Browsing by Author "Liu, Chen"

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    Discontinuous Galerkin Methods for Pore-scale Multiphase Flow: Theoretical Analysis and Simulation
    (2019-04-17) Liu, Chen; Riviere, Beatrice
    In this dissertation, we formulate a pressure-correction projection algorithm, in conjunction with the interior penalty discontinuous Galerkin scheme for time and space discretization to build a single-phase incompressible Navier–Stokes simulator and a two-phase Cahn–Hilliard–Navier–Stokes simulator. The method is a decoupled algorithm, which is especially convenient for large-scale 3D numerical simulations in complex geometry, such as in porous structures obtained from microtomography scanning. The simulators we implemented are robust. The numerical experiment results have been validated on a series of realistic physical problems and exhibit the potential for computing effective properties of single/two-phase flow such as permeability and saturation. Theoretical analysis of the numerical methods for solving multiphase flow model will also contribute to the understanding of the complex multi-scale fluid system from the mathematical point of view. In this dissertation, we also analyze a non-symmetric interior penalty discontinuous Galerkin scheme for solving the mixed form of the Cahn–Hilliard equation and a symmetric interior penalty discontinuous Galerkin scheme for solving the Cahn–Hilliard–Navier–Stokes equations. We prove several numerical properties for these numerical schemes, including unique solvability, stability analysis, and error analysis.
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    Pore-scale Simulation of Fluid Flow Using Discontinuous Galerkin Methods
    (2016-04-26) Liu, Chen; Riviere, Beatrice
    This dissertation concentrates on pore-scale Newtonian fluid flow simulation in three-dimensions. One-component single-phase compressible Navier-Stokes equations are considered as governing equations. Interior penalty discontinuous Galerkin (DG) methods are chosen for numerical discretization. Mass balance equation and momentum balance equations are coupled by fixed-point iteration. The DG methods in this thesis are defined on voxel sets representing the pore space of rock samples at micrometer scale. The methods exhibit optimal convergence and the simulated velocity fields compare well against the ones yielded by analytical solutions for simple geometries. The DG-based simulator also delivers intuitive velocity fields for complex pore geometries.
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    Ultra-high capacity, multifunctional nanoscale sorbents for PFOA and PFOS treatment
    (Springer Nature, 2023) Lee, Junseok; Kim, Changwoo; Liu, Chen; Wong, Michael S.; Cápiro, Natalie L.; Pennell, Kurt D.; Fortner, John D.
    Here, we describe surface functionalized, superparamagnetic iron oxide nanocrystals (IONCs) for ultra-high PFAS sorption and precise, low energy (magnetic) separation, considering perfluorooctanoic acid (PFOA) and perfluorooctanesulfonic acid (PFOS). As a function of surface coating, sorption capacities described are considerably higher than previous studies using activated carbon, polymers, and unmodified metal/metal oxides, among others. In particular, positively charged polyethyleneimine (PEI) coated IONCs demonstrate extreme sorption capacities for both PFOA and PFOS due to electrostatic and hydrophobic interactions, along with high polymer grafting densities, while remaining stable in water, thus maintaining available surface area. Further, through a newly developed method using a quart crystal microbalance with dissipation (QCM-D), we present real-time, interfacial observations (e.g., sorption kinetics). Through this method, we explore underpinning mechanism(s) for differential PFAS (PFOA vs PFOS) sorption behavior(s), demonstrating that PFAS functional head group strongly influence molecular orientation on/at the sorbent interface. The effects of water chemistry, including pH, ionic composition of water, and natural organic matter on sorption behavior are also evaluated and along with material (treatment) demonstration via bench-scale column studies.