(401i) Ewald-like Method for 3d-Confined Systems: Electrostatics and Hydrodynamic Interactions

A 3D-confined Ewald sum is develop to calculate long-range interactions in systems confined between two infinite walls. The method solves for the Green's function, where the field variable is expanded in Fourier series in the two periodic directions and boundary conditions at the walls are enforced by means of the Fourier coefficients. As in conventional Ewald methods for unbounded domains, the fields, i.e. electrostatic potential for electrostatics and the velocity perturbation for hydrodynamics, are split into a near-field part, where a Gaussian distribution is used to decrease the range of the interaction in order to achieve fast convergence in real space, and a far-field part with fast convergence in Fourier space. The near-field is modified with single wall corrections for particles that are closer than the near-field range to the wall. A particle-mesh method is used to calculate the far-field contributions, allowing the use of FFT methods for the solution of the slit-Green's function. The method scales as O(NlogN) where N is the number of particles, so simulations of large number of particles can be performed in reasonable computational times. The method is used to study concentration effects on confined flowing polymer solutions and in non-Brownian self-propelled particles. Also, the effect of hydrodynamic interactions on confined charge-dipoles is simulated in order to analyze the self-assembly of the dipoles in different concentration regimes.