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Title: Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

Abstract

In this paper, we present a consistent implicit incompressible smoothed particle hydrodynamics (I 2SPH) discretization of Navier–Stokes, Poisson–Boltzmann, and advection–diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I 2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. Lastly, the new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Authors:
 [1];  [2];  [2];  [3];  [2]
  1. Univ. of Wisconsin, Madison, WI (United States). Department of Mechanical Engineering
  2. Sandia National Laboratories, NM (United States). Center for Computing Research
  3. Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Advanced Computing, Mathematics, & Data Division
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1341746
Alternate Identifier(s):
OSTI ID: 1396718
Report Number(s):
PNNL-SA-117311
Journal ID: ISSN 0021-9991; PII: S0021999116307069; TRN: US1701046
Grant/Contract Number:
AC02-05CH11231; AC05-76RL01830; AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 334; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Smoothed particle hydrodynamics; Electrokinetic flow; Boundary condition; Implicit scheme

Citation Formats

Pan, Wenxiao, Kim, Kyungjoo, Perego, Mauro, Tartakovsky, Alexandre M., and Parks, Michael L.. Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2016.12.042.
Pan, Wenxiao, Kim, Kyungjoo, Perego, Mauro, Tartakovsky, Alexandre M., & Parks, Michael L.. Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics. United States. doi:10.1016/j.jcp.2016.12.042.
Pan, Wenxiao, Kim, Kyungjoo, Perego, Mauro, Tartakovsky, Alexandre M., and Parks, Michael L.. Tue . "Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics". United States. doi:10.1016/j.jcp.2016.12.042. https://www.osti.gov/servlets/purl/1341746.
@article{osti_1341746,
title = {Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics},
author = {Pan, Wenxiao and Kim, Kyungjoo and Perego, Mauro and Tartakovsky, Alexandre M. and Parks, Michael L.},
abstractNote = {In this paper, we present a consistent implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier–Stokes, Poisson–Boltzmann, and advection–diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. Lastly, the new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.},
doi = {10.1016/j.jcp.2016.12.042},
journal = {Journal of Computational Physics},
number = ,
volume = 334,
place = {United States},
year = {Tue Jan 03 00:00:00 EST 2017},
month = {Tue Jan 03 00:00:00 EST 2017}
}

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  • We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.
  • Cited by 1
  • A numerical model based on smoothed particle hydrodynamics (SPH) was developed and used to simulate immiscible and miscible fluid flows in porous media and to study effects of porous scale heterogeneity and anisotropy on such flows. Models for heterogeneous porous media were generated by using randomly located non-intersecting circular grains of different sizes, and pore scale anisotropy was introduced by randomly inserting non-overlapping particles on either side of the gap between two self-affine fractal curves to create a microfracture. . Different fluid wetting behaviors and surface tensions were modeled using pairwise particle-particle interactions. Particles with different masses and viscosities weremore » used to model multiphase flow. In simulations of miscible fluid flow, particles with variable, composition dependent, masses and viscosities were used. Artificial surface tension effects were avoided by basing the SPH equations on the particle number density.« less
  • We present a smoothed particle hydrodynamic model for incompressible fluids. As opposed to solving a pressure Poisson equation in order to get a divergence-free velocity field, here incompressibility is achieved by requiring as a kinematic constraint that the volume of the fluid particles is constant. We use Lagrangian multipliers to enforce this restriction. These Lagrange multipliers play the role of non-thermodynamic pressures whose actual values are fixed through the kinematic restriction. We use the SHAKE methodology familiar in constrained molecular dynamics as an efficient method for finding the non-thermodynamic pressure satisfying the constraints. The model is tested for several flowmore » configurations.« less