristics of Archimedes screws. It was then evaluated by comparison of equation predictions to existing Archimedes screw hydropower plant installations. The evaluation results indicate a high correlation and reasonable relative difference. Use of the equation eliminates or simplifies several design steps and loops and accelerates the development of initial design estimations of Archimedes screw generators dramatically. Moreover, it helps to dramatically reduce one of the most significant burdens of small projects: the nonscalable initial investigation costs and enables rapid estimation of the feasibility of Archimedes screw powerplants at many potential sites.

Separation of Enantiomers through Local Vorticity: A Screw Model Mechanism

We present a model to explain the mechanism behind enantiomeric separation under either shear flow or local rotational motion in a fluid. Local vorticity of the fluid imparts molecular rotation that couples to translational motion, sending enantiomers in opposite directions. Translation-rotation coupling of enantiomers is explored using the molecular hydrodynamic resistance tensor, and a molecular equivalent of the pitch of a screw is introduced to describe the degree of translation-rotation coupling. Molecular pitch is a structural feature of the molecules and can be easily computed, allowing rapid estimation of the pitch of 85 drug-like molecules. Simulations of model enantiomers in a range of fluids such as $\Lambda$- and $\Delta$-Ru(bpy)_3]Cl_2 in water and (R,R)- and (S,S)-atorvastatin in methanol support predictions made using molecular pitch values.A competition model and continuum drift diffusion equations are developed to predict separation of realistic racemic mixtures. We find that enantiomeric separation on a centimeter length scale can be achieved in hours, using experimentally-achievable vorticities. Additionally, we find that certain achiral objects can also exhibit a non-zero molecular pitch.