Fundamentals of Hydrodynamics

Fluid dynamics, especially hydrodynamics (the study of moving liquids), is of major importance in the design of chemical plant. The hydrodynamics largely determine the energy consumption of the total plant, the separation performance of columns, and the residence-time behavior of reactors turbulent flow can even destroy pipes. The classical equations for describing the state of flow (= velocity field in space and time) of a fluid are due to Navier and Stokes and date back to the 1800s (Equation 2.4-1)  

3 = acceleration (e.g., due to gravity) p = density of fluid P = pressure V = kinematic viscosity, 

The individual terms on the right-hand side of Equation 2.4-2 have the follo ving meaning  

2nd term mass force (force = mass x acceleration) 

This partial differential equation is deterministic by nature. In practice, however, many hydrodynamic phenomena (e.g., transition from laminar to turbulent flow) have chaotic features (deterministic chaos [Stewart 1993]). The reason for this is that the Navier-Stokes equation assumes a homogeneous ideal fluid, whereas a real fluid consists of atoms and molecules. Today highly developed numerical flow simulators (computational fluid dynamics, CFD) are available for solving the Navier-Stokes equation under certain boundary conditions (e.g.. Fluent Deutschland GmbH). These even allow complex flow conditions, including particle, droplet, bubble, plug, and free surface flow, as well as multiphase flow such as that foundin fluidized-bed reactors and bubble columns, to be treated numerically [Fluent 1998]. 

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Fundamentals of Hydrodynamics and Boundary Conditions Descriptions of Slip... 

In this section we show how the fundamental equations of hydrodynamics — namely, the continuity equation (equation 9.3), Euler s equation (equation 9.7) and the Navier-Stokes equation (equation 9.16) - can all be recovered from the Boltzman equation by exploiting the fact that in any microscopic collision there are dynamical quantities that are always conserved namely (for spinless particles), mass, momentum and energy. The derivations in this section follow mostly [huangk63]. 

Scaling has many useful applications. The dynamic characteristics of different bed designs can be quickly compared. The influence of bed diameter on hydrodynamic behavior can be studied by the use of several different size models. The models allow easy experimental examination of existing operating characteristics. The beds also can be used to quickly confirm the influence of proposed modifications. Since the models usually operate at ambient conditions, it is possible to instrument them to observe detailed behavior. This allows a better understanding of the fundamental physics as well as the identification of hydrodynamic factors needed for proper correlation of performance. 

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. 

The fundamental approach used was that of hydrodynamics to obtain solutions of equations for the conservation of mass, momentum arid energy. It is convenient to express these equations in vector notation and to consider small amplitude waves separately from waves of finite amplitude. In what follows, we will first discuss the shock effects of underwater expins and then proceed to a quantitative description of gas bubble motion... 

Finally, a challenging problem is to discuss the influence of hydrodynamic flow fields on the phase behavior of polymer blends. This is of fundamental interest and of technological importance as well since stresses and corresponding deformations are encountered during processing of blends. Extension of studies to blend systems under external flow is necessary for the better understanding of structure formation in polymer blends outside equilibrium. 

The fundamentals of the electrochemical response at electrodes operating in a regime of forced convection, hydrodynamic electrodes, and the information that can be obtained have been reviewed [23, 24]. Some of these electrodes are good candidates for direct introduction into flow systems, in particular tube/channel electrodes and impinging jet (wall-jet and wall-tube) electrodes. Particular practical advantages of these flow-past hydrodynamic electrodes are that there is no reagent depletion while the sample plug passes the electrodes, and there is no build-up of unwanted intermediates or products. Recent advances in instrumentation also mean... 

Refs. [i] Bockris JO M, Reddy AKN, Gamhoa-Aldeco M (2000) Modern electrochemistry, fundamentals of electrodics, vol. 2A, 2 d edn. Kluwer, New York, p 1140 [ii] Acrivos A (1992) Memorial tributes National Academy of Engineering vol. 5. The National Academies Press, Washington DC, pp 165-170 [Hi] Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs, (thefirst Russian edition was published in 1952)... 

