Evaporating front

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. 

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... 

At the evaporation front there is a jump in the flow velocity, which equals Au = l(Pl.g 1) where Pl.g = Pl/Pg Pl and po are the liquid and vapor densities, respectively. Since Pl.g 1 a jump in the flow velocity is expressed approximately... 

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. 

Taking into account the above-mentioned factors it is possible to present the stationary flow in a heated capillary as a flow of liquid and its vapor divided by an infinitely thin evaporation front. The parameters of these flows are related to each other by the condition of mass, momentum and energy conservation at the evaporation front. 

At steady flow in a heated micro-channel the conditions at the evaporation front may be expressed by the continuity of mass, thermal fluxes on the interface surface and the equilibrium of all acting forces (Landau and Lifshitz 1959). With reference to the evaporative meniscus the balance equations have the following form (Peles et al. 1998) ... 

The momentum balance equation at the evaporation front has (neglecting the effect of viscous tension and changing surface tension along of meniscus) the following form ... 

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 experimental investigation of the flow in a heated capillary shows that, depending on the value of the Peclet number, various types of the process occurred. At small Pcl, the dominant role is the bubble formation at the channel wall, whereas for Pcl > 1, liquid evaporation leads to formation of an evaporation front. 

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. 

Velocity of the evaporating front in the system of coordinates associated with the micro-channel walls... 

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. 

The extract is drawn off from the boiler at die end of the time specified, and filtered through a fine sieve or cloth, after which the water is evaporated front it until it becomes of a pasty consistence, when it maybe cut into cakes of any convenient size, and dried in an oven at a low temperature till liard, at which time it is toady for use. 

Thermal degradation, as outlined above, leads to production of volatile, low molecular weight products throughout the binder phase and the removal of the binder by evaporation of a liquid. Binder removal by this mechanism m.ay be quite similar to the drying of a moist granular material considered above (17.2.3.3.1). Considerable redistribution of the liquid occurs, and the evaporation front does not move uniformaly into the bodyT Instead, pore channels first develop deep in the body as liquid from the larger pores is drawn into the smaller pores. 

With impermeable woods - and heartwood - the supply of moisture from the interior eaimot keep paee with evaporation of water vapour from the surface, because mass flow of water is not possible and diffusion is a much slower process. Thus the surfaee moisture eontent quiekly falls below fibre saturation and the evaporative front starts reeeding into the wood. Figure 8.6 shows the parabolic moisture content profile for a slowly air-dried impermeable hardwood. Similarly for permeable softwoods that have been dried below the irreducible moisture content, Stamm (1964, 1967b) reported parabolic moisture profiles that are consistent with diffusion of both water vapour and bound water. 

Metal ring with plastic evaporated Front cover ... 

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