Void fraction critical value

It may be assumed that within limited dragging action of the fluid, the critical value of the void fraction at which coalescence prevails is about 25% (Taitel et al., 1980 Cumo and Naviglio, 1988). 

From the point of view of the ideas discussed above concerning the variability on the free-volume fraction at Tg, even for the same modes of molecular motion in different polymers, there is great interest in some new concepts about the free-volume distribution, in the system, first proposed in 24. The starting point is the suggestion that all molecular motions, like transfer phenomena, can take place only when the size of the voids or holes in the system exceeds a critical value v. This critical volume appears as a result of redistribution of the free-volume within the system. 

The initial porous texture of a catalyst pellet and the change in texture caused by metal deposition in it can be described using the percolation theory. In the percolation approach the pellet is constructed as a binary interdispersion of void space and (deposited) solid material. In this binary interdispersion, the void space can exist as (1) isolated clusters surrounded by solid material or (2) sample overspanning void space that allows mass transport from one side to the other. The total void space c can be split into the sum of the volume fraction of isolated clusters t1 and the volume fraction of accessible void space tA, If is below a critical value, called the percolation threshold all the void space is distributed as isolated clusters and transport is impossible through the pellet. 

Uniform bubbly flow is unstable to void fraction disturbances above some critical value of the void fraction (>45%). 

Biesheuvel and Gorrisen (1990) have derived one-dimensional conservation equations for void fraction disturbances in a uniform bubbly fluid. They have studied the features of the propagation of void fraction disturbances and investigated the stability of uniform bubbly flows. They observed that the voidage fraction waves are unstable for void fractions above some critical value (>45%). Their method of approach was similar to that of Batchelor (1988) in many respects. 

For well-wetting fluids, the peak void fraction reaches a value close to unity at the critical heat flux condition, and this implies that no liquid may be transferred to the surface under... 

Here, the coefficient a is taken to be 2.5 then, the fraction is 13%. When the glass particle is applied as a shock absorber, a is taken to be 1 and i is 33%. In the latter case, glass does not adhere in the plastic phase but gives void for the stress relaxation. These figures are compatible with the experiment of Kinloch et al. [59]. Wu [51] pointed out the existence of a critical value in the distance between rubbery particles, which is about 0.4 //m as a universal constant. 

Attention is drawn to the significance of the void fraction values reported in Table 6.4. Inspection of expressions (6.26) and (6.27) shows that the most critical factor in pressure-drop calculation is the estimate of the bed void fraction since... 

The density of the polymer clearly shows the formation of a foamed polymer. The density values for selected foams together with the polyimide homopolymers are shown in Table 11. The density values for the ODPA/FDA and PM-DA/FDA polyimides were both 1.28 g/cm and 3FDA/PMDA is 1.34, while most of the propylene oxide-based copolymers showed substantially lower values. The densities of the foamed copolymers derived from these copolymers ranged from 1.09 to 1.27 g/cm, which is 85-99 % of that of the polyimide homopolymers. This is consistent with 1-15 % of the film being occupied by voids. From these data (i.e., the comparison of Tables 10 and 11), it appears that the volume fraction of voids or the porosity is substantially less than the volume fraction of propylene oxide in the copolymer (i.e., 70 % or less). Thus the efficiency of foam formation is poor. Conversely, the propylene oxide-based copolymers with PMDA/ODA as the imide component did not show the expected density drop, and the values were essentially identical to that of the homopolymer. In PM-DA/ODA-based systems, molecular ordering and orientation were found to be critical in determining the stability of the foam structure. Where the character-... 

Where fc is the critical void volume fraction, fp is the void volume at failure, and for most metals, f = / q. The existing value of the void volume fraction changes due to the growth of existing voids and the nucleation of new voids and is characterized by ... 

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