Fractional penetration

The grade efficiency T of most collectors can be expressed as a function of the aerodynamic particle size in the form of an exponential equation. It is simpler to write the equation in terms of the particle penetration Pf (those particles not collected), where the fractional penetration = 1 — T, when T is the fractional efficiency. The typical collection equation is... 

The effect of bag failure on bagliouse fractional penetration (or efficiency) can be described by tlie following equation ... 

Neglecting the longitudinal diffusion, for the case of fully developed laminar flow in isothermal channels of the length z, the fractional penetration was found to be... 

FIGURE 10.13 Fractional penetration length at two rock ion-exchange capacities (a). Nmnbers in parentheses are the fractional penetration lengths for continual chemical injection. Source Bunge and Radke (1982). 

Fractional penetration length for alkaline slug injection. Source Bunge and... 

By interpolation from Figure 10.15, if we select the concentration of 0.1 N (0.4 wt.%), 1 PV injection would lead to a fractional penetration (xp) of 0.65. If we inject 0.5 PV, to reach 0.65 fractional penetration, we need to use an injection concentration of 0.8 wt.%. For the first-order reaction, a higher concentration would result in a higher dissolution rate, which was not considered here. Therefore, to reach this fractional penetration, we probably should use an injection concentration of at least 1 wt.%. 

Stephens and Kutscha [28] investigated the effect of the resin molar mass on the bonding behavior of flakeboards. A commercial PF resin was separated into two molar mass fractions by dialysis, and aspen flakeboards were prepared with the separate fractions as well as with mixtures of the resin fractions. Penetration characteristics of the different fractions were determined microscopically. Results indicate that both low and high molar mass components of the resin are needed to achieve boards with acceptable properties. 

In the diffusion battery, the gaseous ions are sorbed by the wall of the diffusion tube while en route through it, analogous to the removal of aerosol particles by the battery wall. The fraction penetrating the battery, F, is given by the equation (Townsend, 1900)... 

---