TY - JOUR

T1 - Computing hydrodynamic interactions in confined doubly periodic geometries in linear time

AU - Hashemi, Aref

AU - Peláez, Raúl P.

AU - Natesh, Sachin

AU - Sprinkle, Brennan

AU - Maxian, Ondrej

AU - Gan, Zecheng

AU - Donev, Aleksandar

N1 - Funding Information:
We thank Leslie Greengard, Kyongmin Yeo, and Amanda Howard for helpful discussions. This work was supported by the NSF under Award No. DMS-2011544 and through a Research and Training Group in Modeling and Simulation under Award No. RTG/DMS-1646339.
Publisher Copyright:
© 2023 Author(s).

PY - 2023/4/21

Y1 - 2023/4/21

N2 - We develop a linearly scaling variant of the force coupling method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally accurate Stokes solver uses the fast Fourier transform in the periodic xy plane and Chebyshev polynomials in the aperiodic z direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the z direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly periodic geometries [Maxian et al., J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement.

AB - We develop a linearly scaling variant of the force coupling method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally accurate Stokes solver uses the fast Fourier transform in the periodic xy plane and Chebyshev polynomials in the aperiodic z direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the z direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly periodic geometries [Maxian et al., J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement.

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U2 - 10.1063/5.0141371

DO - 10.1063/5.0141371

M3 - Article

C2 - 37094003

AN - SCOPUS:85153672066

SN - 0021-9606

VL - 158

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 15

M1 - 154101

ER -