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Solubilization-emulsification mechanisms of detergency

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C.A. Miller and K.H. Raney/Colloids Surfaces A: Physicochem. Eng. Aspects 74 (1993) 169-215 195<br />

critical value ws* given by the following<br />

equation [73]<br />

w s* = w sB F 1(w oC) + w sC F 2 (w oC) (5)<br />

Here w sB and w sC are the surfactant mass<br />

fractions at the L 1 and L 2 ends <strong>of</strong> the limiting tie<br />

line forming one boundary <strong>of</strong> the two-phase<br />

region for these phases, and w oC is the oil mass<br />

fraction at the L 2 end. The quantity w sB is <strong>of</strong>ten<br />

called the "limiting association concentration"<br />

or LAC [56]. The functions F 1 and F 2 are<br />

defined as follows<br />

where D o and D s are the diffusivities <strong>of</strong> the oil<br />

and the surfactant in the L2 phase, D's is the<br />

diffusivity <strong>of</strong> the surfactant in the L1 phase and<br />

hoC is the (constant) value <strong>of</strong> the similarity<br />

parameter [x/(4D.t) 1/2 ] at the L2 end <strong>of</strong> the<br />

limiting tie line (see discussion <strong>of</strong> diffusion path<br />

analysis above).<br />

Vertical cell-contacting experiments gave<br />

results in reasonable agreement with Eq. (3) for<br />

the sodium octanoate-n-decanol-water system<br />

[73]. One might expect that <strong>detergency</strong> would<br />

be improved when the intermediate phase - in<br />

this case the lamellar liquid crystal - is formed<br />

since more <strong>of</strong> the alcohol is solubilized. Indeed,<br />

Kielman and van Steen [11] observed such<br />

behavior in the potassium octanoate-n-decanolwater<br />

system.<br />

The focus <strong>of</strong> this section is the time-dependent<br />

behavior <strong>of</strong> the system if a drop <strong>of</strong> alcohol is<br />

injected into a solution whose surfactant<br />

concentration is below the critical value. The<br />

question to be answered is whether an<br />

intermediate phase will form at some time after<br />

initial contact.<br />

A series <strong>of</strong> such experiments was performed<br />

for the C 12E 5-water-oleyl alcohol system at 30ºC<br />

[74]. The L 1-L 2 coexistence curve and some<br />

interfacial tensions between these two phases<br />

are shown in Fig. 32. Note that the coexistence<br />

curve terminates at a point F corresponding to a<br />

water content <strong>of</strong> about 70 wt.%, which is one<br />

vertex <strong>of</strong> the L 1-Lα-L 2 three-phase triangle.<br />

Video frames taken at various times during an<br />

experiment in which the surfactant<br />

concentration was 1 wt.% are shown in Fig. 33.<br />

Note that the drop, initially some 70 mm in<br />

diameter, swells as it takes up water and<br />

surfactant. After about 23 min, the lamellar (La)<br />

phase begins to develop as myelinic figures<br />

which grow into the aqueous solution.<br />

Eventually, nearly all the alcohol is converted to<br />

liquid crystal.<br />

The order <strong>of</strong> magnitude <strong>of</strong> the time required<br />

for diffusion within the drop is the ratio <strong>of</strong> the<br />

square <strong>of</strong> its radius to the diffusion coefficient.<br />

As this time is much less than that <strong>of</strong> the<br />

experiment, a quasi-steady state scheme may be<br />

used to model drop behavior. Basically, this<br />

means that drop composition may be viewed as<br />

TIE -LINE INTERFACIAL TENSION (dyne/cm)<br />

1 2.52<br />

2 1.03<br />

3 0.25<br />

4 0.03<br />

Fig. 32. Partial ternary phase diagram for the<br />

C 12E 5-water- alcohol system at 30ºC showing the<br />

L 1-L 2 coexistence curve and the limiting tie line EF.<br />

The oil drop composition varies as indicated by the<br />

arrows. The interfacial tensions are between<br />

pre-equilibrated phases for the four tie lines shown<br />

[74]. Reprinted with permission <strong>of</strong> Plenum Press.

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