Interstitial void spaces

In scale-up from laboratory quantities (up to 10 kg) to production batches (300 kg and up), bed depth increases significantly. The most notable consequence is an increase in finished product bulk density, typically in the range of 15% to 20%. In some instances, this is a disadvantage (if product is packed by volume and a low density is desired). However, granule strength is usually greater as a result of the decreased interstitial void space. 

Fujii et al. [13] studied morphological structures of the cross section of various hollow fibers and fiat sheet membranes by high-resolution field emission scanning electron microscopy. Figure 6.8 shows a cross-sectional structure of a flat sheet cellulose acetate RO membrane. The layer near the top surface is composed of a densely packed monolayer of polymeric spheres, which is supported by a layer formed with completely packed spheres. The contours of the spheres in the top layer can be observed. The middle layer is also composed of loosely packed and partly fused spheres, which are larger than the spheres in the surface layer. In the middle layer, there are many microvoids, the sizes of which are the same as the spheres. The layer near the bottom is denser than the middle layer, and the spheres are deformed and fused. Interstitial void spaces between the spheres, which may be called microvoids, are clearly observed. This structure seems common for the flat sheet as well as the hollow fiber membranes. For example. Fig. 6.9 shows a cross section of a hollow fiber made of PMMA B-2 (a copolymer containing methyl methacrylate and a small amount of sulfonate groups). The inside surface layer is composed of the dense structure of compactly packed fine polymeric particles. The particle structure of the middle layer... 

The interstitial void spaces are connected to the openings at the membrane surfaces, forming capillary pores in the membranes. 

Solute or sorbate within the packed section of a column can be in one of three locations. The solute can be in the interstitial void space and be moving at the interstitial velocity v itej,- K the solute is in the... 

Usually, the casting solution for aromatic polyamide reverse osmosis membranes includes the electrolyte additive, and the composition is near the critical concentration. Then the radius of macromolecular spheres should be nearly equal to 52 X, as indicated by Table 2, and their packing fa.shion is close to the cubic packing. Approximating the square-shaped interstitial void area generated between four neighboring spheres (see Figure 4.11) by a circle of equal area, the effective radius of such interstitial void spaces is 27 A. 

Hard spheres have static thermodynamic properties. For hard spheres, a volume fraction < = 1 is unattainable, because there are always interstitial void spaces... 

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