Question 9.17: In an emulsion liquid membrane system, an emulsion (internal...
In an emulsion liquid membrane system, an emulsion (internal phase) is dispersed
into an external liquid medium containing a contaminant. The contaminant is removed
from the external liquid through mass transfer into the emulsion. Internal phase leakage
occurs when portions of the extracted material spill into the external liquid. In the article
“Leakage and Swell in Emulsion Liquid Membrane Systems: Batch Experiments”
(R. Pfeiffer, W. Navidi, and A. Bunge, Separation Science and Technology, 2003:
5 19-539), the effects of five factors were studied to determine the effect on leakage in a
certain system. The five factors were A: surfactant concentration, B: internal phase lithium hydroxide concentration, C: membrane phase, D: internal phase volume fraction, and E: extraction vessel stirring rate. A half-fraction of a 2^5 design was used. The data are presented in the following table (in the actual experiment, each point actually represented the average of two measurements). Leakage is measured in units of percent. Assume that the third-, fourth-, and fifth-order interactions are negligible. Estimate the main effects and two-way interactions. Which, if any, stand out as being noticeably larger than the rest?
| Treatment Leakage | Treatment Leakage | Treatment Leakage | Treatment Leakage | ||||
| e | 0.61 | c | 0.35 | d | 2.03 | cde | 1.45 |
| a | 0.13 | ace | 0.075 | ade | 0.64 | acd | 0.31 |
| b | 2.23 | bce | 7.31 | bde | 11.72 | bcd | 1.33 |
| abe | 0.095 | abc | 0.080 | abd | 0.56 | abcde | 6.24 |
Using the sign table (Table 9.1 2), we compute estimates for the main effects and two-way interactions, shown in the following table.
\begin{array}{lr||lr}\hline \text{Term}& \text{Effect}& \text{Term}& \text{Effect}\\\hline A & -2.36 & A E & -1.15 \\B & 3.00 & B C & 0.20 \\C & -0.11 & B D & 0.86 \\D & 1.68 & B E & 2.65 \\E & 2.64 & C D & -1.30 \\A B & -1.54 & C E & 0.61 \\A C & 1.43 & D E & 1.32 \\A D & 0.17 & & \\\hline\end{array}
Note that we do not bother to compute sums of squares for the estimates, because we have no SSE to compare them to. To determine informally which effects may be most worthy of further investigation, we rank the estimates in order of their absolute values: B: 3.00, BE: 2.65, E: 2.64, A: -2.36, D: 1.68, and so forth. It seems reasonable to decide that there is a fairly wide gap between the A and D effects, and therefore that factors A, B, and E are most likely to be important.
| TABLE 9.12 Sign table for the main effects and selected interactions for the pri nci pal fraction of a 2^5 factori al experiment | ||||||||
| Treatment | A | B | C | D | E = ABCD | AB | CDE | ACDE |
| e | – | – | – | – | + | + | + | – |
| a | + | – | – | – | – | – | – | – |
| b | – | + | – | – | – | – | – | + |
| abe | + | + | – | – | + | + | + | + |
| c | – | – | + | – | – | + | + | – |
| ace | + | – | + | – | + | – | – | – |
| bce | – | + | + | – | + | – | – | + |
| abc | + | + | + | – | – | + | + | + |
| d | – | – | – | + | – | + | + | – |
| ade | + | – | – | + | + | – | – | – |
| bde | – | + | – | + | + | – | – | + |
| abd | + | + | – | + | – | + | + | + |
| cde | – | – | + | + | + | + | + | – |
| acd | + | – | + | + | – | – | – | – |
| bcd | – | + | + | + | – | – | – | + |
| abcde | + | + | + | + | + | + | + | + |