Electroacoustic phenomena in concentrated dispersions: New theory and CVI experiment

There are two quite different approaches to deriving an electroacoustic the ory. The first was suggested by Enderby and Booth 50 years ago and later mo dified by Marlow, Fairhurst and Pendse. The second was suggested by O'Brien about 10 years ago (O'Brien's approach). He introduced a special relations hip between kinetic coefficients that is assumed to be valid in a concentra ted system. This approach requires also a theory for dynamic electrophoreti c 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 mod el. A hybrid of the O'Brien relationship and this new electrophoretic mobil ity theory yields expressions for electroacoustic effects in the concentrat ed systems. We call it "hybrid O'Brien's theory". In principle these two ap proaches must lead to the same result. To test this expectation, we should generalize the first approach such that it is valid for concentrates. We ha ve done this using the Kuvabara cell model for calculating the hydrodynamic drag coefficient and the Shilov-Zharkikh cell model for electrokinetics. I n addition we used a well-known "coupled phase model" for describing the re lative motion between the particles and the liquid in the concentrated syst em. 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'B rien's dilute case theory. Surprisingly, in the concentrated systems this t heory 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 a t the extreme case of the low frequencies when the Onsager relationship is valid. The new theory satisfies the Onsager principle and it converges to t he Smoluchowski limit at any volume fraction assuming thin double layer and negligible surface conductivity. We have tested this new theory experiment ally using silica Ludox TM (30 nm) and rutile R-746 Dupont (about 300 nm). In both cases we performed an equilibrium dilution protocol. This experimen tal test confirmed our new theory for volume fractions up to 45 vol %. It a lso showed that O'Brien's relationship leads to hundreds percents of error in concentrated systems. It is important to mention here the difference bet ween the original O'Brien's theory and software used in the commercially av ailable elecroacoustic spectrometer Acoustosizer. This instrument employs O 'Brien's method, but it contains an additional unavailable empirical correc tion (Hunter, R. J. Colloids Surf. 1998, 141, 37-65) for concentrates. This empirical correction masks original theoretical results.