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Register a new userSelf-diffusion coefficients of charged particles: Prediction of Nonlinear volume fraction dependence
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M. Watzlawek
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We report on calculations of the translational and rotational short-time self-diffusion coefficients $D^t_s$ and $D^r_s$ for suspensions of charge-stabilized colloidal spheres. These diffusion coefficients are affected by electrostatic forces and many-body hydrodynamic interactions (HI). Our computations account for both two-body and three-body HI. For strongly charged particles, we predict interesting nonlinear scaling relations $D^t_spropto 1-a_tphi^{4/3}$ and $D^r_spropto 1-a_rphi^2$ depending on volume fraction $phi$, with essentially charge-independent parameters $a_t$ and $a_r$. These scaling relations are strikingly different from the corresponding results for hard spheres. Our numerical results can be explained using a model of effective hard spheres. Moreover, we perceptibly improve the known result for $D^t_s$ of hard sphere suspensions.
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We report on calculations of the reduced sedimentation velocity $U/U_{0}$ in homogenous suspensions of strongly and weakly charged colloidal spheres as a function of particle volume fraction $phi$. For dilute suspensions of strongly charged spheres at low salinity, $U/U_{0}$ is well represented by the parametric form $1-pphi^alpha$ with a fractional exponent $alpha=1/3$ and a parameter $psimeq 1.8$, which is essentially independent from the macroion charge $Z$. This non-linear volume fraction dependence can be quantitatively understood in terms of a model of effective hard spheres with $phi$-dependent diameter. For weakly charged spheres in a deionized solvent, we show that the exponent $alpha$ can be equal to 1/2, if an expression for $U/U_0$ given by Petsev and Denkov [J. Colloid Interface Sci. 149, 329 (1992)] is employed. We further show that the range of validity of this expression is limited to very small values of $phi$ and $Z$, which are probably not accessible in sedimentation experiments. The presented results might also hold for other systems like spherical proteins or ionic micelles.
Using extensive Brownian dynamics computer simulations, the long-time self-diffusion coefficient is calculated for Gaussian-core particles as a function of the number density. Both spherical and rod-like particles interacting via Gaussian segments ar$ For increasing concentration we find that the translational self-diffusion behaves non-monotonically reflecting the structural reentrance effect in the equilibrium phase diagram. Both in the limits of zero and infinite concentration, it approaches its short-time value. The microscopic Medina-Noyola theory qualitatively accounts for the translational long-time diffusion. The long-time orientational diffusion coefficient for Gaussian rods, on the other hand, remains very close to its short-time counterpart for any density. Some implications of the weak translation-rotation coupling for ultrasoft rods are discussed.
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 re- quired 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.
It is very important to understand stochastic diffusion of energetic charged particles in non-uniform background magnetic field in plasmas of astrophysics and fusion devices. Using different methods considering along-field adiabatic focusing effect, various authors derived parallel diffusion coefficient $kappa_parallel$ and its correction $T$ to $kappa_{parallel 0}$, where $kappa_{parallel 0}$ is the parallel diffusion coefficient without adiabatic focusing effect. In this paper, using the improved perturbation method developed by He & Schlickeiser and iteration process, we obtain a new correction $T$ to $kappa_{parallel 0}$. Furthermore, by employing the isotropic pitch-angle scattering model $D_{mumu}=D(1-mu^2)$, we find that $T$ has the different sign as that of $T$. In this paper the spatial perpendicular diffusion coefficient $kappa_bot$ with the adiabatic focusing effect is also obtained.
For suspensions of permeable particles, the short-time translational and rotational self-diffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a uniformly permeable sphere of a given permeability, with the internal solvent flow described by the Debye-Bueche-Brinkman equation. The particles are assumed to interact non-hydrodynamically by their excluded volumes. The virial expansion of the transport properties in powers of the volume fraction is performed up to the two-particle level. The first-order virial coefficients corresponding to two-body hydrodynamic interactions are evaluated with very high accuracy by the series expansion in inverse powers of the inter-particle distance. Results are obtained and discussed for a wide range of the ratio, x, of the particle radius to the hydrodynamic screening length inside a permeable sphere. It is shown that for x >= 10, the virial coefficients of the transport properties are well-approximated by the hydrodynamic radius (annulus) model developed by us earlier for the effective viscosity of porous-particle suspensions.
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