Experimental examination of the Booth theory on the first-order electroviscous effect in ionic colloidal dispersions

The viscosities of aqueous dispersions of three kinds of colloidal silica and an ionic polymer latex, having a particle radii of (0.04–0.5)×${10}^{\mathrm{-}6}$ m, were measured at sodium chloride concentrations, ${\mathrm{C}}_{\mathrm{s}}$, of 5×${10}^{\mathrm{-}5}$M to ${10}^{\mathrm{-}3}$M. The first-order electroviscous effect was estimated from the experiments and compared with the Booth theory. The effect decreased with increasing particle radius a as expected from the theory. Furthermore, the function Z(κa) (1/κ is the Debye screening length), introduced by Booth to express the deformability of the counterion cloud under a shear field, was estimated from the observed effect, at several κa values between 0.9 and 15. The Z versus κa plot thus obtained for colloids with various a values at various ${\mathrm{C}}_{\mathrm{s}}$’s was well represented by a single curve, and decreased monotonically with increasing κa, whether κ or a was varied. This suggests that Z really is a function of the product κa. In other words, it was shown that the deformability of the counterion cloud is determined by the ratio of the Debye screening length to the particle radius. On the basis of the present finding and previous studies, it was concluded that the Booth theory gives satisfactory agreement with experiment for large κa and small charge numbers.