Diffusion of spheres in a concentrated suspension: Resummation of many-body hydrodynamic interactions

Abstract

We evaluate the wavevector dependent (short-time) diffusion coefficient D(k) for spherical particles in Suspension. Our analysis is valid up to high concentrations and fully takes into account the many-body hydrodynamic interactions between an arbitrary number of spheres. By resumming moreover a certain class of correlations, we obtain results which agree well with avaüable experimental data for the small and large wavevector limits of D(k).

Scaling of transient hydrodynamic interactions in concentrated suspensions

“…Moreover, since each particle moves a distance hr(&A, , a cumulant expansion can be used to approximate the contribution to the correlation function from each individual scattering event, relaxing the usual requirement that Gaussian statistics describe the distribution particle motions, and allowing the motions at the earliest times to be studied. [11,12] and with theoretical predictions [13][14][15]. Fig.…”

Correlated two-particle diffusion in dense colloidal suspensions at early times: Theory and comparison to experiment

“…(7) at small interparticle separations is unclear given its continuum hydrodynamic basis. Moreover, the question of possible exponential screening of near-field hydrodynamic interactions [12][13][14][15][16][17][18][19][20][21] was not considered. Such exponential screening on "molecular" length scales due to multiple scattering effects is well established in 3D polymer solutions [14,15], and also for particle suspensions in rigid porous media [19,20].…”

“…However, it remains debated whether exponential screening exists in colloidal suspensions where all particles are mobile. Arguments for [12] and against [13,14] such screening have been advanced, as has the concept of partial screening [17], and also the idea that screening depends on nonuniversal features such as the range of electrostatic repulsions in colloidal fluids [18]. The issue of exponential screening in dense quasi-2D suspensions seems even more poorly understood.…”

“…Multiple fundamental questions arise including the relative and absolute importance of (i) possible exponential suppression ("screening") [12][13][14][15][16][17][18][19][20] of hydrodynamic forces on "molecular" length scales, (ii) nonhydrodynamic two-particle dynamic correlations (which must exist) due to effective interparticle forces and fluid packing correlations [21][22][23][24][25][26][27][28][29][30][31], and (iii) fluid-density-dependent renormalization (modified prefactor, also called "screening" [15,16,32]) of the very long-range hydrodynamic interactions on scales where the fluid is a structural continuum. A high-level, poorly understood question is the relative importance of solvent-mediated hydrodynamic versus nonhydrodynamic mechanisms for inducing space-time displacement correlations in chemically and structurally distinct suspensions as a function of colloid density, length scale, and (effective) spatial dimensionality.…”

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres

“…With regard to the rooted cluster expansion method for charge-stabilized particles truncated at the three-body level, approximate expressions for the equilibrium triplet distribution functions are required, since these are not known analytically [38][39][40]. The most comprehensive theoretical scheme available so far to calculate short-time properties is the renormalized density fluctuations (named δγ) expansion approach of Beenakker and Mazur [32,[41][42][43][44], commonly referred to as the δγ scheme. This method includes many-body HI in an approximate way through the consideration of so-called ring diagrams.…”