Sedimentation Equilibrium of Mixtures of Charged Colloids

numbers for the parameters Z i , L i , σ i , ρ s , λ B and a mean density ¯ρ i to fix a i .By using an iteration method, shown and discussed in chapter 6, a common,four-year-old computer can calculate the solution for a polydisperse systemof n = 20 components and H = 20cm in a minute. We will now explore somenumerical results, before we continue the analytical path for which we needassumptions.4.3 Binary systemsWe will start with a binary system, i.e. a system with n = 2 colloidalcomponents. The reason for this choice is that, considering these systems,the complexity is still reduced, while several multi-component phenomenacan already be examined. The next examples will show if the componentswill form layers, if they will order, and how their profiles are influenced whenthey are put together.After careful study three binary systems were selected for comparison. Thegravitational length are fixed at L 1 = 1mm, L 2 = 2mm and Z 1 = 250. Thecharge number Z 2 , however, will be varied, in case (a) Z 2 = 125, in case (b)Z = 500, in case (c) Z = 1000. The calculated density profiles are shownbelow in figure 4.1, in terms of the so-called packing fraction, a dimensionlessdensity that expresses the ratio of the volume that is occupied by the colloids,η i (x) = πσ3 i6 ρ i(x). (4.6)The particles of component 2 are twice as heavy as the particles of component1, and on the basis of their gravitational length, component 2 is expected tobe on the bottom. However, due to their charge ratio, other situations mayoccur as well, as is shown. Figure 4.1a shows a strong segregation of thecomponents, not a mixture of barometric distributions like our atmosphere.Although the heavier component 2 is below component 1, the situation isreversed in figure 4.1c. Apparently independent of mass, the colloidal componentscan live together as well in figure 4.1b.How can this be?We cannot see this directly from theory, the ’Donnan-method 2 ’ needed toomany assumptions and the ’PB-method 3 ’ could not be solved analytically.An explanation can still be found after an examination of φ(x), or equivalently,the salt profiles, and related, the electric field (see figure 4.2)2 see section 3.23 see section 3.318