Influence of numerical resolution on the dynamics of finite-size particles with the lattice Boltzmann method

Simulating dynamics of ellipsoidal particles using lattice Boltzmann method

Anisotropic particles are often encountered in different fields of soft matter and complex fluids. In this work, we present an implementation of the coupled hydrodynamics of solid ellipsoidal particles and the surrounding fluid using the lattice Boltzmann method. A standard link-based mechanism is used to implement the solid-fluid boundary conditions. We develop an implicit method to update the position and orientation of the ellipsoid. This exploits the relations between the quaternion which describes the ellipsoid's orientation and the ellipsoid's angular velocity to obtain a stable and robust dynamic update. The proposed algorithm is validated by looking at four scenarios: (i) the steady translational velocity of a spheroid subject to an external force in different orientations, (ii) the drift of an inclined spheroid subject to an imposed force, (iii) three-dimensional rotational motions in a simple shear flow (Jeffrey's orbits), and (iv) developed fluid flows and self-propulsion exhibited by a spheroidal microswimmer. In all cases the comparison of numerical results shows good agreement with known analytical solutions, irrespective of the choice of the fluid properties, geometrical parameters, and lattice Boltzmann model, thus demonstrating the robustness of the proposed algorithm.

Unified directional parabolic-accurate lattice Boltzmann boundary schemes for grid-rotated narrow gaps and curved walls in creeping and inertial fluid flows

The goal of this work is to advance the characteristics of existing lattice Boltzmann Dirichlet velocity boundary schemes in terms of the accuracy, locality, stability, and mass conservation for arbitrarily grid-inclined straight walls, curved surfaces, and narrow fluid gaps, for both creeping and inertial flow regimes. We reach this objective with two infinite-member boundary classes: (1) the single-node "Linear Plus" (LI^{+}) and (2) the two-node "Extended Multireflection" (EMR). The LI^{+} unifies all directional rules relying on the linear combinations of up to three pre- or postcollision populations, including their "ghost-node" interpolations and adjustable nonequilibrium approximations. On this basis, we propose three groups of LI^{+} nonequilibrium local corrections: (1) the LI_{1}^{+} is parametrized, meaning that its steady-state solution is physically consistent: the momentum accuracy is viscosity-independent in Stokes flow, and it is fixed by the Reynolds number (Re) in inertial flow; (2) the LI_{3}^{+} is parametrized, exact for arbitrary grid-rotated Poiseuille force-driven Stokes flow and thus most accurate in porous flow; and (3) the LI_{4}^{+} is parametrized, exact for pressure and inertial term gradients, and hence advantageous in very narrow porous gaps and at higher Reynolds range. The directional, two-relaxation-time collision operator plays a crucial role for all these features, but also for efficiency and robustness of the boundary schemes due to a proposed nonequilibrium linear stability criterion which reliably delineates their suitable coefficients and relaxation space. Our methodology allows one to improve any directional rule for Stokes or Navier-Stokes accuracy, but their parametrization is not guaranteed. In this context, the parametrized two-node EMR class enlarges the single-node schemes to match exactness in a grid-rotated linear Couette flow modeled with an equilibrium distribution designed for the Navier-Stokes equation (NSE). However, exactness of a grid-rotated Poiseuille NSE flow requires us to perform (1) the modification of the standard NSE term for exact bulk solvability and (2) the EMR extension towards the third neighbor node. A unique relaxation and equilibrium exact configuration for grid-rotated Poiseuille NSE flow allows us to classify the Galilean invariance characteristics of the boundary schemes without any bulk interference; in turn, its truncated solution suggests how, when increasing the Reynolds number, to avoid a deterioration of the mass-leakage rate and momentum accuracy due to a specific Reynolds scaling of the kinetic relaxation collision rate. The optimal schemes and strategies for creeping and inertial regimes are then singled out through a series of numerical tests, such as grid-rotated channels and rotated Couette flow with wall-normal injection, cylindrical porous array, and Couette flow between concentric cylinders, also comparing them against circular-shape fitted FEM solutions.

Drag and lift coefficients of ellipsoidal particles under rarefied flow conditions

The capability to simulate a two-way coupled interaction between a rarefied gas and an arbitrary-shaped colloidal particle is important for many practical applications, such as aerospace engineering, lung drug delivery, and semiconductor manufacturing. By means of numerical simulations based on the direct-simulation Monte Carlo (DSMC) method, we investigate the influence of the orientation of the particle and rarefaction on the drag and lift coefficients, in the case of prolate and oblate ellipsoidal particles immersed in a uniform ambient flow. This is done by modeling the solid particles using a cut-cell algorithm embedded within our DSMC solver. In this approach, the surface of the particle is described by its analytical expression and the microscopic gas-solid interactions are computed exactly using a ray-tracing technique. The measured drag and lift coefficients are used to extend the correlations, based on the sine-squared drag law, available in the continuum regime to the rarefied regime, focusing on the transitional and free-molecular regimes. The functional forms of the correlations for the ellipsoidal particles are chosen as a generalization from the spherical case. We show that the fits over the data from numerical simulations can be extended to regimes outside the simulated range of Kn. Our approach allows to achieve a higher precision when compared with existing predictive models from the literature. Finally, we underline the importance of this work in providing correlations for nonspherical particles that can be used for point-particle Euler-Lagrangian simulations to address the problem of contamination from finite-size particles in high-tech mechanical systems.

Effect of interparticle dipolar interaction on pore clogging during microfiltration

We present numerical investigations on the clogging of adhesive particles carrying electric dipoles at pore scale using an adhesive discrete element method (DEM). Based on the simulation results, the long-range dipolar interaction is reported to promote the clogging process, which is quantified by the bulk permeability, the penetrating particle number, and the particle capture efficiency. A clogging phase diagram is constructed in terms of the Stokes number (St) and the adhesion parameter (Ad) for both neutral and polarized particles. The influence of the dipolar interaction on the clogging-nonclogging transition is then described by the shifted boundary on the diagram. Also, the cake structure is characterized by different mathematical descriptions. A looser structure is formed with the increase of both the short-range adhesion and the long-range dipolar interaction. More ordered structures, such as particle chains, are observed in the presence of the stronger dipolar interaction. Furthermore, fluid stress is found to be essential in the compression and restructuring of the cake structure. Finally, a schematic representation of the cake structure is established, which provides a general physical picture showing the relationship between the cake structure and the particle-scale interactions.