Rotational self-diffusion in suspensions of charged particles: simulations and revised Beenakker–Mazur and pairwise additivity methods

Abstract

To the present day, the Beenakker-Mazur (BM) method is the most comprehensive statistical physics approach to the calculation of short-time transport properties of colloidal suspensions. A revised version of the BM method with an improved treatment of hydrodynamic interactions is presented and evaluated regarding the rotational short-time self-diffusion coefficient, D r , of suspensions of charged particles interacting by a hard-sphere plus screened Coulomb (Yukawa) pair potential. To assess the accuracy of the method, elaborate simulations of D r have been performed, covering a broad range of interaction parameters and particle concentrations. The revised BM method is compared in addition with results by a simplifying pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a two-body level. The static pair correlation functions required as input to both theoretical methods are calculated using the Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it systematically and significantly underestimates the rotational diffusion coefficient. The PA method agrees well with the simulation data at lower volume fractions, but at higher concentrations D r is likewise underestimated. For a fixed value of the pair potential at mean particle distance comparable to the thermal energy, D r increases strongly with increasing Yukawa potential screening parameter.b On the leave of absence from:

Generalization of Clausius-Mossotti approximation in application to short-time transport properties of suspensions

“…This question in the case of the Beenakker-Mazur method has been answered in some situations: the Beenakker-Mazur method is rather insensitive to the change in the structure of suspension [21,58]. We are going to address the above questions in our further work.…”

“…Therefore, this propagator A γ 0 is the same for hard-sphere suspension and for suspension of charged particles in equilibrium. On the other hand, the ef- This question in the case of the Beenakker-Mazur method has been answered in some situations: the Beenakker-Mazur method is rather insensitive to the change in the structure of suspension [21,58]. We are going to address the above questions in our further work.…”

Colloidal Soft Matter Physics

“…In the short-time regime [9], the transport coefficients in colloidal suspensions, such as the diffusion coefficients at different length scales and the effective viscosity of a suspension, are entirely determined by the HIs between the colloidal particles. The precise and computationally efficient inclusion of HIs in approximate theoretical schemes or simulations represents a formidable challenge to date: The most complete theory of short-time hydrodynamic interactions in colloids is based on a renormalized fluctuation expansion that was originally introduced by Beenakker and Mazur [149,150], and which has been recently re-adapted [151][152][153]. The modifications allow one the application of the theory in the case of charged colloidal particles and polydisperse systems with different hydrodynamic radii.…”

Short-time diffusion in concentrated bidisperse hard-sphere suspensions

“…A related line of research by part of the present authors is concerned with tests and improvements of the different δγ-scheme approximations (for monodisperse suspensions). 34 Such assessment relies critically on an accurate static structure input, and hence, the RY-scheme is used there.…”

“…Nevertheless, a complementary infinite subset of scattering diagrams is omitted in the δγ scheme which, moreover, fails to include the correct lubrication limits of particle mobilities. Comparisons of the original δγ-scheme predictions to experimental and computer simulation data have revealed a shortcoming of the δγ scheme in its prediction of self-diffusion coefficients 23,24,[28][29][30] , which can be largely overcome by resorting to a modified δγ scheme in which the computation of the self-diffusion coefficients is carried out by a more accurate method 23,24,29 . To date the (modified) δγ scheme remains the only analytical-theoretical approach that captures the essential physics of diffusion in dense suspensions, making predictions at an acceptable accuracy level.…”