Dynamics of permeable particles in concentrated suspensions (original) (raw)
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Short-time dynamics of permeable particles in concentrated suspensions
The Journal of Chemical Physics, 2010
We study short-time diffusion properties of colloidal suspensions of neutral permeable particles. An individual particle is modeled as a solvent-permeable sphere of interaction radius a and uniform permeability k, with the fluid flow inside the particle described by the Debye-Bueche-Brinkman equation, and outside by the Stokes equation. Using a precise multipole method and the corresponding numerical code HYDROMULTIPOLE that account for higher-order hydrodynamic multipole moments, numerical results are presented for the hydrodynamic function, H͑q͒, the short-time self-diffusion coefficient, D s , the sedimentation coefficient K, the collective diffusion coefficient, D c , and the principal peak value H͑q m ͒, associated with the short-time cage diffusion coefficient, as functions of porosity and volume fraction. Our results cover the full fluid phase regime. Generic features of the permeable sphere model are discussed. An approximate method by Pusey to determine D s is shown to agree well with our accurate results. It is found that for a given volume fraction, the wavenumber dependence of a reduced hydrodynamic function can be estimated by a single master curve, independent of the particle permeability, given by the hard-sphere model. The reduced form is obtained by an appropriate shift and rescaling of H͑q͒, parametrized by the self-diffusion and sedimentation coefficients. To improve precision, another reduced hydrodynamic function, h m ͑q͒, is also constructed, now with the self-diffusion coefficient and the peak value, H͑q m ͒, of the hydrodynamic function as the parameters. For wavenumbers qa Ͼ 2, this function is permeability independent to an excellent accuracy. The hydrodynamic function of permeable particles is thus well represented in its q-dependence by a permeability-independent master curve, and three coefficients, D s , K, and H͑q m ͒, that do depend on the permeability. The master curve and its coefficients are evaluated as functions of concentration and permeability.
Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions
The European Physical Journal E - Soft Matter, 2004
We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective diffusion coefficients DT (ρ)/D0 and DC (ρ)/D0, where D0 is the single-particle diffusion coefficient, as a function of the density of the colloids ρ. At low Schmidt numbers Sc = O(1), we find that hydrodynamics has essentially no effect on the behaviour of DT (ρ)/D0. At larger Sc, DT (ρ)/D0 is enhanced at all densities, although the differences compared to the case without hydrodynamics are minor. The collective diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case.
Rotational and translational self-diffusion in concentrated suspensions of permeable particles
The Journal of Chemical Physics, 2011
In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of short-time dynamic properties were calculated, except for the rotational self-diffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational self-diffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45% and for a wide range of permeability values. From the simulation results and earlier results for the first-order virial coefficient, we find that the rotational self-diffusion coefficient of permeable spheres can be scaled to the corresponding coefficient of impermeable particles of the same size. We also show that a similar scaling applies to the translational self-diffusion coefficient considered earlier. From the scaling relations, accurate analytic approximations for the rotational and translational self-diffusion coefficients in concentrated systems are obtained, useful to the experimental analysis of permeable-particle diffusion. The simulation results for rotational diffusion of permeable particles are used to show that a generalized Stokes-Einstein-Debye relation between rotational self-diffusion coefficient and high-frequency viscosity is not satisfied.
2021
We study self-diffusion and sedimentation in colloidal suspensions of nearly-hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne–Prager–Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in BD and BD+RPY, and the sedimentation coefficient in MD+MPCD is in good agreement with that in BD+RPY, suggesting that MD+MPCD gives a reasonable description of the hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extende...
Physics of Fluids, 2011
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.
Dynamics of suspensions of hydrodynamically structured particles: Analytic theory and experiment
2015
We present an easy-to-use analytic toolbox for the calculation of short-time transport properties of concentrated suspensions of spherical colloidal particles with internal hydrodynamic structure, and direct interactions described by a hard-core or soft Hertz pair potential. The considered dynamic properties include self-diffusion and sedimentation coefficients, the wavenumber-dependent diffusion function determined in dynamic scattering experiments, and the high-frequency shear viscosity. The toolbox is based on the hydrodynamic radius model (HRM) wherein the internal particle structure is mapped on a hydrodynamic radius parameter for unchanged direct interactions, and on an existing simulation data base for solvent-permeable and spherical annulus particles. Useful scaling relations for the diffusion function and self-diffusion coefficient, known to be valid for hard-core interaction, are shown to apply also for soft pair potentials. We further discuss extensions of the toolbox to long-time transport properties including the low-shear zero-frequency viscosity and the long-time self-diffusion coefficient. The versatility of the toolbox is demonstrated by the analysis of a previous light scattering study of suspensions of non-ionic PNiPAM microgels [Eckert et al., J. Chem. Phys., 2008, 129, 124902] in which a detailed theoretical analysis of the dynamic data was left as an open task. By the comparison with Hertz potential based calculations, we show that the experimental data are consistently and accurately described using the Verlet-Weis corrected Percus-Yevick structure factor as input, and for a solvent penetration length equal to three percent of the excluded volume radius. This small solvent permeability of the microgel particles has a significant dynamic effect at larger concentrations.
