Condensers vapor transportion rate

As also noted in the preceding chapter, it is customary to divide adsorption into two broad classes, namely, physical adsorption and chemisorption. Physical adsorption equilibrium is very rapid in attainment (except when limited by mass transport rates in the gas phase or within a porous adsorbent) and is reversible, the adsorbate being removable without change by lowering the pressure (there may be hysteresis in the case of a porous solid). It is supposed that this type of adsorption occurs as a result of the same type of relatively nonspecific intermolecular forces that are responsible for the condensation of a vapor to a liquid, and in physical adsorption the heat of adsorption should be in the range of heats of condensation. Physical adsorption is usually important only for gases below their critical temperature, that is, for vapors. 

Levels of volatility that would lead to unacceptable rates of vapor transport-driven sintering, attrition of catalytically-active materials, or corrosion of catalytic materials or support oxides by transport from contaminants or substrate materials can be estimated given equilibrium vapor pressures and a few assumptions about evaporation rates and mass transport. In particular, the rate of condensation of a vapor species on its source solid phase at high temperatures is almost certainly non-activated and may show little configurational restriction. Therefore, using the principle of microscopic reversibility, we can take the rate constant for condensation to be approximately equal to the collision frequency. 

The transpiration method is a simple and versatile method for vapor pressure measurement at high temperatures. An inert carrier gas is passed over the condensed substance in a constant temperature furnace zone. The flow rate of the carrier gas is constant and sufficiently small so that the carrier gas is saturated with vapor, which condenses at some point downstream. The mass of vapor transported by a known volume of carrier gas is determined. If the total vapor pressure is known, from the boiling point method, the results from the transpiration method may be used to calculate the average molar mass of the vapor. 

The rate of gas absorption during water vapor condensation or evaporation is a function of both the rate of diffusion in the liquid phase, and the rate at which the water is transported. In order to isolate the effect of the water vapor transport on the rate of absorption, the increase in the amount of gas absorbed and the corresponding increase in the amount of water condensed for different SSR was determined for fixed values of time. 

For a given powder system, if it is assumed that grain boundary diffusion and vapor transport (evaporation/condensation) are the dominant mass transport mechanisms, the rates of sintering by these two mechanisms vary with the scale of the system with the following relations ... 

In systems where a liquid metal is used as the working fluid (e.g., the Rankine-cycle), liquid is converted to vapor in one part of the system and vapor to liquid in another part. The distillation effects of the vaporization process result in extremely pure condensing vapor that may be able to dissolve and transport container material. As opposed to an aU-liquid system, where the liquid is always partially saturated with container material constituents, dissolution in the condenser region can continue undiminished the dissolution rate will depend on the condensation rate and temperature. In contrast, hquid in the evaporator section will ultimately become supersaturated with respect to container material constituents, so that the heated sections of a liquid metal boiUng system will be subject to deposition rather than corrosion [S/]. 

Under steady-state operation, local mechanical equilibrium prevails at all microscopic and macroscopic interfaces in the membrane. It fixes the stationary distribution of absorbed water. The condition of chemical equilibrium is, however, lifted to allow for the flux of water. Continuity of the net water flux in the PEM and across its interfaces with adjacent media adjusts the gradients in water activity or pressure in the system. Water fluxes occur by diffusion, hydraulic permeation, and electro-osmotic drag. At external interfaces, vaporization and condensation proceed at rates that match the net water flux. These mechanisms apply to PEM operation in a working cell, as well as to ex situ water flux measurements that are conducted in order to investigate the transport properties of PEMs. 

The fundamental concept of heat transport controlled moisture uptake [17] is shown in Eq. (22), where the rate of heat gained at the solid/vapor surface (W AH) is balanced exactly by the heat flow away from the surface (Q). The term All is the heat generated by unit mass of water condensed on the surface. The two most probable sources of heat generation are the heat of water condensation and the heat of dissolution. A comparison of the heat of water condensation (0.58 cal/mg water) with the heat of dissolution for a number of salts indicates that the heat of dissolution can be neglected with little error for many materials. 

The treatment is divided into four sections. Section II deals with estimation of coefficients of heat transfer and of mass transfer. Because most, or all, of the latent heat of evaporation of the moisture is normally derived from the sensible heat of the carrier gas, our knowledge of the pertinent coefficients of heat transfer from the gas to the surface of the drying solid is summarized. A summary of the analogous mass-transfer coefficients records in condensed form gives our current knowledge of the means of estimating the rate of transport from the solid to the gas of the vapor evolved. 

Capillary condensation provides the possibility of blocking pores of a certain size with the liquid condensate simply by adjusting the vapor pressure. A permporometry lest usually begins at a relative pressure of 1, thus all pores filled and no unhindered gas transport. As the pressure is reduced, pores with a size corresponding to the vapor pressure applied become emptied and available for gas transport. The gas flow through the open mesopores is dominated by Knudsen diffusion as will be discussed in Section 4.3.2 under Transport Mechanisms of Porous Membranes. The flow rate of the noncondensable gas is measured as a function of the relative pressure of the vapor. Thus it is possible to express the membrane permeability as a function of the pore radius and construct the size distribution of the active pores. Although the adsorption procedure can be used instead of the above desorption procedure, the equilibrium of the adsorption process is not as easy to attain and therefore is not preferred. 

J is the number of nuclei formed per unit time per unit volume, No is the number of molecules of the crystallizing phase in a unit volume, v is the frequency of atomic or molecular transport at the nucleus-liquid interface, and AG is the maximum in the Gibbs free energy change for the formation of clusters at a certain critical size, 1. The nucleation rate was initially derived for condensation in vapors, where the preexponential factor is related to the gas kinetic collision frequency. In the case of nucleation from condensed phases, the frequency factor is related to the diffusion process. The value of 1 can be obtained by minimizing the free energy function with respect to the characteristic length. 

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