# Hydrodynamics

On triangular diagrams, comparisons of calculated and experimental results can be deceiving. A more realistic representation is provided by Figure 18, comparing experimental solute distributions with those calculated from the UNIQUAC equation for four ternary systems. For three of these systems, calculations were made using the parameters determined from binary data plus one ternary tie line however, for the 2,2,4-trimethylpen-tane-furfural-cyclohexane system, parameters were obtained from binary data alone. With the exception of the region very near the plait point, calculated distributions are good. Fortunately, commercial extractions are almost never conducted near the plait point since the small density difference in the plait-point region causes hydrodynamic difficulties (flooding). [c.71]

When two metallic surfaces are lubricated in a hydrodynamic regime, the oil film is stable and problems of wear are not very important. In severe service, the film can be destroyed from then on the metallic parts rubbing on each other can cause first metal loss and then even the seizing of the parts by welding. [c.362]

If, however, the reservoir pressure drops below the bubble point, then gas will be liberated in the reservoir. This liberated gas may flow either towards the producing wells under the hydrodynamic force imposed by the lower pressure at the well, or it may migrate [c.111]

Once the liberated gas has overcome a critical gas saturation in the pores, below which it is immobile in the reservoir, it can either migrate to the crest of the reservoir under the influence of buoyancy forces, or move toward the producing wells under the influence of the hydrodynamic forces caused by the low pressure created at the producing well. In order to make use of the high compressibility of the gas, it is preferable that the gas forms a secondary gas cap and contributes to the drive energy. This can be encouraged by reducing the pressure sink at the producing wells (which means less production per [c.186]

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate [c.202]

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]. [c.613]

Since the drop volume method involves creation of surface, it is frequently used as a dynamic technique to study adsorption processes occurring over intervals of seconds to minutes. A commercial instrument delivers computer-controlled drops over intervals from 0.5 sec to several hours [38, 39]. Accurate determination of the surface tension is limited to drop times of a second or greater due to hydrodynamic instabilities on the liquid bridge between the detaching and residing drops [40], [c.21]

A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. [c.35]

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. [c.120]

The effects of electric fields on monolayer domains graphically illustrates the repulsion between neighboring domains [236,237]. A model by Stone and McConnell for the hydrodynamic coupling between the monolayer and the subphase produces predictions of the rate of shape transitions [115,238]. [c.139]

V. G. Levich, Physicochemical Hydrodynamics, translated by Scripta Technica, Inc., Prentice-Hall, Englewood Cliffs, NJ, 1962, p. 603. [c.162]

Marlow and Rowell discuss the deviation from Eq. V-47 when electrostatic and hydrodynamic interactions between the particles must be considered [78]. In a suspension of glass spheres, beyond a volume fraction of 0.018, these interparticle forces cause nonlinearities in Eq. V-47, diminishing the induced potential E. [c.188]

The thickness of an adsorbed polymer layer is important for many applications. Thus many studies have centered on measuring a moment of the concentration profile. Ellipsometric techniques reveal an optical thickness that depends on the index of refraction difference between the polymer and the solvent [78,79]. This measure of thickness weights the loop and train contributions more heavily than the tails. The influence of the tails enters into hydrodynamic measurements of polymer layer thicknesses either through dynamic light scattering [80] or viscometry on colloidal particles [81] or permeability of pores carrying adsorbed polymer [82]. The adsorbed polymer thickness increases with the adsorbed amount and the polymer molecular weight, the thickness scaling as a power of the molecular weight with the exponent varying from 0.4 to 0.7. Generally, the hydrodynamic measures of thickness are larger owing to the significant drag exerted on the fluid by the dangling tails. [c.403]

TWo limiting conditions exist where lubrication is used. In the first case, the oil film is thick enough so that the surface regions are essentially independent of each other, and the coefficient of friction depends on the hydrodynamic properties, especially the viscosity, of the oil. Amontons law is not involved in this situation, nor is the specific nature of the solid surfaces. [c.443]

Fig. XII-6. Regions of hydrodynamic and boundary lubrications. (From Ref. 42.) |

The preceding treatment relates primarily to flocculation rates, while the irreversible aging of emulsions involves the coalescence of droplets, the prelude to which is the thinning of the liquid film separating the droplets. Similar theories were developed by Spielman [54] and by Honig and co-workers [55], which added hydrodynamic considerations to basic DLVO theory. A successful experimental test of these equations was made by Bernstein and co-workers [56] (see also Ref. 57). Coalescence leads eventually to separation of bulk oil phase, and a practical measure of emulsion stability is the rate of increase of the volume of this phase, V, as a function of time. A useful equation is [c.512]

