Evaporation, steady state

The basic assumption is that the Langmuir equation applies to each layer, with the added postulate that for the first layer the heat of adsorption Q may have some special value, whereas for all succeeding layers, it is equal to Qu, the heat of condensation of the liquid adsorbate. A furfter assumption is that evaporation and condensation can occur only from or on exposed surfaces. As illustrated in Fig. XVII-9, the picture is one of portions of uncovered surface 5o, of surface covered by a single layer 5, by a double-layer 52. and so on.f The condition for equilibrium is taken to be that the amount of each type of surface reaches a steady-state value with respect to the next-deeper one. Thus for 5o... 

SJng Je Rod-Fed Electron Beam Source. The disadvantages of multiple sources for alloy deposition can be avoided by using a single wire-fed or rod-fed source (Fig. 3) (3). A molten pool of limited depth is above the soHd rod. If the equiUbrium vapor pressures of the components of an alloy A B are in the ratio of 10 1 and the composition of the molten pool is A qB, under steady-state conditions, the composition of the vapor is the same as that of the soHd being fed into the molten pool. The procedure can be started with a pellet of appropriate composition A qB on top of a rod A B to form the molten pool initially, or with a rod of alloy A B to evaporate the molten pool until it reaches composition A qB. The temperature and volume of... 

Fig. 3. AHoy evaporation from a single rod-fed source under steady-state conditions p° = 10p° AB feed rod, A B molten pool, A qB and vapor and deposit, A B, where p° = the equilibrium vapor pressure of component B B, and p° = the equilibrium vapor pressure of component A A. Part (a) shows...

For the air—water system, the humidity is easily measured by using a wet-bulb thermometer. Air passing the wet wick surrounding the thermometer bulb causes evaporation of moisture from the wick. The balance between heat transfer to the wick and energy requited by the latent heat of the mass transfer from the wick gives, at steady state,... 

Most theories of droplet combustion assume a spherical, symmetrical droplet surrounded by a spherical flame, for which the radii of the droplet and the flame are denoted by and respectively. The flame is supported by the fuel diffusing from the droplet surface and the oxidant from the outside. The heat produced in the combustion zone ensures evaporation of the droplet and consequently the fuel supply. Other assumptions that further restrict the model include (/) the rate of chemical reaction is much higher than the rate of diffusion and hence the reaction is completed in a flame front of infinitesimal thickness (2) the droplet is made up of pure Hquid fuel (J) the composition of the ambient atmosphere far away from the droplet is constant and does not depend on the combustion process (4) combustion occurs under steady-state conditions (5) the surface temperature of the droplet is close or equal to the boiling point of the Hquid and (6) the effects of radiation, thermodiffusion, and radial pressure changes are negligible. 

The most important consideration in controUing the quality of concentrate from an evaporator is forcing the vapor rate to match the flow of excess solvent entering in the feed. The mass flow of sohd material entering and leaving are equal in the steady state ... 

Under steady-state conditions the temperature of the evaporating surface increases until the rate of sensible heat transfer to the surface equals the rate of heat removed by evaporation from the surface. To calculate this temperature, it is convenient to modify Eq. (12-26) in terms of humidity rather than partial-pressure difference, as follows ... 

In tire steady state, where these two rates are equal, the depletion of the surface, and hence the lowering of the surface concentration, and therefore the free evaporation rate of manganese below tire initial value for the alloy, which is given above, is... 

Centrifugal blowers or turbines usually cannot generate enough pressure difference to overcome the added resistance of the recycle pipes. In addition, some components may condense out in the cooler, especially with high-boiling materials or at high pressures. These must be recycled by a liquid pump through an evaporator. This in turn makes them approach a steady-state slowly. ... 

In the application of the previous chemical methods, a certain amount of steady-state continuity has been built into the system. To accomplish this, initial concentrated alkaline and acid rinse wastewaters are retained after dumping in the waste holding tank [T-91] (Figure 6.4) and acid chromium plating wastewater is stored in the waste holding tank [T-51], Extremely concentrated chromium plating wastewater from rinse step No. 1 is sent to an evaporation tank [T-40] for... 

In a highly idealized case representing the case of steady-state evaporation into a vacuum (pG = 0), Hsu and Graham (1976) use Eq. (2-92) to compute the rates of... 

Groendes and Mesler (1982) studied the saturated film boiling impacts of a 4.7 mm water droplet on a quartz surface of 460 °C. The fluctuation of the surface temperature was detected using a fast-response thermometer. The maximal temperature drop of the solid surface during a droplet impact was reported to be about 20 °C. Considering the lower thermal diffusivity of quartz, this temperature drop implies a low heat-transfer rate on the surface. Biance et al. (2003) studied the steady-state evaporation of the water droplet on a superheated surface and found that for the nonwetting contact condition, the droplet size cannot exceed the capillary length. 

Steady-state mathematical models of single- and multiple-effect evaporators involving material and energy balances can be found in McCabe et al. (1993), Yannio-tis and Pilavachi (1996), and Esplugas and Mata (1983). The classical simplified optimization problem for evaporators (Schweyer, 1955) is to determine the most suitable number of effects given (1) an analytical expression for the fixed costs in terms of the number of effects n, and (2) the steam (variable) costs also in terms of n. Analytic differentiation yields an analytical solution for the optimal n, as shown here. 

This problem illustrates the solution approach to a one-dimensional, non-steady-state, diffusional problem, as demonstrated in the simulation examples, DRY and BNZDYN. The system is represented in Fig. 4.2. Water diffuses through a porous solid, to the surface, where it evaporates into the atmosphere. 

The steady state material and energy balances for the evaporator are listed in Table VI and VII, and the notation in Table VIII. Table IX lists the enthalpy relationships for the various streams as well as the boiling point versus pressure and concentration relationships in functional form for NaOH solutions and pure water. The list of unknown variables and the numbers assigned to each is given in Table X. At this stage in the analysis there are 25 equations and 27 unknown variables. Another pair of equations comes from the problem statement in which the following is given... 

Stewart, G. and BEVERIDGE, G. S. G. Computers and Chemical Engineering 1 (1977). 3. Steady-state cascade simulation in multiple effect evaporation. 

Nguyen et al. [205] used a technique in which a constant mass flow rate of water-saturated air was forced through a water-saturated sample. It was explained that the shear force of the gas flow dragged water out of the sample. In addition, the saturated air was needed in order to prevent water loss from the sample by evaporation. Once a steady state was achieved, the pressure difference between the inlet and outlet of the apparatus was recorded. After the tests were completed, the sample was weighed to obtain its water content. Thus, the relative permeability was calculated from the pressure drop, the water content in the sample, and the mass flow rate [205]. 

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