Kernel volume average

If the rate of change of internal coordinates, the rate of formation of the disperse phase, and the kernels for second- and first-order processes do not exhibit a strong variation according to the spatial coordinates, then their volume-average values appearing in Eq. (7.146) can be easily estimated. 

In all the other cases the parameters appearing in the rates and kernels responsible for spatial dependences must be identified and their variation throughout the vessel must be quantified, by identifying their volume distribution. The latter quantity can be typically measured or estimated through simulations. Once these distributions are known, they can be used to estimate the volume-average rates and kernels that appear inEq. (7.146). 

In addition, when the inverse problem is solved, namely the volume-average rates and kernels are identified by comparison between experiments and model predictions under the assumption of perfect mixing (or, in other words, by using Eq. (7.146)), one must remember that the volume-average rates and kernels are not truly kinetic parameters but contain some fluid-dynamic factors in them. This is why, on transferring these rates and kernels to different operating conditions or from one system to another, very poor performances can be observed. 

A sphere whose volume is equal to the volume of a grain kernel is defined as the equivalent sphere of the kernel. The diameter of the sphere of equivalent volume is defined as the equivalent diameter of the kernel. The average equivalent volume of kernels can be determined by using a particle density method (see Section 27.2.2) and counting the kernels. The equivalent diameter is calculated from the measured volume as... 

The common mature coconut fruit weighs more that 1 kg and is ovoid in shape and green or yellow in color. The nut has a smooth epidermis over a fibrous mesocarp (husk) that covers the hard endocarp (shell). Within the shell is the endosperm (kernel, meat) approximately 1-2 cm thick. A thin brown layer called testa separates the kernel from the inner surface of the shell. The cavity within the kernel has an average volume of 300 mL and contains the endosperm liquid (coconut water) (see Figure 2). 

Commonly, the volume occupied by 1000 kernels (randomly selected) is measured and the average equivalent volume and the diameter are calculated and reported (Table 27.4). 

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