in which L is the bed height as a function of flow velocity (u) and L
0 represents the initial settled bed height at a flow velocity of 0 cm/h. B can be obtained as the slope constant and L
0, the curve intercept from a linear regression analysis (Figure 2). The linearity of bed height to flow appears at various
aspect ratios (AR) defined as the ratio between initial bed height (L
0) and column diameter (D). By allowing the resin to consolidate by flow, this approach provides the advantage of reducing
wall support effects that lead to variability in the resin quantification and allow for a homogeneous settling with results
obtained much faster than the GS method.
Figure 2. Flow consolidation method
For a constant cross-sectional area (AC) of the column, the volumetric concentration of the resin can be determined from Equation
2 by associating the intercept L
0 from linear regression analysis with the initial amount of slurry poured in the column as follows:
in which LS is the slurry height poured into the column.
This method requires using a complex and expensive setup to quantify resin, which is not ideal for a manufacturing environment
because of sensitivity.
The quantification of solids by weight through centrifugation was also developed for this application.2 After a resin sample is loaded on the top section, centrifugal force pushes the liquid through the filter into a receiver.
Centrifugal speed and time are controlled to minimize variability. The amount of resin is then determined based on net mass
retained in the centrifuge concentrator. The mass is then normalized against the total slurry weight poured into the concentrator
defining the weight ratio MR (Equation 3):
in which MassRETAINED and MassSLURRY are the net masses of the resin (top reservoir) after centrifugation and the total slurry (top and bottom reservoirs) respectively.
Although there are concentrators with volumetric marks for volume determination, this approach provided less accuracy than
using an analytical scale for measuring resin amount.
The disadvantage of this method is that a volumetric relationship must be established to adapt the model to a manufacturing
environment, in which packing procedures call for volumetric amounts. In addition, the developed correlation is specific to
the type of resin and its interactions with the storage media and its physical properties.