There have been some studies of the equilibrium shape of two droplets pressed against each other (see Ref. 59) and of the rate of film Winning [60, 61], but these are based on hydrodynamic equations and do not take into account film-film barriers to final rupture. It is at this point, surely, that the chemistry of emulsion stabilization plays an important role. [c.513]

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. [c.671]

Examples of even processes include heat conduction, electrical conduction, diflfiision and chemical reactions [4], Examples of odd processes include the Hall effect [12] and rotating frames of reference [4], Examples of the general setting that lacks even or odd synnnetry include hydrodynamics [14] and the Boltzmaim equation [15]. [c.693]

Fox R F and Uhlenbeck G E 1970 Contributions to non-equilibrium thermodynamics. I. Theory of hydrodynamical fluctuations P/rys. Fluids 13 1893 [c.714]

A3.3.2.2 FLUCTUATIONS IN THE HYDRODYNAMIC DOMAIN [c.720]

Interesting pattern formations also occur in surfactants spreading on water due to a hydrodynamic instability [52]. The spreading velocity from a crystal may vary with direction, depending on the contour and crystal facet. There may be sufficient imbalance to cause the solid particle to move around rapidly, as does camphor when placed on a clean water surface. The many such effects have been reviewed by Stemling and Scriven [53]. [c.112]

Quantitative measurements of flocculation rates have provided estimates of Hamaker constants in qualitative agreement with theory. One assumes diffusion-limited flocculation where the probability to aggregate decreases with the exponential of the potential energy barrier height of the type illustrated in Fig. Vl-5. The barrier height is estimated from the measured flocculation rate other measurements (see Section V-6) give the surface (or zeta) potential leaving the Hamaker constant to be determined from Equations like VI-36 [47 9]. Complications arise from the assumption of constant surface potential during aggregation, double-layer relaxation during aggregation [50-52], and nonuniform charge distribution on the particles [53-55], In studies of the stability of ZnS sols in NaCl and CaC Duran and co-workers [56] found they had to add the Lewis acid-base interactions developed by van Oss [57] to the DLVO potential to model their measurements. Alternatively, the initial flocculation rate may be measured at an ionic strength such that no barrier exists. By this means Apwp was found to be about 0.7 x 10 erg for aqueous suspensions of polystyrene latex [58]. The hydrodynamic resistance between particles in a viscous fluid must generally be recognized to obtain the correct flocculation rates [3]. [c.242]

Other SFA studies complicate the picture. Chan and Horn [107] and Horn and Israelachvili [108] could explain anomalous viscosities in thin layers if the first layer or two of molecules were immobile and the remaining intervening liquid were of normal viscosity. Other inteipretations are possible and the hydrodynamics not clear, since as Granick points out [109] the measurements average over a wide range of surface separations, thus confusing the definition of a layer thickness. McKenna and co-workers [110] point out that compliance effects can introduce serious corrections in constrained geometry systems. [c.246]

Since wetting films and coating processes involve the flow of fluid over the solid, the contact angle cannot be viewed as simply a static quantity, it also depends on the speed with which the three-phase line advances or recedes. An understanding of the dynamic contact angle requires detailed hydrodynamic analysis outside the scope of this book hence, we simply summarize the basic findings and refer to the reader to several good references [87-90]. The key element of the analysis is the proper definition of the boundary condition at the three-phase line. The presence of a singularity at the moving contact [c.361]

The fundamental dimensionless parameter characterizing the speed of contact line motion is the capillary number, Ca = 1//i/7lv, where U is the velocity and /i is the fluid viscosity. Ca represents the relative importance of intertia to interfacial tension in determining the shape of the free surface near the contact line. Recent experimental work by Garoff and co-workers [89, 92, 93] has provided a measurement of the liquid-vapor profile in the vicinity of the contact line. They found that the profiles were consistent with either the slip or thin-film boundary conditions except at the highest Ca (9 x 10 ). In an analysis of dewetting situations, Brochard-Wyart and deGennes [90] found that hydrodynamic effects dominate at low contact angles and low velocities but molecular effects become important when the contact angle is large and the velocity is high, a situation frequently encountered in practical applications. Neumann and co-workers have developed a high-precision capillary rise technique to measure contact angles at low velocities [94]. [c.362]

Much attention has been devoted in recent years to wetting, dewetting, and instabilities at the wetting front. As with the contact angle, recent theoretical work has focused on the importance of long-range forces [1] and hydrodynamics [2, 3] on wetting. The structural forces in simple liquids result in stratified flows of molecular dimension [4, 5]. The primary effect of long-range interactions is that liquids do not spread down to monolayer dimensions but rather retain a panctdce structure of finite thickness. The pancake structure has been revealed by ellipsometric studies by Cazabat and co-workers [6] and is nicely summarized in a review [7]. The effect of the surface energy has been studied using Langmuir-Blodgett films or self-assembled monolayers to create surfaces of different energies [8, 9]. In the case of dry wetting where a nonvolatile material is spreading onto a surface where 5l/s is nearly zero, Silberzan and Leger found wetting behavior between partial and total wetting [9]. In this regime, the spreading is highly sensitive to the surface polarizability. [c.466]

