RATE OF DRYING

Terminal conditions of the air are read off the adiabatic saturation line and appear on the sketch  

An approximation that may be justifiable is that the critical moisture content is roughly independent of the drying conditions and that the falling rate curve is linear. Then the rate equations may be written 

Examples 9.3 and 9.4 apply these relations to a countercurrent dryer in which the humidity driving force and the equilibrium moisture content vary throughout the equipment. 

In some practical kinds of dryers, the flow patterns of gas and solid are so complex that the kind of rate equation discussed in this section cannot be applied readily. The sizing of such equipment is essentially a scale-up of pilot plant tests in similar equipment. Some manufacturers make such test equipment available. The tests may establish the residence time and the terminal conditions of the gas and solid. 

In an effort to reduce exhaust to the atmosphere, save heat, minimize pollutant discharges, and keep costs at a minimum, partial recycle is used (Cook, 1996). 

Diying Time over Constant and Falling Rate Periods with Constant Gas Conditions 

During the constant rate period, it is assumed that drying takes place from a saturated surface of the material by diffusion of the water vapour through a stationary air film into the air stream. Gilliland(8) has shown that the rates of drying of a variety of materials in this stage are substantially the same as shown in Table 16.1. 

In order to calculate the rate of drying under these conditions, the relationships obtained in Volume 1 for diffusion of a vapour from a liquid surface into a gas may be used. The simplest equation of this type is  

Since the rate of transfer depends on the velocity u of the air stream, raised to a power of about 0.8, then the mass rate of evaporation is  

This type of equation, used in Volume 1 for the rate of vaporisation into an air stream, simply states that the rate of transfer is equal to the transfer coefficient multiplied by the driving force. It may be noted, however, that (Ps — Pw) is not only a driving force, but it is also related to the capacity of the air stream to absorb moisture. 

These equations suggest that the rate of drying is independent of the geometrical shape of the surface. Work by Powell and Griffiths(9) has shown, however, that the ratio of the length to the width of the surface is of some importance, and that the evaporation rate is given more accurately as  

During constant-rate period, the free moisture leaves the saturated surface of the material by diffusion through a stationary air film into air stream. GiUiland[3] showed that the drying rate for this period for variety of material is essentially the same (around 2.0-2.8 kg/rrP/K). 

The mass rate of evaporation (W) is found to be dependent on partial pressure 

surface area A, velocity of air stream u, and ratio of length L to width B of the surface and is given below [3]. 

However, for most practical purposes drying at a constant-rate period can be assumed to be proportional to (p s — Pw) given by, 

The simple expression of time required for drying period can be expressed in terms of moisture content Wi and final moisture content equal to critical moisture content Wc as  

Other criteria for dryers and cooling towers will be cited later. 

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II This dual tilling permits the absorption of both acid smd basic vapours which may be evolved. Thus an amine hydrochloride, which has been recrystallised from concentrated hydrochloric acid, may be readily dried in such a desiccator. If concentrated sulphuric acid alone were used, so much hydrogen chloride would be liberated that tlie pressure inside the desiccator would rise considerably, smd the rate of drying would be reduced. With sodium hydroxide present, however, the hydrogen chloride is removed, smd tho water is absorbed in the normal manner by the reagents but largely by the acid. 

In paste drying the leather is spread on glass or porcelain plates and held in place with a low strength water-soluble paste. The plates are on a conveyor and the drying is done in a drying tunnel. The dryer usually has several temperature- and humidity-controUed zones to control the rate of drying and to prevent overdrying. 

There are many materials containing water of crystallization that simply cannot be dried under ordinary conditions. These materials would loose all or a portion of this water. Under such widely varying conditions drying must be accomplished in a drier that takes into consideration the rate of drying, the condition of the drying medium, and the nature of the exposed surfaces of the material. Each of these factors is complex and requires careful engineering. 

The rate of drying is high for a period initially (Figure 4.26) and then deelines. 

In the eonstant drying rate period, the rate of drying is determined by the humidity driving foree... 

Emulsion-based primer plus alkyd finish These are based on acrylic resin dispersions and have the advantage of a rapid rate of drying. They generally have excellent adhesion and flexibility but lack the sealing properties of aluminum primers. 

Temperature Although ambient temperature would be expected to have an influence on the rate of rusting, its effect is not clearly defined despite the efforts of workers to establish a relationship . It has an effect on relative humidity and consequently an indirect effect on corrosion. However, fluctuations in temperature may be more important than average temperatures because they influence condensation and the rate of drying of moisture in contact with steel. 

During the first period of drying, the liquid that covers the particle external surface and is present in the macropores evaporates. The material structure does not affect the rate of evaporation. The liquid evaporates with the rate at which heat is supplied to the surface. The rate of drying is thus limited by heat transfer between the particles and their surroundings. The temperature at the particle surface remains constant. If heat is delivered by convection this temperature is the wet-bulb gas temperature. In case of radiation (e.g. microwave driers) or conduction (e.g. indirect contact driers) the surface temperature ranges between the wet-bulb gas temperature and the boiling point of the liquid. The moisture content at the end of the constant rate of drying period is called the critical moisture content. 

The critical moisture content is a complex function of material properties, particle size (the critical moisture content is higher for large granules), and rate of drying during the constant rate period (the lower the rate, the less the critical moisture content). Therefore, the critical moisture content is difficult to predict and should be determined experimentally for the selected drier and conditions of drying. 

The rate of drying during the constant rate period can be expressed by the following equation ... 

In this paper we summarize some of the results of our measurements of rates of dry oxidation. Results of chemical analyses of residues produced by heating in flowing nitrogen atmosphere (distillation) are also reported and combined with our kinetic data to obtain values of kinetic parameters. Preliminary results of measurements of rates of wet oxidation are presented. 

Experimental conditions and initial rates of oxidation are summarized in Table V. For comparison, initial rates of dry oxidation at the same temperature and pressure of oxygen predicted by Equation 9 are included in parentheses. The predicted dry rate, measured dry rate, and measured wet rates are compared in Figure 2. The logarithms of the initial rates of heat production during wet oxidation increase approximately linearly (correlation coefficient = 0.92) with the logarithm of the partial pressure of oxygen and lead to values of In k = 2.5 and r = 0.9, as compared with values of In k = 4.8 and r = 0.6 for dry oxidation at this temperature. 

The baked pretzels are then fed through a drying stage at 120°C for 0.5 1.5 hours, depending on the size of the piece. The reason for the length of the drying step is that the rate of drying is controlled by the rate of diffusion of water in the product. The finished product is then wrapped to keep the moisture level below 3.5% (which is the point when the product become unacceptable). 

Mg of dry mass of a non-porous solid is dried under constant drying conditions in an air stream flowing at 0.75 m/s. The area of surface drying is 55 m2. If the initial rate of drying is 0.3 g/m2s, how long will it take to dry the material from 0.15 to 0.025 kg water/kg dry solid The critical moisture content of the material may be taken as 0.125 kg water/kg dry solid. If the air velocity were increased to 4.0 m/s, what would be the anticipated saving in time if the process were surface-evaporation controlled ... 

During the constant rate period, that is whilst the moisture content falls from 0.15 to 0.125 kg/kg, the rate of drying is ... 

A 100 kg batch of granular solids containing 30 per cent of moisture is to be dried in a tray dryer to 15.5 per cent moisture by passing a current of air at 350 K tangentially across its surface at the velocity of 1.8 m/s. If the constant rate of drying under these conditions is 0.7 g/sm2 and the critical moisture content is 15 per cent, calculate the approximate drying time. It may be assumed that the drying surface is 0.03 m2/kg dry mass. 

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