Dispersions doublet formation

Here, we have also assumed that the particles do not interact before they are in contact and all collisions lead to doublet formation. Moreover, hydrodynamic interactions have been neglected. An experimental verification of this formula showed, not unexpectedly, deviations. The coagulation was slower than that predicted by the rate constant given in equation (1.31). Derjaguin, in 1966, proposed the reason for this was that the particles interact hydrodynamically when they were sufficiently close to each other. The dispersion medium has to be removed from the space between the particles when they approach one another and the motion of the particles is retarded. The effect is in many cases quite large, i.e. about a factor of 2. This can be expressed as a reduction in the diffusion coefficient. Honig and co-workers have derived an approximate equation for how the diffusion coefficient D(H) varies with the interparticle surface-to-surface distance H. The expression is as follows ... 

Figure 5 shows the results obtained from a nominal 65nm latex dispersion (Polyscience). Four separate samples were run, each showing bimodality with peaks at 5 +/- 1nm and 93 +/- 5nm, suggesting the formation of doublets. The discrepancy between the nominal and measured values, as well as the lack of monodispersity, is quite common for several other samples and sizes from the same source. 

Since the formation of double peaks recently has become recognized as a source of new information, it is important to discuss the mechanisms by means of which doublet peaks are formed from a single injected zone. The formation of double peaks may be due to physical dispersion processes alone or to a combination of the dispersion process and the chemical processes that form a detectable species. 

The stability of the colloid may be interpreted as the difficulty which the particles experience in getting over the energy battier. Particles which have been prepared in the fully dispersed state, for example by precipitation, have a distribution of velocities with an average thermal energy 3kT/2. Particles in the distribution with energy greater than Sj have sufficient impetus to cross the barrier, so then doublets will form in the adhesive potential well. Treating the formation of doublets as a reaction... 

In the two-well test, water is pumped from one well and injected into the other at the same rate to create a steady-state flow regime. The tracer is added in the injection well and monitored in the withdrawal well. Also, dispersivity estimates can be improved by adding more observation wells between the pumping-injection doublets. In general, these tests can be performed over several hundreds of meters in sandy formations. Analytical solutions are provided by Grove and Beetem (1970) and Maloof and Protopapas (2001). 

---