Themiodynamics is a phenomenological theory based upon a small number of fundamental laws, which are deduced from tire generalization and idealization of experimental observations on macroscopic systems. The goal of statistical mechanics is to deduce the macroscopic laws of themiodynamics and other macroscopic theories (e.g. hydrodynamics and electromagnetism) starting from mechanics at a microscopic level and combining it with the mles of probability and statistics. As a branch of theoretical physics, statistical mechanics has extensive applications in physics, chemistry, biology, astronomy, materials science and engineering. Applications have been made to systems which are in themiodynamic equilibrium, to systems in steady state and also to non-equilibrium systems. Even though the scope of statistical mechanics is quite broad, this section is mostly lunited to basics relevant to equilibrium systems. [c.378]

The practical value of the Boltzmaim equation resides in tlie utility of the predictions that one can obtain from it. The fomi of the Boltzmaim is such that it can be used to treat systems with long range forces, such as Leimard-Jones particles, as well as systems with finite-range forces. Given a potential energy frmction, one can calculate the necessary collision cross sections as well as the various restituting velocities well enough to derive practical expressions for transport coefficients from the Boltzmaim equation. The method for obtaining solutions of the equation used for fluid dynamics is due to Enskog and Chapman, and proceeds by finding solutions that can be expanded in a series whose first temi is a Maxwell-Boltzmaim distribution of local equilibrium fomi. That is, the first takes the fomi given by (A3.1.55). witli the quantities A, p and u being fimctions of r and t. One then assumes that the local temperature, (/rgP) mean velocity, u, and local density, n, are slowly varying in space and time, where the distance over which they change, L, say is large compared with a mean free path, L. The higher temis in the Chapman-Enskog solution are then expressed in a power series in gradients of the five variables, n, p and u, which can be shown to be an expansion in powers of l/L < 1. Explicit results are then obtained for the first, and higher, order solution in / /L, which in turn lead to Navier-Stokes as well as higher order hydrodynamic equations. Explicit expressions are obtained for the various transport coefficients, which can then be compared with experimental data. The agreement is sufficiently close that the theoretical results provide a usefiil way for checking the accuracy of various trial potential energy fimctions. A complete account of the Chapman-Enskog solution method can be found in the book by Chapman and Cowling [3], and comparisons with experiments, the extension to polyatomic molecules, and to quantum gases, are discussed at some length in the books of Hirslifelder et al [4], of Hanley [5] and of Kestin [VT as well as in an enomious literature. [c.686]

A proposal based on Onsager s theory was made by Landau and Lifshitz [27] for the fluctuations that should be added to the Navier-Stokes hydrodynamic equations. Fluctuating stress tensor and heat flux temis were postulated in analogy with the Onsager theory. Flowever, since this is a case where the variables are of mixed time reversal character, tlie derivation was not fiilly rigorous. This situation was remedied by tlie derivation by Fox and Ulilenbeck [13, H, 18] based on general stationary Gaussian-Markov processes [12]. The precise fomi of the Landau proposal is confimied by this approach [14]. [c.705]

Depending on the type of scattering probe and the scattering geometry, other experiments can probe other similar correlation fiinctions. Elastic scattering experiments effectively measure frequency integrated spectra and, hence, probe only the space-dependent static structure of a system. Electron scattering experiments probe charge density correlations, and magnetic neutron scattering experiments the spin density correlations. Inelastic themial neutron scattering from a non-magnetic system is a sharper probe of density-density correlations in a system but, due to the shorter wavelengths and higher frequencies involved, these results are complementary to those obtained from inelastic polarized light scattering experunents. The latter provide space-time correlations in the long-wavelength hydrodynamic regime. [c.718]

In dense systems like liquids, the molecular description has a large number of degrees of freedom. There are, however, a few collective degrees of freedom, collective modes, which when perturbed tliroiigh a fliicPiation, relax to equilibrium very slowly, i.e. with a characteristic decay time that is long compared to die molecular interaction time. These modes involve a large luimber of particles and their relaxation time is proportional to the square of their characteristic wavelength, which is large compared to the intemioleciilar separation. Hydrodynamics is suitable to describe the dynamics of such long-wavelength, slowly-relaxing modes. [c.721]

See pages that mention the term

**Hydrodynamics**:

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Corrosion, Volume 2 (2000) -- [ c.2 , c.9 ]