Nonsteady Flow

Papadopoulos, I. S., 1965, Nonsteady Flow to a Well in an Infinite Anisotropic Aquifer In Proceedings of the Symposium on Hydrology of Fractured Rocks, IAHS, Dubrovnik, pp. 21-31. 

G. Rudinger, Wave Diagrams for Nonsteady Flow in Ducts, New York D. van Nostrand, 1955. 

By using the results of Sparrow and Gregg, who solved the nonsteady flow problem, the low-frequency expression of / can be obtained following the present notation as ... 

Stemling and Scriven wrote the interfacial boundary conditions on nonsteady flows with free boundary and they analyzed the conditions for hydrodynamic instability when some surface-active solute transfer occurs across the interface. In particular, they predicted that oscillatory instability demands suitable conditions cmcially dependent on the ratio of viscous and other (heat or mass) transport coefficients at adjacent phases. This was the starting point of numerous theoretical and experimental studies on interfacial hydrodynamics (see Reference 4, and references therein). Instability of the interfacial motion is decided by the value of the Marangoni number, Ma, defined as the ratio of the interfacial convective mass flux and the total mass flux from the bulk phases evaluated at the interface. When diffusion is the limiting step to the solute interfacial transfer, it is given by... 

The material presented earlier was confined to steady-state flows over simply shaped bodies such as flat plates, with and without pressure gradients in the streamwise direction, or stagnation regions on blunt bodies. The simplicity of these flow configurations allows reduction of the problems to the solution of steady-state ordinary differential equations. The evaluation of convective heat transfer to more complex three-dimensional configurations, characteristic of real aerodynamic vehicles, involves the solution of partial differential equations. Even when the latter are confined to steady-state problems, they require extensive use of computers in the solution of finite difference or finite element formulations Nonsteady flows further complicate the problems by introducing another dimension, namely, time. 

To gain insight into the hemodynamic analog of c, one needs to apply the PDF model to obtain a relationship that relates to pressure and flow. A natural starting point is the Bernoulli equation for nonsteady flow ... 

The secondary flows from natural convection can become larger than the primary flow, so it seems likely that the secondary flows might become turbulent or nonsteady. Shown in Tables 1 and 2 are the dimensionless groups at the inlet and outlet, based on cup-average quantities, as well as the Reynolds numbers for the primary and secondary flows (Reynolds numbers defined in terms of the respective total mass flowrate, the viscosity and the ratio of tube perimeter to tube area). 

PF Ni, NFH Ho, JF Fox, H Leuenberger, WI Higuchi. Theoretical model studies of intestinal drug absorption. V. Nonsteady-state fluid flow and absorption. Int J Pharm 5 33-47, 1980. 

R Zipp, NFH Ho. Nonsteady state model of absorption of suspensions in the GI tract Coupling multi-phase intestinal flow with blood level kinetics. Pharm Res 10 S210, 1993. 

A group of scientists have studied current transients in biased M-O-M structures.271,300 The general behavior of such a system may be described by classic theoretical work.268,302 However, the specific behavior of current transients in anodic oxides made it necessary to develop a special model for nonsteady current flow applicable to this case. Aris and Lewis have put forward an assumption that current transients in anodic oxides are due to carrier trapping and release in the two systems of localized states (shallow and deep traps) associated with oxygen vacancies and/or incorporated impurities.301 This approach was further supported by others,271,279 and it generally resembles the oxide band structure theoretically modeled by Parkhutik and Shershulskii62 (see. Fig. 37). 

Semibatch or semiflow processes are among the most difficult to analyze from the viewpoint of reactor design because one must deal with an open system under nonsteady-state conditions. Hence the differential equations governing energy and mass conservation are more complex than they would be for the same reaction carried out batchwise or in a continuous flow reactor operating at steady state. 

Figure 2a represents the concentration profile of the tin species during the service life of the coating. The diffusion in the polymer matrix is represented by Fick s second law for nonsteady state flow ... 

Detonation, Steady and Nonsteady State in (Steady Flaw or Streamline Flow and Nonsteady State in). This is the case when every particle that flows past a fixed point in space will have the same q, p and P at that point independent of time. In this condition, every point of the fluid continuum has a corresponding fluid velocity vector q. The term streamlines signifies a family of curves which are everyr where tangent to q thus, the direction of each streamline is everywhere that of the motion of the fluid... 

