Simulating non-Brownian suspensions with non-homogeneous Navier slip boundary conditions

TL;DR

This work addresses how surface slip alters suspension dynamics by introducing an implicit-solvent method for non-homogeneous Navier slip boundary conditions, modeled via a regularized boundary-integral framework. The method efficiently couples surface slip, traction, and rigid-body motion, enabling scalable simulations of large suspensions with spatially varying slip lengths $l(r)$. Validation against analytical results for drag and mobility on homogeneous and Janus particles demonstrates accuracy within a few percent across slip regimes, and the study reveals how slip length and slip patterns influence suspension viscosity, including a decrease of $ ext{eta}_{eff}$ with increasing slip up to about $10R$. The approach supports complex slip distributions and non-spherical geometries, offering substantial memory savings over explicit-solvent methods and paving the way for future extensions to Brownian suspensions and large-scale microfluidic applications.

Abstract

Fluid-structure interactions are commonly modeled using no-slip boundary conditions. However, small deviations from these conditions can significantly alter the dynamics of suspensions and particles, especially at the micro and nano scales. This work presents a robust implicit solvent method for simulating non-colloidal suspensions with non-homogeneous Navier slip boundary conditions. Our approach is based on a regularized boundary integral formulation, enabling accurate and efficient computation of hydrodynamic interactions. This makes the method well-suited for large-scale simulations. We validate the method by comparing computed drag forces on homogeneous and Janus particles with analytical results. Additionally, we consider the effective viscosity of suspensions with varying slip lengths, benchmarking against available analytical no-slip and partial-slip theories.

Figures (11)

• Figure 1: Examples of discretized spherical particles with different slip distributions: homogeneous no-slip, homogeneous full-slip and Janus slip distribution which we model with slip lengths $\ell / R = 10^{-3}$ and $\ell / R = 10^{3}$ respectively, where $R$ is the particle radius. The surface normals are denoted as $\text{n}$.
• Figure 2: Convergence of preconditioned GMRES to solve the mobility problem Eq. \ref{['eq:linear_system']} for a single particle discretized with a different number of blobs. The figure shows results for no-slip (left) and full-slip (right) BCs.
• Figure 3: GMRES convergence to solve the mobility problem Eq. \ref{['eq:linear_system']} for $\boldsymbol{M}$ particles, from 1 to 4096, forming a simple cubic lattice with a distance between first neighbors equal to two particle diameters. The particles are discretized with $N_b$ = 42 blobs.
• Figure 4: Drag force $f_d$ on a sphere with different slip lengths, $\ell$, ranging from no-slip to full-slip. The curve represents the analytical result and the symbols the numerical results for two discretizations with $N_b=42$ and 642 blobs respectively. The numerical results are normalized with the hydrodynamic radius, $R_h$, computed in the no-slip case ($\ell / R \approx 10^{-4}$).
• Figure 5: Janus particles have one half (colored yellow) representing a no-slip surface, while the other half (colored purple) represents a full-slip surface. The interphase line region is an average slip length. The scheme illustrates examples of Janus particles aligned along the particle axis at three angles: 0, 45, and 90 degrees from the horizontal x-axis. In all cases, the applied force acts along the horizontal x-axis.