Hydrodynamic theories

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

Martin P C, Parodi O and Pershan P S 1972 Unified hydrodynamic theory for crystals, liquid crystals and normal fluids Phys.Rev. A 6 2401-20... 

A detailed hydrodynamic theory has been developed by Kirkwood and Riseman which indeed reduces to the limits predicted above. 

State For Gases at Extremely High Pressure And Temperatures From the Hydrodynamic Theory of Detonation , JChemPhys 15, 518-24 (1947) CA 41, 6047 (1947) 54) W.D. Crater,... 

Hydrodynamic Theory of Detonation, I. Thermochemistry And Equation of State of The Explosion Products of Condensed Explosives , Res (London) 1, 132-44 (1947) CA 44, 10321 (1950) 66) J. Svadeba, Impact Sens -... 

The CMP process is regarded as a combination of chemical effect, mechanical effect, and hydrodynamic effect [110-116]. Based on contact mechanics, hydrodynamics theories and abrasive wear mechanisms, a great deal of models on material removal mechanisms in CMP have been proposed [110,111,117-121]. Although there is still a lack of a model that is able to describe the entire available CMP process, during which erosion and abrasive wear are agreed to be two basic effects. 

A great deal of research remains to be done in this area. We are currently extending in the study of spatial correlations in the non-equilibrium fluids to time correlations with the hope of establishing a correspondence between MD and fluctuating hydrodynamic theory. We are also using these systems to study the roles of viscosity and conductivity in fluid behavior under different external constraints. Finally, we plan to continue our research into the formation of spatial structures in fluids. 

Hydrodynamic theory shows that the thickness, 8, of the boundary layer is not constant but increases with increasing distance y from the flow s stagnation point at the surface (Fig. 4.4) it also depends on the flow velocity ... 

Huan et al. [41] measured the behavior of a small fluidized bed consisting of 45-80 mustard seeds in a small-bore vertical magnet. The small sample size allowed short pulses, and spatial distribution of collision correlation times and granular temperature were measured directly and compared with the hydrodynamic theory of Garzo and Dufty [42], This paper [41] contains an excellent survey of previous experiments on fluidized beds. 

Lienhard, J. H., and V. K. Dhir, 1973b, Extended Hydrodynamic Theory of the Peak and Minimum Pool-Boiling Heat Fluxes, NASA CR-2270, UCLA, Los Angeles, CA. (2)... 

Flow of trains of surfactant-laden gas bubbles through capillaries is an important ingredient of foam transport in porous media. To understand the role of surfactants in bubble flow, we present a regular perturbation expansion in large adsorption rates within the low capillary-number, singular perturbation hydrodynamic theory of Bretherton. Upon addition of soluble surfactant to the continuous liquid phase, the pressure drop across the bubble increases with the elasticity number while the deposited thin film thickness decreases slightly with the elasticity number. Both pressure drop and thin film thickness retain their 2/3 power dependence on the capillary number found by Bretherton for surfactant-free bubbles. Comparison of the proposed theory to available and new experimental... 

These are the basic equations of the hydrodynamic theory of detonation. If p2 and v2 can be determined, they enable the remaining features of the detonation wave to be calculated. Unfortunately p2 and v, relate to conditions in the detonation wave and not to the lower pressure conditions which the explosion products would reach at equilibrium in, for example, a closed vessel. Therefore, further calculations are needed to determine p2 and v2. 

The major difficulty in applying this hydrodynamic theory of detonation to practical cases lies in the calculation of E2, the specific internal energy of the explosion products immediately behind the detonation front, without which the Rankine-Hugoniot curve cannot be drawn. The calculations require a knowledge of the equation of state of the detonation products and also a full knowledge of the chemical equilibria involved, both at very high temperatures and pressures. The first equation of state used was the Abel equation... 

Extension of the hydrodynamic theory to explain the variation of detonation velocity with cartridge diameter takes place in two stages. First, the structure of the reaction zone is studied to allow for the fact that the chemical reaction takes place in a finite time secondly, the effect of lateral losses on these reactions is studied. A simplified case neglecting the effects of heat conduction or diffusion and of viscosity is shown in Fig. 2.5. The Rankine-Hugoniot curves for the unreacted explosive and for the detonation products are shown, together with the Raleigh line. In the reaction zone the explosive is suddenly compressed from its initial state at... 

The Hydrodynamic Theory of fluidized bed stability was proposed by Foscolo and Gibilaro who adapted the stability principle of Wallis. They postulated that a fluidized bed is composed of two interpenetrating fluids. One fluid is the gas phase, and the solids phase is also considered as a continuous fluid phase. In this theory, voidage disturbances in the bed propagate as dynamic and kinetic waves. The stability of the fluidized bed depends upon the relative velocities of these two waves. The velocities of the kinetic wave (ue) and the dynamic wave (nj are ... 

The Hydrodynamic Theory of Foscolo and Gibilaro has been shown to predict the increase in emb with temperature and pressure very well. This is shown in Figs. 7 and 8, respectively, for the data of Rapagna (1994) and Crowther et al., (1978). Jacob and Weimer (1987) also reported that the Foscolo and Gibilaro theory successfully predicted the increase in emb with increasing pressure. 

Equation (459), together with Eq. (450), is in agreement with classical hydrodynamical theory, except that in this latter case the boundary conditions on the two spheres allow us to set... 

Combining the above descriptions leads to a picture that describes the experimentally observed concentration dependence of the polymer diffusion coefficient. At low concentrations the decrease of the translational diffusion coefficient is due to hydrodynamic interactions that increase the friction coefficient and thereby slow down the motion of the polymer chain. At high concentrations the system becomes an entangled network. The cooperative diffusion of the chains becomes a cooperative process, and the diffusion of the chains increases with increasing polymer concentration. This description requires two different expressions in the two concentration regimes. A microscopic, hydrodynamic theory should be capable of explaining the observed behavior at all concentrations. 

Monteiro, C. Herve du Penhoat, C. Translational Diffusion of Dilute Aqueous Solutions of Sugars as Probed by NMR and Hydrodynamic Theory. J. Phys. Chan. A 2001, 105, 9827-9833. 

In a hydrodynamic theory of the free, clean, surface of a turbulent liquid, Levich 19a) postulates that there exists an upper zone of liquid, of thickness X, in which the turbulent regime is so altered by the surface tension (which opposes local deformations) that within this zone the turbulence is severely damped. Right in the plane of the surface (at... 

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