Long-time dynamics of charged colloidal suspensions: hydrodynamic interaction effects

Sedimentation of Strongly and Weakly Charged Colloidal Particles: Prediction of Fractional Density Dependence

“…(21) is restricted to small values of Z, but still sufficiently large that the second term in eq. (20) plays the dominant role compared to the hard core contribution 6.55φ. We mention already here that due to the strong approximations made in deriving eqs.…”

“…The brackets indicate an equilibrium ensemble average. H(q) can be regarded as a generalized (short-time) sedimentation coefficient of particles exposed to spatially periodic external forces aligned withq, and derived from a weak potential proportional to exp [−iq · r] [20,32]. In principle, one needs to distinguish the short-time sedimentation velocity U, defined through eq.…”

“…In this work, we use eqs. (6,11) together with the series expansions of A(r) and B(r) for calculating U/U 0 , by including contributions up to order (a/r) 20 . When terms only up to O(r −4 ) in the series expansions of A(r) and B(r) are employed, U/U 0 is given explicitly as…”

“…Therefore only the Oseen-term is considered here, leading to the second term in the bracket of eq. (20). We will provide a critical discussion of this approximation in the following section.…”

“…In fact, in the past the effects of HI have been frequently considered to be negligible for dilute suspensions of charged particles [12,13]. However, recent calculations have clearly demonstrated for these systems that HI is of importance at small φ not only for sedimentation [14][15][16], but also for short-time [17,18] and long-time [19] collective diffusion, and for long-time self-diffusion [20]. Moreover, it was shown theoretically for dilute suspensions of charged colloids without added electrolyte that U follows a non-linear φ-dependence of the parametric form [14,15,18]…”