Incorporating Electrokinetic Phenomena into EBNavierStokes

Motivated by the recent interest in using electrokinetic effects within microfluidic devices, they have extended the EBNavierStokes code to be able to handle electrokinetic effects. With this added functionality, the code becomes more useful for understanding and designing microfluidic devices that take advantage of electrokinetic effects (e.g. pumping and mixing). Supporting the simulation of electrokinetic effects required three main extensions to the existing code: (1) addition of an electric field solver, (2) development of a module for accurately computing the Smulochowski slip-velocity at fluid-solid boundaries, and (3) extension of the fluid solver to handle nonuniform inhomogeneous Dirichlet boundary conditions. The first and second extensions were needed to compute the electrokinetically generated slip-velocity at fluid-solid boundaries. The third extension made it possible for the fluid flow to be driven by a slip-velocity boundary condition (rather than by a pressure difference between inflow and outflow). In addition, several small changes were made throughout the code to make it compatible with these extensions. This report documents the changes to the EBNavierStokes code required to support the simulation of electrokinetic effects. They begin with a brief overview of the problem of electrokinetically driven flow. Next, they present a detailed description of the changes to the EBNavierStokes code. Finally, they present some preliminary results and discuss future directions and improvements to the code

Simulation of Flow and Transport at the Micro (Pore) Scale

An important problem in porous media involves the ability of micron and submicron-sized biological particles such as viruses or bacteria to move in groundwater systems through geologic media characterized by rock or mixed gravel, clay and sand materials. Current simulation capabilities require properly upscaled (continuum) models of colloidal filtration and adsorption to augment existing theories of fluid flow and chemical transport. Practical models typically address flow and transport behavior in aquifers over distances of 1 to 10 km where, for example, fluid momentum balance is governed by the simple Darcy's Law as a function of a pressure gradient, elevation gradient and a medium-dependent permeability parameter. In addition to fluid advection, there are multiple transport processes occurring in these systems including diffusion, dispersion and chemical interactions with solids or other aqueous chemical species. Particle transport is typically modeled in the same way as dissolved species, except that additional loss terms are incorporated to model particle filtration (physical interception), adsorption (chemical interception) and inactivation. Proper resolution of these processes at the porous medium continuum scale constitutes an important closure problem in subsurface science. We present a new simulation capability based on enabling technologies developed for microfluidics applications to model transport of colloidal-sized particles at the microscale, with relevance to the pore scale in geophysical subsurface systems. Particulate is represented by a bead-rod polymer model and is fully-coupled to a Newtonian solvent described by Navier-Stokes. Finite differences are used to discretize the interior of the domain; a Cartesian grid embedded boundary/volume-of-fluid method is used near boundaries and interfaces. This approach to complex geometry is amenable to direct simulation on grids obtained from surface extractions of tomographic image data. Short-range interactions are included in the particle model. This capability has been previously demonstrated on polymer flow in spatially-resolved packed bed (3D) and post array (2D) systems. We also discuss the advantages of this approach for the development of high-resolution adaptive algorithms for multiscale continuum-particle and mesoscale coarse-grained molecular dynamics models

Toward a Mesoscale Model for the Dynamics of Polymer Solutions

To model entire microfluidic systems containing solvated polymers we argue that it is necessary to have a numerical stability constraint governed only by the advective CFL condition. Advancements in the treatment of Kramers bead-rod polymer models are presented to enable tightly-coupled fluid-particle algorithms in the context of system-level modeling

A Penalty Method to Model Particle Interactions in DNA-laden Flows

We present a hybrid fluid-particle algorithm to simulate flow and transport of DNA-laden fluids in microdevices. Relevant length scales in microfluidic systems range from characteristic channel sizes of millimeters to micron scale geometric variation (e.g., post arrays) to 10 nanometers for the length of a single rod in a bead-rod polymer representation of a biological material such as DNA. The method is based on a previous fluid-particle algorithm in which long molecules are represented as a chain of connected rods, but in which the physically unrealistic behavior of rod crossing occurred. We have extended this algorithm to include screened Coulombic forces between particles by implementing a Debye-Hueckel potential acting between rods. In the method an unsteady incompressible Newtonian fluid is discretized with a second-order finite difference method in the interior of the Cartesian grid domain; an embedded boundary volume-of-fluid formulation is used near boundaries. The bead-rod polymer model is fully coupled to the solvent through body forces representing hydrodynamic drag and stochastic thermal fluctuations. While intrapolymer interactions are modeled by a soft potential, polymer-structure interactions are treated as perfectly elastic collisions. We demonstrate this method on flow and transport of a polymer through a post array microchannel in 2D where the polymer incorporates more realistic physical parameters of DNA, and compare to previous simulations where rods are allowed to cross. We also show that the method is capable of simulating 3D flow in a packed bed micro-column

A Hard Constraint Algorithm to Model Particle Interactions in DNA-laden Flows

We present a new method for particle interactions in polymer models of DNA. The DNA is represented by a bead-rod polymer model and is fully-coupled to the fluid. The main objective in this work is to implement short-range forces to properly model polymer-polymer and polymer-surface interactions, specifically, rod-rod and rod-surface uncrossing. Our new method is based on a rigid constraint algorithm whereby rods elastically bounce off one another to prevent crossing, similar to our previous algorithm used to model polymer-surface interactions. We compare this model to a classical (smooth) potential which acts as a repulsive force between rods, and rods and surfaces

A Hybrid Godunov Method for Radiation Hydrodynamics

From a mathematical perspective, radiation hydrodynamics can be thought of as a system of hyperbolic balance laws with dual multiscale behavior (multiscale behavior associated with the hyperbolic wave speeds as well as multiscale behavior associated with source term relaxation). With this outlook in mind, this paper presents a hybrid Godunov method for one-dimensional radiation hydrodynamics that is uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds that the technique preserves certain asymptotic limits. The method incorporates a backward Euler upwinding scheme for the radiation energy density and flux as well as a modified Godunov scheme for the material density, momentum density, and energy density. The backward Euler upwinding scheme is first-order accurate and uses an implicit HLLE flux function to temporally advance the radiation components according to the material flow scale. The modified Godunov scheme is second-order accurate and directly couples stiff source term effects to the hyperbolic structure of the system of balance laws. This Godunov technique is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The Godunov scheme is explicit on the material flow scale but is unsplit and fully couples matter and radiation without invoking a diffusion-type approximation for radiation hydrodynamics. This technique derives from earlier work by Miniati & Colella 2007. Numerical tests demonstrate that the method is stable, robust, and accurate across various parameter regimes.Comment: accepted for publication in Journal of Computational Physics; 61 pages, 15 figures, 11 table