Quasi-fluid properties

Fluidized-bed CVD is a special technique which is used primarily in coating particles, such as nuclear fuel. A flowing gas imparts quasi-fluid properties to the particles. Figure 5.17 shows a typical fluidized-bed CVD reactor. 

The next slightly more complicated situation concerns a fluid confined to a nanoscopic slit-pore by structured rather than unstructured solid surfaces. For the time being, we shall restrict the discussion to cases in which the symmetry of the external field (represented by the substrates) i)reserves translational invarianee of fluid properties in one spatial dimension. An example of such a situation is depicted in Fig. 5.7 (see Section 5.4.1) showing substrates endowed with a chemical structm e that is periodic in one direction (x) but quasi-infinite (i.e., macroscopically large) in the other one (y). 

The quasi-one-dimensional model of laminar flow in a heated capillary is presented. In the frame of this model the effect of channel size, initial temperature of the working fluid, wall heat flux and gravity on two-phase capillary flow is studied. It is shown that hydrodynamical and thermal characteristics of laminar flow in a heated capillary are determined by the physical properties of the liquid and its vapor, as well as the heat flux on the wall. 

Below the system of quasi-one-dimensional equations considered in the previous chapter used to determine the position of meniscus in a heated micro-channel and estimate the effect of capillary, inertia and gravity forces on the velocity, temperature and pressure distributions within domains are filled with pure liquid or vapor. The possible regimes of flow corresponding to steady or unsteady motion of the liquid determine the physical properties of fluid and intensity of heat transfer. 

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

All of the experiments in pure and mixed SSME systems, as well as in the Af-stearoyltyrosine systems, have one common feature, which seems characteristic of chiral molecular recognition in enantiomeric systems and their mixtures enantiomeric discrimination as reflected by monolayer dynamic and equilibrium properties has only been detected when either the racemic or enantiomeric systems have reverted to a tightly packed, presumably quasi-crystalline surface state. Thus far it has not been possible to detect clear enantiomeric discrimination in any fluid or gaseous monolayer state. 

The analysis of the conditions within a gas channel can also be assumed to be onedimensional given that the changes in properties in the direction transverse to the streamwise direction are relatively small in comparison to the changes in the stream-wise direction. In this section, we examine the transport in a fixed cross-sectional area gas channel. The principle conserved quantities needed in fuel cell performance modeling are energy and mass. A dynamic equation for the conservation of momentum is not often of interest given the relatively low pressure drops seen in fuel cell operation, and the relatively slow fluid dynamics employed. Hence, momentum, if of interest, is normally given by a quasi-steady model,... 

Samalam [43] modeled the convective heat transfer in water flowing through microchannels etched in the back of silicon wafers. The problem was reduced to a quasi-two dimensional non-linear differential equation under certain reasonably simplified and physically justifiable conditions, and was solved exactly. The optimum channel dimensions (width and spacing) were obtained analytically for a low thermal resistance. The calculations show that optimizing the channel dimensions for low aspect ratio channels is much more important than for large aspect ratios. However, a crucial approximation that the fluid thermophysical properties are independent of temperature was made, which could be a source of considerable error, especially in microchannels with heat transfer. 

During the extraction phase the whole mass transfer may be regarded as a quasi-stationary process. Scale-up rules therefore take account of external mass transfer from the solid surface to the supercritical fluid only. If pilot and production plants are required to display the same mass transfer properties, then... 

In this equation T is the mean fluid temperature at any time, T is the wall temperature, 7] is the mean temperature of the quiescent fluid before the transient is initiated, and L is the length of the cylinder. All physical properties are evaluated at T . The length scales L and D were not sufficiently different to affect the correlation much, and L was arbitrarily chosen. The heat transfer coefficient q"l(T - T) remained constant throughout the quasi-steady period. Hiddink et al. [138] found that Eq. 4.137 also correlated data for heating only the bottom and side walls of vertical cylinders provided the cylinder diameter replaced L, and a coefficient of 0.52 rather than 0.55 was used. Their experiments were performed for length-to-diameter ratios of 0.25 to 2.0 and for 5 < Pr < 83,000. 

The equations governing the fluid motion and heat transfer in these quasi-steady regimes are (if the property values and boundary conditions are the same) identical to those for steady-state convection in the same geometry with a uniform internal generation of energy [73]. The heat transfer equations from one situation can therefore be readily transferred to the other by replacing the constant pcp dT/dt by the internal generation rate q " (in W/m3 or Btu/h-ft3). 

Rigid non-polarizable models for water attempt to approximate, via a two-body interaction, the many-body polarization effects which are responsible for a substantial contribution to the properties of the condensed phase of highly polar fluids such as water [58], especially on the dielectric constant [59], by having a large effective dipole moment. While a two-body model might work well in approximating quasi-... 

Two major features must be introduced into the standard thermodynamic framework in order to apply thermodynamics at meso-scales fluctuations and local (coordinate-dependent) properties. Thermodynamics of equilibrium fluctuations is a well developed science and we will briefly address this topic in this section. Incorporating the local inhomogeneities is another task of mesoscopic thermodynamics. In this section we introduce a phenomenological approach, which is restricted to fluids with smoothly varying properties, known as local or quasi thermodynamics, and which dates back to van der Waals. ... 

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