Vapor domain

Chapter 9 is devoted to regimes of capillary flow with a distinct interface. The effect of certain dimensionless parameters on the velocity, temperature and pressure within the liquid and vapor domains are considered. The parameters corresponding to the steady flow regimes, as well as the domains of flow instability are defined. 

The forced fluid flow in heated micro-channels with a distinct evaporation front is considered. The effect of a number of dimensionless parameters such as the Peclet, Jacob numbers, and dimensionless heat flux, on the velocity, temperature and pressure within the liquid and vapor domains has been studied, and the parameters corresponding to the steady flow regime, as well as the domains of flow instability are delineated. An experiment was conducted and demonstrated that the flow in microchannels appear to have to distinct phase domains one for the liquid and the other for the vapor, with a short section of two-phase mixture between them. 

Fig. 9.2 The velocity, temperature and pressure distributions along the axis of a heated capillary (A = w, T, P), G and L correspond to vapor and liquid domains, respectively. Solid line indicates the liquid domain, and dotted line indicates the vapor domain (concave meniscus). Reprinted from Peles et al. (2001) with permission...

Using the system (9.15-9.17) we determine the distribution of velocity, temperature and pressure within the liquid and vapor domains. We render the equations dimensionless by the following characteristic scales l,o for velocity, 7l,o for temperature, Pl,o for density, Pl,q for pressure, Pl,o Lo f " force and L for length... 

Considering the pressure distribution in the liquid and vapor domains and taking into account that the drag force F takes the form... 

The temperature distribution within the liquid and vapor domains of a heated micro-channel is plotted in Pig. 9.3. The liquid entering the channel absorbs heat... 

The temperature distribution in the capillary slot is presented in Fig. 10.18. These data show the wall superheat influence on temperature fields in liquid and vapor domains. In these cases, significant heterogeneity of temperature fields is observed. 

The temperature distribution in a heated micro-channel is not uniform (Fig. 11.2, Peles et al. 2000). The liquid entering the channel absorbs heat from the walls and its temperature increases. As the liquid flows toward the evaporating front it reaches a maximum temperature and then the temperature begins to decrease up to the saturated temperature. Within the vapor domain, the temperature increases monotoni-cally from saturation temperature Ts up to outlet temperature Tg.q. 

Figure 25-11. Liquid-vapor separation curve in the T, v diagram. Note that solid-liquid and solid-vapor domains are not shown for clarity.

The substituted five-ring OPVs have been processed into poly crystal line thin films by vacuum deposition onto a substrate from the vapor phase. Optical absorption and photolumincscence of the films are significantly different from dilute solution spectra, which indicates that intermolecular interactions play an important role in the solid-state spectra. The molecular orientation and crystal domain size can be increased by thermal annealing of the films. This control of the microstruc-ture is essential for the use of such films in photonic devices. 

The onset of flow instability in a heated capillary with vaporizing meniscus is considered in Chap 11. The behavior of a vapor/liquid system undergoing small perturbations is analyzed by linear approximation, in the frame work of a onedimensional model of capillary flow with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes on the flow stability is studied. A scenario of a possible process at small and moderate Peclet number is considered. The boundaries of stability separating the domains of stable and unstable flow are outlined and the values of the geometrical and operating parameters corresponding to the transition are estimated. 

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. 

Evaporative two-phase flow in a heated micro-channel resembles a two-phase slug flow with distinct domains of liquid and vapor. These domains are divided by the infinitely thin evaporating front, which propagates relatively to the fluid with a velocity u f equal (numerically) to the linear rate of liquid evaporation. In the frame of reference associated with micro-channel walls, the velocity of the evaporation front is... 

The temperature distribution has a characteristic maximum within the liquid domain, which is located in the vicinity of the evaporation front. Such a maximum results from two opposite factors (1) heat transfer from the hot wall to the liquid, and (2) heat removal due to the liquid evaporation at the evaporation front. The pressure drops monotonically in both domains and there is a pressure jump at the evaporation front due to the surface tension and phase change effect on the liquid-vapor interface. 

Thus the maximum of the vapor (Xmo) and liquid (imL) temperatures are located at the outlet cross-section of the micro-channel, and in front of the evaporation front (inside the liquid domain), respectively. 

The quasi-one-dimensional model described in the previous chapter is applied to the study of steady and unsteady flow regimes in heated micro-channels, as well as the boundary of steady flow domains. The effect of a number of dimensionless parameters on the velocity, temperature and pressure distributions within the domains of liquid vapor has been studied. The experimental investigation of the flow in a heated micro-channel is carried out. 

An increase of the Peclet number leads to a decrease of the length of liquid domain, as well as an increase of the liquid-vapor heat flux ratio at the evaporating front. 

The general features of two-dimensional flow with evaporating liquid-vapor meniscus in a capillary slot were studied by Khrustalev and Faghri (1996). Following this work we present the main results mentioned in their research. The model of flow in a narrow slot is presented in Fig. 10.16. Within a capillary slot two characteristic regions can be selected, where two-dimensional or quasi-one-dimensional flow occurs. Two-dimensional flow is realized in the major part of the liquid domain, whereas the quasi-one-dimensional flow is observed in the micro-film region, located near the wall. 

The results of numerical calculations of the velocity distribution within the vapor and liquid domains for two values of the difference between wall and saturation temperatures are shown in Fig. 10.17. It is seen that the vapor velocity reaches 100-150 m/s in the region of micro-film. The liquid velocity is much smaller than those in vapor. 

Under severe conditions (above 700°C), a potassium vapor is formed. It plays a special role in the activation of carbonaceous materials, easily penetrating in the graphitic domains that form cage-like micropores. The efficient development of micropores, which often gives a few-fold increase of the total specific surface area, is very useful for the application of these materials in supercapacitors [13-14]. 

Combined light diffraction and interference on hierarchical nanostructures Combined action of adsorption and capillary condensation of vapors in the domains of ordered hierarchical nanostructures 19... 

A new value of frequency is specified and the calculations repeated. Table 12.3 gives a FORTRAN program that performs alt these calculations, The initial part of the program solves for all the steadystate compositions and flow rates, given feed composition and feed flow rate and the desired bottoms and distillate compositions, by converging on the correct value of vapor boilup Vg. Next the coeflicients for the linearized equations arc calculated. Then the stepping technique is used to calculate the intermediate g s and the final P(j transfer functions in the frequency domain. 

For typical catalyst layers impregnated with ionomer, sizes of hydrated ionomer domains that form during self-organization are of the order of 10 nm. The random distribution and tortuosity of ionomer domains and pores in catalyst layers require more complex approaches to account properly for bulk water transport and interfacial vaporization exchange. A useful approach for studying vaporization exchange in catalyst layers could be to exploit the analogy to electrical random resistor networks of... 

---