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Register a new userSpectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions
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In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics (SEASD), a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions. SEASD is based on the framework of Stokesian Dynamics (SD) with extension to compressible solvents, and uses the Spectral Ewald (SE) method [Lindbo & Tornberg, J. Comput. Phys. 229 (2010) 8994] for the wave-space mobility computation. To meet the performance requirement of dynamic simulations, we use Graphic Processing Units (GPU) to evaluate the suspension mobility, and achieve an order of magnitude speedup compared to a CPU implementation. For further speedup, we develop a novel far-field block-diagonal preconditioner to reduce the far-field evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of the mean-field Brownian approximation of Banchio & Brady [J. Chem. Phys. 118 (2003) 10323]. We extensively discuss implementation and parameter selection strategies in SEASD, and demonstrate the spectral accuracy in the mobility evaluation and the overall $mathcal{O}(Nlog N)$ computation scaling. We present three computational examples to further validate SEASD and SEASD-nf in monodisperse and bidisperse suspensions: the short-time transport properties, the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear Brownian rheology. Our validation results show that the agreement between SEASD and SEASD-nf is satisfactory over a wide range of parameters, and also provide significant insight into the dynamics of polydisperse colloidal suspensions.
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We propose a novel approach to the numerical simulation of thin film flows, based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin film equations are recovered and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop towards its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied, and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem of a droplet sliding on an inclined plane, finding that the Capillary number scales linearly with the Bond number, in agreement with experimental results. At last, we demonstrate the ability of the method to handle heterogenous and complex systems by showcasing the controlled dewetting of a thin film on a chemically structured substrate.
An articulated body is defined as a finite number of rigid bodies connected by a set of arbitrary constraints that limit the relative motion between pairs of bodies. Such a general definition encompasses a wide variety of situations in the microscopic world, from bacteria to synthetic micro-swimmers, but it is also encountered when discretizing inextensible bodies, such as filaments or membranes. Simulating suspensions of such articulated bodies requires to solve the hydrodynamic interactions between large collections of objects of arbitrary shape while satisfying the multiple constraints that connect them. Two main challenges arise in this task: limiting the cost of the hydrodynamic solves, and enforcing the constraints within machine precision at each time-step. To address these challenges we propose a formalism that combines the body mobility problem in Stokes flow with a velocity formulation of the constraints, resulting in a mixed mobility-resistance problem. While resistance problems are known to scale poorly with the particle number, our preconditioned iterative solver is not sensitive to the system size. Constraint violations, e.g. due to discrete time-integration errors, are prevented by correcting the particles positions and orientations at the end of each time-step. Our correction procedure, based on a nonlinear minimisation algorithm, is negligible in terms of computational cost and preserves the accuracy of the time-integration scheme. We showcase the robustness and scalability of our method by exploring the locomotion modes of a model microswimmer inspired by the diatom colony Bacillaria Paxillifer, and by simulating large suspensions of bacteria interacting near a no-slip boundary. Finally, we provide a Python implementation of our framework in a collaborative publicly available code.
We introduce a numerical solver for the spatially inhomogeneous Boltzmann equation using the Burnett spectral method. The modelling and discretization of the collision operator are based on the previous work [Z. Cai, Y. Fan, and Y. Wang, Burnett spectral method for the spatially homogeneous Boltzmann equation, arXiv:1810.07804], which is the hybridization of the BGK operator for higher moments and the quadratic collision operator for lower moments. To ensure the preservation of the equilibrium state, we introduce an additional term to the discrete collision operator, which equals zero when the number of degrees of freedom tends to infinity. Compared with the previous work [Z. Hu, Z. Cai, and Y. Wang,Numerical simulation of microflows using Hermite spectral methods, arXiv:1807.06236], the computational cost is reduced by one order. Numerical experiments such as shock structure calculation and Fourier flows are carried out to show the efficiency and accuracy of our numerical method.
Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multi-component fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.
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