Lattice Boltzmann simulations of two-phase flow in a microchannel model and colloids transport with a study of electrostatic force for nanoparticles

Wang, Lian-PingIn this dissertation, a numerical approach is developed to investigate the colloid transport in an unsaturated micro-scale flow system. The motivation for this work was to advance the understanding of colloids facilitated contamination and pollution penetration into the underground water system. The numerical study is conducted under similar configurations and physical conditions as the parallel experimental study performed by Professor Jin’s group at UD. Our focus is to study the effects of unique features in unsaturated porous medium, such as air-water interface and moving contact line, on the colloid transport in order to probe the relevant mechanisms with the level of details that may be difficult to achieve experimentally. ☐ Due to the small size and low volume fraction of colloids, the pore-scale flow is unaffected by the presence of colloids. Therefore the numerical approach contains two tasks: simulation of the micro-channel interfacial flow followed by the modeling of transport of colloid particles in the simulated flow. Specifically, a mesoscopic computational approach known as the lattice Boltzmann approach (LBM) is employed to simulate two-phase flow in the interfacial regions and the trajectories of colloids in the resulting flow under hydrodynamic and various physicochemical forces are numerically integrated. A Navier-Stokes based Volume-Of-Fluid Interface Tracking (VOFIT) method is used to cross validate the flow simulation. LBM results of moving interface shape and dynamic contact angles are in quantitative agreement with the VOFIT results and experimental observations. Due to the numerical instability, the density and viscosity ratios across the gas-liquid interface are initially set to one as the base case. A few improvements in LBM are made to gradually approach experimental conditions. The Chapman-Enskog expansion of the two-phase LBM model reveals that the anisotropic terms in the inter-particle interaction model due to discretization are the major contributors of spurious currents. This numerical artifact is significantly reduced by introducing a higher-order discretization scheme and a more realistic equation of state, making it possible for the LBM model to handle a density ratio up to 100. The sensitivity study has shown that the density difference alone has little influence on the interface shape and the flow field at the high-density liquid side. The interface fingering instability is observed in the simulated air-advancing case (less viscous fluid penetrating into more viscous one with a dynamic viscosity ratio of 13), which significantly alters the interfacial flow dynamics when compared to the base case. On the other hand, the water-front interface shape and the corresponding flow pattern near the contact line are only slightly affected by the viscosity ratio. The simulated interface shapes agree reasonably well with observations reported in the literature. Although the LBM simulations could not match the realistic Capillary number in the experiments at this point, simulation data are consistent with the trend expected for the small Capillary number limit. ☐ A Lagrangian particle tracking approach was developed to simulate colloid transport and retention under Stokes drag force, Brownian diffusion, and colloid-collector interaction forces. It is found that the hydrodynamic force and Brownian motion are dominant compared to other interfacial forces. Colloids mainly follow the streamline and are subject to localized interaction forces including colloid-AWI (air water interface), colloid-wall and colloid-colloid forces, similar to the observations in parallel experiments. ☐ The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory on electrostatic double-layer (EDL) assumes a thin EDL thickness relative to the colloid size (typically on the order of 1μm). However, this assumption may become invalid for nanoparticles. Lattice Boltzmann method was developed to solve the governing equation for electrostatic potential and EDL interaction force. Several configurations were considered: charged planar surfaces and spheres when maintained at either constant surface potential or charge. The simulation results are compared with those from commonly used approximations: Derjaguin Approximation (DA) and linear superposition approximation (LSA), which allow us to assess their applicability when applied to nanoparticles. The simulated interaction energy for closely spaced surfaces with large constant potentials (> 25mV ) are much higher than both DA and LSA predicted. For example, when κd = 0.1, the simulated normalized interaction energy is 10%-30% higher than DA results and over three times more than what LSA predicted for surface potentials of −75mV and −125mV . The deviation grows with the magnitude of the surface potentials. Overall, LSA became invalid when charged surfaces are close. DA is only a reasonable approximation for planar surfaces of surface potentials less than 25mV in magnitude. The simulation results provide new benchmark data for interaction energy between two surfaces of large surface potential especially when they are close to each other, which can be useful when developing a more general parameterization in the future. ☐ When two planes are maintained at constant charge instead, the electrostatic potentials based on DA agree well with simulation results for the surface charge up to σ/ǫ0ǫr = 5 × 105 V/M, which is equivalent to 42mV , with κd ranges from 5 to 10. DA over-predicts the electrostatic potential for higher surface charge and at lower κd values. The interaction force can be reasonably predicted by DA within the parameter ranges stated above. Otherwise, DA predicts much larger interaction force than the value found in our simulation: at κd = 1.46, the interaction force from DA is found to be roughly twice the simulated values for surface charge at σ/ǫ0ǫr = 5×106 V/M; the LSA prediction, on the other hand, is only one third of the simulated value. ☐ LBM has also been developed to treat cylindrical and spherical nanoparticles. For this purpose, the collision step is revised to recover the Poisson equation in the cylindrical coordinate system. This newly proposed scheme is first validated using the analytical transient solution for the case with fixed surface potential at the cylinder boundaries. The numerical results are then compared with two commonly used approximations–Hogg’s DA and Gregory’s LSA . For the interaction between two charged spheres, the DA based Hogg’s expression can predict the interaction force under small surface potential. However, Hogg’s results deviate significantly from the simulation results at close distance of two surfaces due to the lack of treatment of excess charge density. Gregory’s LSA based expression has decent performance by predicting only 10% less than simulated interaction force for κa = 1 and κd = 1.7 of two spheres with surface potentials of −125 and −45mV , respectively. For large surface potentials, the simulated interaction force falls in between Hogg (DA based) and Gregory (LSA based) predictions when 2 < κd < 10.University of Delaware, Department of Mechanical EngineeringPh.D