Review of Hydrodynamics

In discussing forces and motion of particles one uses Newton s law, which states that the acceleration of a particle is proportional to the force acting on the particle. If we denote dv/dt to mean the rate of change of the velocity of a given fluid particle as it moves in space, Newton s equation becomes 

This concept is generalized in the definition of the total derivative, where 

Consider a volume of fluid. The sum of all the forces on all of the particles within this volume is the total force, F, which obeys Newton s law  

dv/dt is the local acceleration, p is the local density, and V is the volume. Next, consider a small volume with forces on the surface that are given by a stress tensor, II, where the surface force, F5, is given by 

So the force is related to the gradient of the pressure and the second derivative of the velocity. Combining Eqs. (1.140,1.144,1.146) results in the famous Navier-Stokes equation for the balance of forces in a fluid  

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Grasser, T., Tang, T.W., Kosina, H. and Selberherr, S. (2003) A Review of Hydrodynamic and Energy-Transport Models for Semiconductor Device Simulation. Proc. IEEE, 91, 251-274. 

Extensive reviews of hydrodynamic of two-phase flow systems in fixed beds appeared in the last five decades [1, 12-15], and there is no point in repeating here the numerous tables and references that were provided in these reviews. We attempt here to summarize the key findings that ought to be of importance to the research and potentially plant engineers. 

Reviews of concentration polarization have been reported (14,38,39). Because solute wall concentration may not be experimentally measurable, models relating solute and solvent fluxes to hydrodynamic parameters are needed for system design. The Navier-Stokes diffusion—convection equation has been numerically solved to calculate wall concentration, and thus the water flux and permeate quaUty (40). 

Suitable equations have been given for pipelines in Fig. 2.4 and these may be compared with the equation for impinging jets and nozzles or orifices. A more detailed review of this and other hydrodynamic relationships are given by B. Poulson. ... 

Dudukovic, M. P., Trends in catalytic reaction engineering, Catal. Today, 48, 5-15 (1999). A comprehensive review of the complex hydrodynamic issues associated with three-phase reactors is given in... 

In this chapter, we describe some of the more widely used and successful kinetic techniques involving controlled hydrodynamics. We briefly discuss the nature of mass transport associated with each method, and assess the attributes and drawbacks. While the application of hydrodynamic methods to liquid liquid interfaces has largely involved the study of spontaneous processes, several of these methods can be used to investigate electrochemical processes at polarized ITIES we consider these applications when appropriate. We aim to provide an historical overview of the field, but since some of the older techniques have been reviewed extensively [2,3,13], we emphasize the most recent developments and applications. 

Perhaps the best starting point in a review of the nonequilibrium field, and certainly the work that most directly influenced the present theory, is Onsager s celebrated 1931 paper on the reciprocal relations [10]. This showed that the symmetry of the linear hydrodynamic transport matrix was a consequence of the time reversibility of Hamilton s equations of motion. This is an early example of the overlap between macroscopic thermodynamics and microscopic statistical mechanics. The consequences of time reversibility play an essential role in the present nonequilibrium theory, and in various fluctuation and work theorems to be discussed shortly. 

The two goals of this chapter were to provide a critical review of the current state of the art in the field of two-phase flow with heat transfer and to provide procedures which can be used for the design of tubular fluid-fluid systems. Both heat transfer without phase change and with phase change were discussed in detail. In each case the analysis was based on an understanding of the flow patterns and the hydrodynamics of the system. 

Gogate PR, Pandit AB (2005) A review and assessment of hydrodynamic cavitation as a technology for the future. Ultrason Sonochem 12 21-27... 

It is not the goal of this section to provide a thorough review of the role of hydrodynamics on nutrient uptake to plankton. Indeed, the reader is referred to more complete treatments on the subject [25-27,34—37], including work found in Chapter 3 of this volume [32]. Instead, the main objective of this section is... 

We begin in Section II with a review of the fundamental concepts of hydrodynamics and boundary conditions. In Section III, we present some common descriptions of coupling, followed in Section IV by a discussion of viscoelastic adsorbate films and the so-called inner slip. In Section V, we consider with the concept of stochastic boundary conditions, which we believe will be an important topic in situations where random fluctuations are strong. Finally, in Section VI, we present our concluding ideas and discuss some areas for future study. 

