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We present a novel computational framework for the simulation of rigid spherical Janus particle suspensions in Stokes flow. For a wide array of Janus particle types, we show long-range interactions may be resolved using fast, spectrally accurate boundary integral methods. We incorporate this to our rigid body Stokes platform, which resolves hydrodynamic interactions and contact. Our approach features the use of spherical harmonic expansions for spectrally accurate integral operator evaluation, complementarity-based collision resolution, and optimal O (n) scaling with the number of particles when accelerated via fast summation techniques. We demonstrate the versatility of our simulation platform through three test cases involving Janus particle systems prominent in applications: amphiphilic, bipolar electric and phoretic particles. For each test case, we formulate Janus particle interactions in boundary integral form and use our framework to demonstrate examples of self-assembly and complex collective behavior characteristic of these systems. [ABSTRACT FROM AUTHOR]

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical expressions for evaluating the operators away from the boundary. When two particle are located close to each other, we use a truncated series expansion to compute the hydrodynamic interaction. On the other hand, we use the standard spectrally accurate quadrature scheme to evaluate smooth integrals on the far-field, and accelerate the resulting discrete sums using the fast multipole method (FMM). We employ this discretization scheme to analyze several boundary integral formulations of interest including those arising in porous media flow, active matter and magneto-hydrodynamics of rigid particles. We provide numerical results verifying the accuracy and scaling of their evaluation. [ABSTRACT FROM AUTHOR]

We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in O ( n ) time, where n denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples. [ABSTRACT FROM AUTHOR]

• Collision resolution by convex quadratic programming. • Scalable and efficient parallel algorithm and implementation. • Accurate second-kind boundary integral formulation. We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric 'non-overlapping' constraints imposed at each time-step. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to 8 × 10 4 particles with approximately 4 × 10 7 degrees of freedom on 1792 cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate. [ABSTRACT FROM AUTHOR]