A general model for frictional contacts in colloidal systems

TL;DR

The paper addresses thermodynamically consistent modeling of frictional contacts in colloidal systems, where surface friction couples translation and rotation and must satisfy fluctuation-dissipation. It derives a general stochastic framework for tangential friction forces, yielding a generalized DPD-type thermostat that includes rotation–translation coupling, with explicit forms for additive and multiplicative noise under different stochastic calculi. The framework is validated in passive, driven, and active contexts: neglecting frictional noise leads to non-Maxwellian distributions and incorrect nonequilibrium behavior, while including the correct noise terms preserves Boltzmann sampling and reveals realistic rheology and phase behavior. Overall, the work provides a practical, thermodynamically sound toolkit for simulating frictional contacts in colloids and active matter, with implications for flow rheology, surface slip, and motility-induced phase separation.

Abstract

In simulations of colloidal matter, frictional contacts between particles are often neglected. For spherical colloids, such an approximation can be problematic, since frictional contacts couple translational and rotational degrees of freedom, which may affect the collective behavior of, e.g., colloids under shear and chiral active matter. Deterministic models for frictional contacts have been proposed in the granular matter community. On the colloidal scale, however, thermal fluctuations are important and should be included in a thermodynamically consistent manner. Here, we derive the correct fluctuation-dissipation relation for linear and nonlinear instantaneous frictional contact interactions. Among other, this generates a new generalized class of dissipative particle dynamics (DPD) thermostats with rotation-translation coupling. We demonstrate effects of frictional contact interactions using the examples of Poiseuille flow and motility induced phase separation in active Langevin particles.

Figures (14)

• Figure 1: Sketch of a two-particle configuration subject to tangential friction
• Figure 2: (a) Speed histograms and (b) angular speed histograms for a two-dimensional passive colloid system with frictional contact interactions according to the Coulomb friction model, Eq. (\ref{['eq:constant']}), for different friction constants $\kappa_f$ as indicated. Stars (labelled "no fn") show data from simulations without stochastic contact friction terms, circles (labelled "fn") data for the full model. Solid colored lines are fits to appropriate Maxwell-Boltzmann distribution with fitted effective temperature, $T_\text{eff}$, black solid line gives the theoretical expectation for $k_{\text{B}}T_\text{eff} = k_{\text{B}}T$. The inset shows the corresponding Kullback-Leibler divergence between the distribution measured in simulations and the fitted Maxwell-Boltzmann distribution.
• Figure 3: $T_\mathrm{eff}$ Effective kinetic temperatures obtained by fitting speed (green) and angular speed (blue) histograms to the corresponding Maxwell-Boltzmann distributions from simulations without (stars) and with (circles) stochastic contact friction terms in two-dimensional (left) and three dimensional (right) systems and for different friction types: (a) linear friction model (b) Coulomb friction model, (c,d) Coulomb-Newton friction model with (c) fixed $\kappa_\text{f}=5$ and varying $\gamma_\text{f}$, and (d) fixed $\gamma_\text{f}=6 \: k_{\text{B}}T t_{_0}/\sigma^2$ and varying $\kappa_\text{f}$.
• Figure 4: Examples of velocity profiles for fluids with frictional contact interactions of the Coulomb-Newton type with parameter $\kappa_\text{f}=5$ and different values of $\gamma_\text{f}$ as indicated, which are confined between walls with roughness parameter $\delta_w=0$ (see text) and subject to a bulk force $F=0.01 \: k_{\text{B}}T/\sigma$. Solid lines show fit to a parabolic profile. Inset shows corresponding profiles of the $z$-component of the angular velocity.
• Figure 5: Dynamic viscosity $\eta$ (top), distance between the hydrodynamic boundary and the physical boundary $y_\text{B}$ (middle), and slip length $\delta_\text{B}$ (bottom) as obtained from parametric fits to Poiseuille flow and Couette flow simulation profiles as in Fig. \ref{['fig:poiseuille']} and Fig. S6 of fluids with frictional contact interactions of the Coulomb-Newton type in slit geometry. The results are shown for various values of the surface roughness parameter $\delta_w$ as functions of the friction parameter $\kappa_\text{f}$ with fixed $\gamma_\text{f} = 6\: k_{\text{B}}T t_{_0}/\sigma^2$ (left), and $\gamma_\text{f}$ with fixed $\kappa_\text{f} = 5$ (right). Error bars represent the one standard deviation uncertainties of the fitted parameters.