Flows and Hydrodynamics

One of the most striking properties of liquid crystals is their ability to flow freely while exhibiting various anisotropic and crystalline properties. It is this dual nature of liquid crystals that makes them very interesting materials to study it also makes the theoretical formalism very complex. 

The main feature that distinguishes liquid crystals in their ordered mesophases (e.g., the nematic phase) from ordinary fluids is that their physical properties are dependent on the orientation of the director axis ) these orientation flow processes 

We begin our discussion by reviewing first the hydrodynamics of an ordinary fluid. This is followed by a discussion of the general hydrodynamics of liquid crystals. Specific cases involving a variety of flow-orientational couplings are then treated. 

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Teeuu, D. and Hesselink, F.T. "Power-Law Flow and Hydrodynamic Behavior of Biopolymer Solutions In Porous Media," SPE paper 8982, 1980 SPE Fifth International Symposium on Oilfield and Geothermal Chemistry, Stanford, May 28 30. 

The mass flux of a solute can be related to a mass transfer coefficient which gathers both mass transport properties and hydrodynamic conditions of the system (fluid flow and hydrodynamic characteristics of the membrane module). The total amount transferred of a given solute from the feed to the receiving phase can be assumed to be proportional to the concentration difference between both phases and to the interfacial area, defining the proportionality ratio by a mass transfer coefficient. Several types of mass transfer coefficients can be distinguished as a function of the definition of the concentration differences involved. When local concentration differences at a particular position of the membrane module are considered the local mass transfer coefficient is obtained, in contrast to the average mass transfer coefficient [37]. 

Flow cytometers distribute suspensions of cells into a single column by laminar flow and hydrodynamic focusing. Individual cells are then intercepted by a laser source, and the scattered light and fluorescence emission (when using... 

Fully thermalized particles of A can leave the cell volume by two processes by diffusing to the boundaries of the cell or by being entrained in the helium flow and hydrodynamically pulled out of the exit hole. In order to determine which regime is applicable, the timescales for each process need to be compared. 

Mathematical modeling and determination of the characteristic parameters to predict the performance of membrane solvent extraction processes has been studied widely in the literature. The analysis of mass transfer in hollow fiber modules has been carried out using two different approaches. The first approach to the modeling of solvent extraction in hollow fiber modules consists of considering the velocity and concentration profiles developed along the hollow fibers by means of the mass conservation equation and the associated boundary conditions for the solute in the inner fluid. The second approach consists of considering that the mass flux of a solute can be related to a mass transfer coefficient that gathers both mass transport properties and hydrodynamic conditions of the systan (fluid flow and hydrodynamic characteristics of the manbrane module). 

Teeuw, D. and F. T. Hesselink (1980). Power-law flow and hydrodynamic behaviour of biopolymer solutions in porous media. SPE Oilfield and Geothermal Chemistry Symposium. Stanford, California, 1980,. American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. 

If a particularly parallel beam is required in the chamber into which it is flowing the beam may be skimmed in the region of hydrodynamic flow. A skimmer is a collimator which is specially constructed in order to avoid shockwaves travelling back into the gas and increasing 7). The gas that has been skimmed away may be pumped off in a separate vacuum chamber. Further collimation may be carried out in the region of molecular flow and a so-called supersonic beam results. When a skimmer is not used, a supersonic jet results this may or may not be collimated. 

In this ehapter, the transport proeesses relating to partiele eonservation and flow are eonsidered. It starts with a brief introduetion to fluid-particle hydrodynamics that deseribes the motion of erystals suspended in liquors (Chapter 3) and also enables solid-liquid separation equipment to be sized (Chapter 4). This is followed by the momentum and population balances respeetively, whieh deseribe the eomplex flows and mixing within erystallizers and, together with partieulate erystal formation proeesses (Chapters 5 and 6), enable partiele size distributions from erystallizers to be analysed and predieted (Chapters 7 and 8). 

This is based on the flow and specific energy produced by the pump at its best efficiency point of performance following the approach stated by Wisclicenus Any fixed value of the specific speed describes a combination of operating conditions that permits similar flow conditions in geometrically similar hydrodynamic machines. ... 

A similar, but highly porous, vitreous carbon material—reticulated vitreous carbon (RVC)—has found widespread application for flow analysis and spectro-electrochemistry (25). As shown in Figure 4-10, RVC is an open-pore ( spongelike ) material such a network combines the electrochemical properties of glassy carbon with many structural and hydrodynamic advantages. These include a very high surface area ( 66 cm2 cm-3 for the 100-ppi grade), 90-97% void volume, and a low resistance to fluid flow. 

In Chap. 5 the available data related to flow and heat transfer of a gas-liquid mixture in single and parallel channels of different size and shape are presented. These data concern flow regimes, void fraction, pressure drop and heat transfer. The effects of different parameters on flow patterns and hydrodynamic and thermal characteristics of gas-liquid flow are discussed. 

Below we consider a quasi-one-dimensional model of flow and heat transfer in a heated capillary, with hydrodynamic, thermal and capillarity effects. We estimate the influence of heat transfer on steady-state laminar flow in a heated capillary, on the shape of the interface surface and the velocity and temperature distribution along the capillary axis. 

The flow and heat transfer in heated micro-channels are accompanied by a number of thermohydrodynamic processes, such as liquid heating and vaporization, boiling, formation of two-phase mixtures with a very complicated inner structure, etc., which affect significantly the hydrodynamic and thermal characteristics of the cooling systems. 

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow —the natural science of fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics offers a systematic structure that underlies these practical disciplines, that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as velocity, pressure, density, viscosity and temperature, as functions of space and time. 

Sundararajan et al. [131] in 1999 calculated the slurry film thickness and hydrodynamic pressure in CMP by solving the Re5molds equation. The abrasive particles undergo rotational and linear motion in the shear flow. This motion of the abrasive particles enhances the dissolution rate of the surface by facilitating the liquid phase convective mass transfer of the dissolved copper species away from the wafer surface. It is proposed that the enhancement in the polish rate is directly proportional to the product of abrasive concentration and the shear stress on the wafer surface. Hence, the ratio of the polish rate with abrasive to the polish rate without abrasive can be written as... 

The volume averaging approach discussed in the section on diffusive transport can also be extended to account for electrophoresis [215] and hydrodynamic flow [215,436]. Locke [215] considered the application of volume averaging to the determination of the effective... 

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