Soft Matter, 2015
We present an easy-to-use analytic toolbox for the calculation of short-time transport properties of concentrated suspensions of spherical colloidal particles with internal hydrodynamic structure, and direct interactions described by a hard-core or soft Hertz pair potential. The considered dynamic properties include self-diffusion and sedimentation coefficients, the wavenumber-dependent diffusion function determined in dynamic scattering experiments, and the high-frequency shear viscosity. The toolbox is based on the hydrodynamic radius model (HRM) wherein the internal particle structure is mapped on a hydrodynamic radius parameter for unchanged direct interactions, and on an existing simulation data base for solvent-permeable and spherical annulus particles. Useful scaling relations for the diffusion function and self-diffusion coefficient, known to be valid for hard-core interaction, are shown to apply also for soft pair potentials. We further discuss extensions of the toolbox to long-time transport properties including the low-shear zero-frequency viscosity and the long-time self-diffusion coefficient. The versatility of the toolbox is demonstrated by the analysis of a previous light scattering study of suspensions of non-ionic PNiPAM microgels [Eckert et al., J. Chem. Phys., 2008, 129, 124902] in which a detailed theoretical analysis of the dynamic data was left as an open task. By the comparison with Hertz potential based calculations, we show that the experimental data are consistently and accurately described using the Verlet-Weis corrected Percus-Yevick structure factor as input, and for a solvent penetration length equal to three percent of the excluded volume radius. This small solvent permeability of the microgel particles has a significant dynamic effect at larger concentrations.
The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods
The Journal of Chemical Physics, 2008
The short-time self diffusion coefficient of a sphere in a suspension of rigid rods is calculated in first order in the rod volume fraction φ. For low rod concentrations the correction to the Einstein diffusion constant of the sphere due to the presence of rods is a linear function of φ with the slope α proportional to the equilibrium averaged mobility diminution trace of the sphere interacting with a single freely translating and rotating rod. The two-body hydrodynamic interactions are calculated using the so-called bead model in which the rod of aspect ratio p is replaced by a stiff linear chain of touching spheres. The interactions between spheres are calculated using the multipole method with the accuracy controlled by a multipole truncation order and limited only by the computational power. A remarkable accuracy is obtained already for the lowest truncation order, which enables calculations for very long rods, up to p = 1000. Additionally, the bead model is checked by filling the rod with smaller spheres. This procedure shows that for longer rods the basic model provides reasonable results varying less than 5% from the model with filling. An analytical expression for α as a function of p is derived in the limit of very long rods. We show that in the first order in 1/ log p the correction to the Einstein diffusion constant does not depend on the size of the tracer sphere. The higher order corrections depending on the applied model are computed numerically.
Three-particle contribution to sedimentation and collective diffusion in hard-sphere suspensions
Chemical Physics, 2002
The virial expansion of the collective mobility ͑sedimentation͒ coefficient is considered for hard sphere suspensions at equilibrium. The term of the second order in volume fraction, which involves three-particle hydrodynamic interactions, is calculated with high accuracy. To achieve that we represent the collective mobility coefficient as the sum of convergent integrals over particle configurations. In this way the short-wave-number limit k→0 is avoided. Moreover, an efficient numerical procedure is applied to evaluate the hydrodynamic interactions. The algorithm is based on the multipole expansion, corrected for lubrication. The method allows us to analyze contributions to the collective mobility coefficient from different configurations of three particles and to select the dominant part. This suggests a general approximation scheme.
The Journal of Chemical Physics, 2012
We consider tracer diffusion in colloidal suspensions under solid loading conditions, where hydrodynamic interactions play an important role. To this end, we carry out computer simulations based on the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) technique. Many details of the simulation method are discussed in detail. In particular, our choices for the SRD-MD parameters and for the different scales are adapted to simulating colloidal suspensions under realistic conditions. Our simulation data are compared with published theoretical, experimental and numerical results and compared to Brownian dynamics simulation data. We demonstrate that our SRD-MD simulations reproduce many features of the hydrodynamics in colloidal fluids under finite loading. In particular, finite-size effects and the diffusive behavior of colloids for a range of volume fractions of the suspension show that hydrodynamic interactions are correctly included within the SRD-MD technique.