Section 4.6 may be considered the prototype of modem electrokinetics, because all relevant features were covered the coupling of hydrodynamic and electric fluxes and double layer polarization. However, the elaboration remained restricted to electrophoresis, which is the most familiar electrokinetlc phenomenon. Other types of electrokinetics, summarized in table 4.1. basically require the same theory, although there may be considerable differences in the elaboration (what is stationary what is moving boundiuy condition , etc.). With sec. 4.6 we consider the fundamentals sufficiently explained and illustrated and we shall therefore not repeat and apply this theory to other electrokinetlc phenomena. Instead, two important extensions will now be briefly reviewed inclusion of double layer overlap, as occurs in plugs, in the present section and measurement in alternating fields in the following. 

Hinze, J. O., (1955), Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes, AIChEJl,pp. 269-295. 

The components of co, co and due to the velocity gradient, have been evaluated for ellipsoids of revolution by Jeffery (55) from the fundamental equations of hydrodynamics ... 

Currently, the most important uses of hydrodynamic voltammetry include (1) detection and determination of chemical species as they exit from chromatographic columns or a continuous-flow apparatus (2) routine determination of oxygen and certain species of biochemical interest, such as glucose, lactate, and sucrose (3) detection of end points in coulometric and volumetric titrations and (4) fundamental studies of electrochemical processes. 

Ultrasonic irradiation produces a number of significant benefits in a wide range of electrochemical systems. Thus in electroanalysis it provides another time-dependent variable to be used for mechanistic elucidation, and which further extends the range of hydrodynamic regimes available to the modem electroanalyst. The technique also provides a probe into the fundamental physicochemical principles of electrolyte solutions, electrode phenomena, and associated processes. 

The fluidized bed systems have been utilized extensively in many physical, chemical, petrochemical, electrochemical, and biochemical processes. Successful applications of the fluidization systems lie in a comprehensive understanding of hydrodynamics, heat and mass transfer properties, and mixing. Various non-intrusive measurement techniques, such as electric capacitance tomography and radioactive particle tracking technique, are available to advance the fundamental understanding of the microscopic and macroscopic phenomena of fluidization. Till date, the... 

In addition to these complications, Moad (1999) notes that, for typical reactive modifications, the amount of modification can be quite small (0.5-2 mol%) and therefore very difficult to characterize. However, Moad (1999) does suggest some techniques such as chemical methods, FT-IR, NMR and DSC that may be useful to aid characterization. Janssen (1998) also notes complications of thermal, hydrodynamic and chemical instabilities that can occur in reactive extrusion that must be addressed by combining knowledge of the chemistry and of the physics (flow behaviour, mixing) of the reactive extrusion process. Xanthos (1992) presents the importance of understanding both the chemistry and the reaction engineering fundamentals of reactive extrusion, in order better to understand and model the process in practice. 

The book contains a concise and systematic exposition of fundamental problems of hydrodynamics, heat and mass transfer, and physicochemical hydrodynamics, which constitute the theoretical basis of chemical engineering science. 

The introduction of hydrodynamic considerations led to direct calculations of unsaturated hydraulic conductivity at the pore and sample scale and provide the basis for incorporating fundamental aspects of reactive solute transport. 

J. Boyd and A. A. Raimondi, Hydrodynamic Lubrication-Fundamental Requirements, Chapter 3 of Standard Handbook of Lubrication Engineering, J. J. O Connor, Editor, McGraw-Hill, New York, 1968. A digest of the principal simple formulas of hydrodynamic lubrication. 

In comparison with distillation, the most widely used process, knowledge of the fundamentals of Uquid/liquid extraction is limited. A sufficiently accurate description of the hydrodynamics and mass-transfer rates of liquid systems for the design of apparatus is currently not possible for many practical applications.The development of an extraction apparatus generally requires cost-intensive and timepilot plants. Tests with original solutions, for example, from an integrated miniplant, are especially important here (see Section 4.5). 

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