can be held in varying degrees of bonding. Formerly, it was considered
that water in a food came into one or other of two categories, free water
or bound water. This now appears to be an oversimplification and such
clear demarcations are no longer considered useful. Water is held by forces
whose intensity ranges from the very weak forces retaining surface moisture
to very strong chemical bonds.
In many cases, a substantial part of the water is found to be loosely bound. This water can, for drying purposes, be considered as free water at the surface. A comparison of the drying rates of sand, a material with mostly free water, with meat containing more bound water shows the effect of the binding of water on drying rates. Drying rate curves for these are shown in Fig. 7.5.
However in food, unlike impervious materials such as sand, after a period of drying at a constant rate it is found that the water then comes off more slowly. A complete drying curve for fish, adapted from Jason (1958), is shown in Fig. 7.6. The drying temperature was low and this accounts for the long drying time.
Another point of importance is that many foods such as potato do not show a true constant rate drying period. They do, however, often show quite a sharp break after a slowly and steadily declining drying rate period and the concept of constant rate is still a useful approximation.
The end of the constant rate period, when X = Xc at the break point of drying-rate curves, signifies that the water has ceased to behave as if it were at a free surface and that factors other than vapour-pressure differences are influencing the rate of drying. Thereafter the drying rate decreases and this is called the falling-rate period of drying. The rate-controlling factors in the falling-rate period are complex, depending upon diffusion through the food, and upon the changing energy-binding pattern of the water molecules. Very little theoretical information is available for drying of foods in this region and experimental drying curves are the only adequate guide to design.
In the constant-rate period, the water is being evaporated from what is effectively a free water surface. The rate of removal of water can then be related to the rate of heat transfer, if there is no change in the temperature of the material and therefore all heat energy transferred to it must result in evaporation of water. The rate of removal of the water is also the rate of mass transfer, from the solid to the ambient air. These two - mass and heat transfer - must predict the same rate of drying for a given set of circumstances.
Considering mass transfer, which is fundamental to drying, the driving force is the difference of the partial water vapour pressure between the food and the air. The extent of this difference can be obtained, knowing the temperatures and the conditions, by reference to tables or the psychrometric chart. Alternatively, the driving force may be expressed in terms of humidity driving forces and the numerical values of the mass-transfer coefficients in this case are linked to the others through the partial pressure/humidity relationships such as eqns. (7.4) and (7.5).
From charts, the humidity of saturated air at 40°C is 0.0495 kg kg-1.
From charts, the humidity of saturated air at 28°C is 0.0244 kg kg-1 = Ys
Latent heat of evaporation of water at 28°C = 2.44 x 103 kJ kg-1
Heat energy supply rate per square metre = 6.9 x 10-5 x 2.44 x 103 kJ s-1
The problem in applying such apparently simple relationships to provide the essential rate information for drying, is in the prediction of the mass transfer coefficients. In the section on heat transfer, methods and correlations were given for the prediction of heat transfer coefficients. Such can be applied to the drying situation and the heat transfer rates used to estimate rates of moisture removal. The reverse can also be applied.
Heat-flow rate = q = 168 J s -1 from Example 7.13.
Following on the psychrometric chart the wet-bulb line from the entry point at 60°C and 10%RH up to the intersection of that line with a constant humidity line of 0.021 kg kg-1, the resulting temperature is 41°C and the RH 42%.
the equations for predicting heat-transfer coefficients, for situations
commonly encountered, are extensive and much more widely available than
mass-transfer coefficients, the heat-transfer rates can be used to estimate
drying rates, through the Lewis ratio.
A convenient way to remember the inter-relationship is that the mass transfer coefficient from a free water surface into air expressed in g m-2 s-1 is numerically approximately equal to the heat-transfer coefficient from the air to the surface expressed in J m-2 s-1 °C-1.
The highest rate of drying is normally the constant rate situation, then as drying proceeds the moisture content falls and the access of water from the interior of the food to the surface affects the rate and decreases it. The situation then is complex with moisture gradients controlling the observed drying rates. Actual rates can be measured, showing in the idealized case a constant rate continuing up to the critical moisture content and thereafter a declining rate as the food, on continued drying, approaches the equilibrium moisture content for the food. This is clearly shown by the drying curve of Fig. 7.7 and at low moisture contents the rates of drying become very low. The actual detail of such curves depends, of course, on the specific material and conditions of the drying process.
Drying rates, once determined experimentally or predicted from theory, can then be used to calculate drying times so that drying equipment and operations can be designed. In the most general cases, the drying rates vary throughout the dryer with time as drying proceeds, and with the changing moisture content of the material. So the situation is complicated. However, in many cases a simplified approach can provide useful results. One simplification is to assume that the temperature and RH of the drying air are constant.
In this case, for the constant-rate period, the time needed to remove the quantity of water which will reduce the food material to the critical moisture content Xc (that corresponding to the end of the constant-rate period and below which the drying rate falls) can be calculated by dividing this quantity of moisture by the rate.
where (dw /dt )const. = k'gA(Ys -Ya)
and Xo is the initial moisture content and Xc the final moisture content (the critical moisture content in this case) both on a dry basis, w is the amount of dry material in the food and (dw/dt )const is the constant-drying rate.
Where the drying rate is reduced by a factor f then this can be incorporated to give:
and this has to be integrated piecemeal down to X = Xf where subscript f denotes the final water content, and f expresses the ratio of the actual drying rate to the maximum drying rate corresponding to the free surface-moisture situation.
From the data
and from the psychrometric chart, Ys = 0.087 and Ya = 0.054 kg kg-1
During the falling-rate period, the procedure outlined above can be extended, using the drying curve for the particular material and the conditions of the dryer. Sufficiently small differential quantities of moisture content to be removed have to be chosen, over which the drying rate is effectively constant, so as to give an accurate value of the total time. As the moisture content above the equilibrium level decreases so the drying rates decrease, and drying times become long.
Equation (7.7) Dt = w ( DX) / [f(dw /dt)const]
can be applied, over small intervals of moisture content and multiplying the constant rate by the appropriate reduction factor (f) read of from Fig. 7.7. This can be set out in a table. Note the temperature and humidity of the air were assumed to be constant throughout the drying.
= 7918 s = 2.2 h (to remove 6.6 kg of water) = time at falling rate
The example shows how as the moisture level descends toward the equilibrium value so the drying rate becomes slower and slower. In terms of the mass transfer equations, the humidity or partial pressure driving force is tending to zero as the equilibrium moisture content is approached. In terms of the heat transfer equations, the surface temperature rises above the wet-bulb temperature once the surface ceases to behave as a wet surface. The surface temperature then climbs towards the dry-bulb temperature of the air as the moisture level continues to fall, thus leading to a continuously diminishing temperature driving force for surface heat transfer.
This calculation procedure can be applied to more complicated dryers, considering them divided into sections, and applying the drying rate equations and the input and output conditions to these sections sequentially to build up the whole situation in the dryer.
Drying > CONDUCTION DRYING
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