H) W. Fickett W.W. Wood, The Physics of Fluids 1 (6), 528-34 (Nov-Dec 1958) (Detonation-product equations of state, known as "constant-/ and "constant-)/ , obtained from hydrodynamic data) I) J.J. Erpenbeck D.G. Miller, IEC 51, 329-31 (March 1959) (Semiempirical vapor pressure relation based on Dieterici s equation of state J) K.A. Kobe P.S. Murti, IEC 51, 332 (March 1959) (Ideal critical volumes for generalized correlations) (Application to the Macleod equation of state) Kj) S. Katz et al, jApplPhys 10, 568-76(April 1959) (Hugoniot equation of state of aluminum and steel) K2) S.J. Jacobs, jAmRocketSoc 30, 151(1960) (Review of semi-empirical equations of state)... 

Important work on the theory of detonation process was performed during WWII in the US by-Division 8 of NDRC under G.B. Kistiakowsky, by.E.B. Wilson Jr and others. Summary of this work was given by S.R. Brinkley-Jr in Ref 39, pp 83-88 and we are using this important work in compiling this section of the Encyclopedia The NDRC review begins with. a qualitative discussion of the building up of a "discontinuous shock front . Then the Riemann formulation of the equation of hydrodynamics is introduced. This formulation was published in 1860 (Ref 1)... 

Hydrodynamics. Flow systems are governed by the laws of hydrodynamics. How these laws relate to detonation was discussed in Vol 4, pp D602-22. Recent books and reviews on this subject are listed below ... 

The impact of hydrodynamic stress on animal cells has been reviewed extensively (29,43). Most of the work reported in the literature on cell damage in agitated bioreactors has been done at bench-scale. Kunas and Papoutsakis (44) reported that in 1-2 L bioreactors equipped with a 7 cm diameter pitched-blade impeller, cell damage was not observed until the impeller rate was raised to above 700 rpm (tip speed 513cm/s), as long as air entrapment did not occur. However, it is not clear how these bench-scale observations translate into damaging impeller rates at manufacturing scale. 

The second section presents a review of studies concerning counter-currently and co-currently down-flow conditions in fixed bed gas-liquid-solid reactors operating at elevated pressures. The various consequences induced by the presence of elevated pressures are detailed for Trickle Bed Reactors (TBR). Hydrodynamic parameters including flow regimes, two-phase pressure drop and liquid hold-up are examined. The scarce mass transfer data such gas-liquid interfacial area, liquid-side and gas-side mass transfer coefficients are reported. 

A large number of models consider the macroscopic approach for the prediction of the hydrodynamic behaviour of TBR. In this subsection some of the reported models are presented. First, an example of the macroscopic approach developed by the team of Sundaresan [22-24] is detailed. Next, a rapid review of the other models is given. 

Chapter 1 serves as an introduction to both volumes and is a survey of the fundamental principles of electrode kinetics. Chapter 2 deals with mass transport — how material gets to and from an electrode. Chapter 3 provides a review of linear sweep and cyclic voltammetry which constitutes an extensively used experimental technique in the field. Chapter 4 discusses a.c. and pulse methods which are a rich source of electrochemical information. Finally, Chapter 5 discusses the use of electrodes in which there is forced convection, the so-called hydrodynamic electrodes . 

The conformation of the peptide chain will affect all hydrodynamic spectral and optical rotatory properties and will influence the chemical behavior of specific functional groups. The relationships between these measurable variables and the actual conformations remain elusive, but changes in the parameters may be used to indicate changes in conformation. Unfortunately, the magnitude of the structural changes to be inferred are not always clear. [See the general review of protein de-naturation by Tanford (333).]... 

Various other instances of hydrodynamic and electrohydrodynamic instabilities in nematic and, to a lesser extent, smectic liquid crystals have been investigated. No attempt is made here to review this work. For the present discussion, it is sufficient to note that (a) most of the work has dealt with oriented layers having anisotropic properties, and (b) some interesting instabilities arise in oriented layers which do not occur for isotropic materials. An example of the latter is cellular convection in a fluid layer confined between horizontal plates maintained at different temperatures. With an isotropic fluid, convection can arise only if the lower plate is hotter than the upper plate. Then, fluid near the lower plate is less dense and tends to rise while fluid near the upper plate is denser and tends to sink. With an oriented layer, however, convection can arise even when the upper plate is hotter if the anisotropy of thermal conduction properties is of a particular type (8). 

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