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Concept# Fluid mechanics

Summary

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology.
It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.
It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a macroscopic viewpoint rather than from microscopic. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to

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PHYS-201(d): General physics: electromagnetism

The topics covered by the course are concepts of fluid mechanics, waves, and electromagnetism.

ME-474: Numerical flow simulation

This course provides practical experience in the numerical simulation of fluid flows. Numerical methods are presented in the framework of the finite volume method. A simple solver is developed with Matlab, and a commercial software is used for more complex problems.

ME-201: Continuum mechanics

Continuum conservation laws (e.g. mass, momentum and energy) will be introduced. Mathematical tools, including basic algebra and calculus of vectors and Cartesian tensors will be taught. Stress and deformation tensors will be applied to examples drawn from linear elastic solid mechanics.

Hydrodynamics at the nanoscale involves both fundamental study and application of fluid and mass transport phenomena in nanometer-sized confinements. Nanopores in single-layer graphene can be highly attractive for exploring the molecular transport of gas and water molecules and hydrated ions at the ultimate scales of pore size and pore length. However, the experimental data is limited, and the state-of-the-art artificial nanopores still underperform compared to biological channels in cellular membranes. This dissertation focuses on developing ultimate graphene nanopore devices to study mass transport phenomena under controlled spatial confinement. We first investigated the kinetics of liquidâvapor transport from nanoscale confinements which is attractive for novel evaporation and separation applications; however, it is not explored at the ultimate confinement limit, i.e., at the atomic-thick and Ã-scale nanopore placed at the liquidâvapor interface. We show that the evaporation flux from such nanopores increases with decreasing pore size by up to one order of magnitude relative to the bare liquidâvapor interface. Molecular dynamics simulations reveal that oxygen-functionalized nanopores render rapid rotational and translational dynamics to water molecules by reducing and shortening the lifetime of waterâwater hydrogen bonds. Graphene nanopores also enable the study of ion transport across sub-nanometer-scale 2D confinements. We produce tailor-made nanopores approaching the size of hydrated ions by decoupling the pore nucleation and expansion. Monovalent metal ions are efficiently sieved from divalent ions, with K+/Mg2+ selectivity up to 70 and Li+/Mg2+ selectivity up to 50, corresponding to a sieving resolution of 1 Ã. Mitigating the non-selective pore formation further enhance the ion-sieving performance, reaching K+/Mg2+ selectivity up to 350 and Li+/Mg2+ selectivity up to 260. The pore size and structure allow adjusting the diffusion of ions across the nanopores, suggesting that the sterically induced partial dehydration process may play an important role in the observed cation selectivities. These selectivities were realized from centimeter-scale suspended graphene membranes, prepared in crack-free fashion by using dual layer reinforcement strategy where the first layer is 200-nm-thick nanoporous carbon (NPC) film hosting 20 nm pores which ensures a conformal contact and reinforcement of the graphene film and the second (top) layer is Nafion.Finally, a dual layer reinforcement is also demonstrated for preparing crack-free centimeter-scale gas separation membranes to utilize the full potential of graphene nanopores for energy-efficient applications. The bottom layer of the composite film is NPC film while the top layer is made of a 500-nm thick multi-walled carbon nanotube (MWNT) film with a pore size ranging from 200 to 300 nm. The obtained selectivities from crack-free centimeter-scale graphene membranes for H2/CH4 and H2/CO2 are 11â23 and 5â8, respectively, which is significantly higher than the corresponding Knudsen selectivities. Overall, this dissertation presents a graphene nanopore toolkit for studying fluid mechanics at the ultimate scales. The findings of enhanced water evaporation rate and ion selectivity using the nanopore platform could enrich our understanding of mass transport under extreme confinement and open new opportunities for a range of separation applications.

The aim of this principally experimental study is to understand from fluid mechanic principles why an insignificant anesthetic dose administered as a short bolus into the cerebrospinal fluid inside the subarachnoid space provides greater pain relief than a larger dose continuously injected over a longer period. The subarachnoid space is modeled as an annular gap of constant or slowly varying cross section into which a catheter is introduced. The cerebrospinal fluid is replaced by water of 37°C which has very similar properties. This fluid in the annular gap is subjected to oscillations of amplitude and frequency (heart frequency) typically found in the subarachnoid space. The anesthetic is replaced by a fluorescent dye injected through the catheter. To study its dispersion, we have developed a 400 Hz laser scanning setup with which we perform quasi-instantaneous, quantitative 3D laser induced fluorescence (LIF) as well as 2D particle image velocimetry (PIV). The experiments are supplemented by an analytical axi-symmetric model as well as an exploratory numerical model to help interpret the results. The study has identified steady streaming (a nonlinear effect associated with the fluid oscillation) and enhanced diffusion (an effect associated with oscillating shear flow) as the principal agents of dye (anesthetic) dispersion. Besides the slowly varying cross section, the catheter tip has been identified as an important cause for steady streaming. In an attempt to identify optimal injection parameters of use for clinicians, a rough parametric model of the primary factors influencing drug spread (fluid oscillation frequency and amplitude, geometry, and injection rate) has been constructed.

We present a multi-level algorithm to approximate the inverse of the fluid block in a Navier-Stokes saddle-point matrix where the coarse level is defined as a restriction of the degrees of freedom to those of lower order finite elements. A one-level scheme involving P1 and P2 finite elements is studied in details and several transfer operators are compared by means of two reference problems. Numerical results show that restriction and prolongation operators based on L2 projection lead to faster GMRES convergence of the fluid part, for all the examined combinations of mesh size, time step and Reynolds number.

2013