The treatment of nonsteady-state diffusion is a question of solving Fick s second law of diffusion. In many cases, however, the equations can be taken from the treatments of the analogous problems in heat flow in solids. The point is that heat flow and diffusion are described by mathematically similar methods. 

Which experimental method should be used depends on the type of reactor and how it will be operated, and if clean or process water is to be used for the measurement. Nonsteady state methods are generally simpler and faster to perform if kLa is to be determined in clean water without reaction. For processes that are operated at steady state with a reaction, determination of kLa using steady state methods are preferred, since continuous-flow processes need not be interrupted and operating conditions similar to the normal process conditions can be used. This is especially important for systems with reactions because the reaction rate is usually dependent on the concentration of the reactants present. They are thus often applied for investigations of the mass transfer coefficient under real process conditions with chemical reactions kLa(02) or biological activity kLa(02), e. g. in waste water treatment systems. 

The continuous-flow nonsteady state measurements can be made after the reactor has reached steady state, which usually takes at least 3 to 5 times the hydraulic retention time under constant conditions. Then an appropriate amount of the compound to be oxidized (e. g. Na2S03) is injected into the reactor. An immediate decrease in the liquid ozone concentration to c, 0 mg L-1 indicates that the concentration is correct. Enough sulfite has to be added to keep cL = 0 for at least one minute so that it is uniformly dispersed throughout the whole reactor. Thus a bit more than one mole of sodium sulfite per mole ozone dissolved is necessary. The subsequent increase in cL is recorded by a computer or a strip chart. The data are evaluated according to equation 3-24, the slope from the linear regression is - (2/,/Vj + KLa(03)). 

Rudinger, G. and Chang, A. (1964). Analysis of Nonsteady Two-Phase Flow. Phys. Fluids, 7,1747. Soo, S. L. (1960). Effect of Transport Process on Attenuation and Dispersion in Aerosols. J. Acoustical Society of America, 32,943. 

The pressure and velocity profiles derived above are applicable to steady (time-independent) gas flow. Equations describing nonsteady gas flow (pressure pulses and transients, etc.) can be found elsewhere [9]. 

In a third paper by the Bernard and Holm group, visual studies (in a sand-packed capillary tube, 0.25 mm in diameter) and gas tracer measurements were also used to elucidate flow mechanisms ( ). Bubbles were observed to break into smaller bubbles at the exits of constrictions between sand grains (see Capillary Snap-Off, below), and bubbles tended to coalesce in pore spaces as they entered constrictions (see Coalescence, below). It was concluded that liquid moved through the film network between bubbles, that gas moved by a dynamic process of the breakage and formation of films (lamellae) between bubbles, that there were no continuous gas path, and that flow rates were a function of the number and strength of the aqueous films between the bubbles. As in the previous studies (it is important to note), flow measurements were made at low pressures with a steady-state method. Thus, the dispersions studied were true foams (dispersions of a gaseous phase in a liquid phase), and the experimental technique avoided long-lived transient effects, which are produced by nonsteady-state flow and are extremely difficult to interpret. 

An alternative is the use of an optical method to measure particulate concentrations and size distributions. This technique has the obvious advantage of having a negligible effect on the particulates since the equipment would be external to the exhaust system. An optical method also has the potential to be much simpler to use since it would eliminate the need for elaborate and cumbersome systems containing probes, stack samplers, flow development tunnels, filters, and heat exchangers. In addition, final data from an optical system could be immediately obtained electronically as opposed to weighing the various filters in a particle impactor by hand, and as such, the optical analyzer is a real time instrument capable of following exhaust gas fluctuations and other nonsteady effects. 

Next, a mathematical model that allows description of the separation and concentration of the components of a metallic mixture will be detailed the principal assumptions of the model are (1) convective mass transfer dominates diffusive mass transfer in the fluid flowing inside the HFs, (2) the resistance in the membrane dominates the overall mass transport resistance, therefore the overall mass transfer coefficient was set equal to the mass transfer coefficient across the membrane, and (3) chemical reactions between ionic species are sufficiently fast to ignore the contribution of the chemical reaction rates. Thus, the reacting species are present in equilibrium concentration at the interface everywhere [31,32,58,59]. For systems working under nonsteady state, it is also necessary to describe the change in the solute concentration with time both in the modules and in the reservoir tanks. The reservoir tanks will be modeled as ideal stirred tanks. 

Nonsteady, One-Dimensional, Internal, Compressible Flows, JOHN A.C. KENTFIELD, Oxford University Press 1993... 

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