Simulation of claylike colloids

We investigate the properties of dense suspensions and sediments of small spherical silt particles by means of a combined molecular dynamics and stochastic rotation dynamics (SRD) simulation. We include van der Waals and effective electrostatic interactions between the colloidal particles, as well as Brownian motion and hydrodynamic interactions which are calculated in the SRD part. We present the simulation technique and first results. We have measured velocity distributions, diffusion coefficients, sedimentation velocity, spatial correlation functions, and we have explored the phase diagram depending on the parameters of the potentials and on the volume fraction.

Figure 1

DLVO potentials for ${\mathrm{Al}}_2{\mathrm{O}}_3$ spheres of $R=0.5\mu \mathrm{m}$ diameter suspended in water. These are typical potentials used for our simulations as described below. The primary minimum at $d∕R=2.0$ is not reproduced correctly by the DLVO theory. It has to be modeled separately. In most of our cases the existence of the secondary minimum determines the properties of the simulated system.

Figure 2

Velocity distribution of fluid (a) and colloid (b) particles in a SRD simulation after thermalization. Particle density is $3900\mathrm{kg}∕{\mathrm{m}}^3$, the time step $2.0\mu \mathrm{s}$, model temperature $T=10.57\mathrm{mK}$, fluid particle mass $m_f=1.0667\times {10}^{-18}$, and particle diameter $d=0.5\mu \mathrm{m}$. The theoretical Gaussian curve is plotted as well as the measured velocity distributions.

Figure 3

(a) Evaluation of $D$ using the Green-Kubo method: the plot shows the sum of ${\sum }_{j=1,\dots ,n}{g}_{x,y,z}\left(j\right)$ and the estimated $D$. (b) The decay of the contributions $g_{x,y,z}\left(j\right)$. We have measured the diffusion constant of soft spheres coupled with coupling II to the SRD at low volume fractions.

Figure 4

Mean sedimentation velocity over porosity $(1-\varphi )$ according to Eq. (37): measured values and fit curve in a log-log-plot. The Peclet number of this simulation is 1. Coupling method II has been used for this plot.

Figure 5

(Color online) Correlation function of ${\mathrm{Al}}_2{\mathrm{O}}_3$ for ${\Psi }_0=50\mathrm{mV}$ and $\kappa =3\times {10}^8∕\mathrm{m}$. The potential is attractive; thus, peaks (labeled by letters) can be identified and assigned to special local configurations (see text).

Figure 6

Correlation function of ${\mathrm{Al}}_2{\mathrm{O}}_3$ for ${\Psi }_0=50\mathrm{mV}$ and $\kappa =7.3\times {10}^7∕\mathrm{m}$. Repulsive potentials. One can see oscillations caused by the excluded volume.

Figure 7

Plot of the correlation function of Fig. 6 together with the potential used in this simulation. One can see that the maximum of the correlation function occurs for the distance, at which the very shallow secondary minimum of the potential is located.

Figure 8

Velocity distribution of colloidal particles for each direction. Semilogarithmic plot where deviations from a Gaussian would be visible by deviations from a parabolic profile.

Figure 9

(Color online) Snapshots from the phase diagram of ${\mathrm{Al}}_2{\mathrm{O}}_3$: For the DLVO potentials with different effective surface charge and different screening length one can either observe cluster formation or single particles in suspension. The simulation was done at room temperature for $1\mathrm{s}$ of real time and a particle diameter of $0.5\mu \mathrm{m}$. Gravity has not been applied here. The pictures are corresponding to the values written on the axis. For this figure we have chosen the simulation runs for 14% volume fraction with 462 colloidal particles.

Figure 10

Correlation function and its dependence on the inverse Debye screening length $\kappa$. ${\Psi }_0=20\mathrm{mV}$ and $\Phi =0.14$ have been kept constant. For shorter Debye screening lengths the attractive force becomes stronger and leads to clustering, which is reflected in the appearance of peaks. The single curves have been shifted with respect to each other.

Figure 11

Correlation function and its dependence on the effective surface potential ${\Psi }_0$. $\kappa =2\times {10}^8{\mathrm{m}}^{-1}$ and $\Phi =0.14$ have been kept constant. The higher the effective surface potential, the stronger the attraction force, and clustering can be seen in the growing peaks.

Figure 12

Correlation function and its dependence on the volume fraction $\Phi$. Effective surface potential ${\Psi }_0=20\mathrm{mV}$ and $\kappa =1.4\times {10}^8{\mathrm{m}}^{-1}$ have been kept constant. For center-center distances between six and eight particle radii broad peaks start to appear for larger volume fractions.

Figure 13

Correlation function and its dependence on the volume fraction $\Phi$. Effective surface potential ${\Psi }_0=20\mathrm{mV}$ and $\kappa =1.6\times {10}^8{\mathrm{m}}^{-1}$ have been kept constant. Due to a small change in $\kappa$ with respect to Fig. 12, one can cross the phase border between suspended particles and clustering regime. Also here long-range correlations become more pronounced for high volume fractions.

Figure 14

Mean-square displacement (projection on each of the axis). For this simulation ${\Psi }_0=50\mathrm{mV}$ and $\kappa =3\times {10}^8∕\mathrm{m}$ have been used. First particles move by diffusion, are attracted, and then form clusters of larger size and lower mobility, which can be observed in a decay of the diffusion length for a given period of time. We have simulated 1155 particles in a cube with $6\mu \mathrm{m}$ extension, which results in a volume fraction of 35%.