Electroacoustic phenomena in concentrated dispersions: New theory and CVI experiment

There are two quite different approaches to deriving an electroacoustic theory. The first was suggested by Enderby and Booth 50 years ago and later modified by Marlow, Fairhurst and Pendse. The second was suggested by O'Brien about 10 years ago (O'Brien's approach). He introduced a special relationship between kinetic coefficients that is assumed to be valid in a concentrated system. This approach requires also a theory for dynamic electrophoretic mobility. The most recent version of this theory for concentrated systems was created by Ohshima, Shilov, and A. Dukhin on the basis of the cell model. A hybrid of the O'Brien relationship and this new electrophoretic mobility theory yields expressions for electroacoustic effects in the concentrated systems. We call it "hybrid O'Brien's theory". In principle these two approaches must lead to the same result. To test this expectation, we should generalize the first approach such that it is valid for concentrates. We have done this using the Kuvabara cell model for calculating the hydrodynamic drag coefficient and the Shilov-Zharkikh cell model for electrokinetics. In addition we used a well-known "coupled phase model" for describing the relative motion between the particles and the liquid in the concentrated system. The coupled phase model allows us to eliminate superposition assumption for hydrodynamic fields for incorporating particle polydispersity into the theory. For dilute systems the new theory gives exactly same result as O'Brien's dilute case theory. Surprisingly, in the concentrated systems this theory yields a new relationship for electroacoustic phenomena. It does not converge to the "hybrid O'Brien theory". Why? It turned out that O'Brien's relationship contradicts the Onsager relationship in concentrated systems at the extreme case of the low frequencies when the Onsager relationship is valid. The new theory satisfies the Onsager principle and it converges to the Smoluchowski limit at any volume fraction assuming thin double layer and negligible surface conductivity. We have tested this new theory experimentally using silica Ludox TM (30 nm) and rutile R-746 Dupont (about 300 nm). In both cases we performed an equilibrium dilution protocol. This experimental test confirmed our new theory for volume fractions up to 45 vol %. It also showed that O'Brien's relationship leads to hundreds percents of error in concentrated systems. It is important to mention here the difference between the original O'Brien's theory and software used in the commercially available elecroacoustic spectrometer Acoustosizer. This instrument employs O'Brien's method, but it contains an additional unavailable empirical correction (Hunter, R. J. Colloids Surf. 1998, 141, 37-65) for concentrates. This empirical correction masks original theoretical results.