Adaptive Mesh Refinement Strategies for a Novel Modelof Immiscible Fluid Flow in Fractures

In this paper, we consider two Adaptive Mesh Refinement (AMR) methods to simulate flow through fractures using a novel multiphase model. The approach represents the fluid using a two-dimensional parallel-plate model that employs techniques adapted from lattice-Boltzmann simulations to track the fluid interface. Here, we discuss different mesh refinement strategies for the model and compare their performance to that of a uniform grid. Results from the simulations are demonstrated showing excellent agreement between the model and analytical solutions for both unrefined and refined meshes. We also present results from the study that illustrate the behavior of the AMR front-tracking method. The AMR model is able to accurately track the interfacial properties in cases where uniform fine meshes would significantly increase the simulation cost.The ability of the model to dynamically refine the domain is demonstrated by presenting the results from an example with evolving interfaces.

Instability of a planar fluid interface under a tangential electric field in a stagnation point flow

The interface between two immiscible fluids can become unstable under the effect of an imposed tangential electric field along with a stagnation point flow. This canonical situation, which arises in a wide range of electrohydrodynamic systems including at the equator of electrified droplets, can result in unstable interface deflections where the perturbed interface gets drawn along the extensional axis of the flow while experiencing strong charge build-up. Here, we present analytical and numerical analyses of the stability of a planar interface separating two immiscible fluid layers subject to a tangential electric field and a stagnation point flow. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic conduction, advection by the flow and finite charge relaxation. Using this model, we perform a local linear stability analysis in the vicinity of the stagnation point to study the behaviour of the system in terms of the relevant dimensionless groups of the problem. The local theory is complemented with a numerical normal-mode linear stability analysis based on the full system of equations and boundary conditions using the boundary element method. Our analysis demonstrates the subtle interplay of charge convection and conduction in the dynamics of the system, which oppose one another in the dominant unstable eigenmode. Finally, numerical simulations of the full nonlinear problem demonstrate how the coupling of flow and interfacial charge dynamics can give rise to nonlinear phenomena such as tip formation and the growth of charge density shocks.

Numerical Solution of the Time-Depending Flow of Immiscible Fluids with Fuzzy Boundary Conditions

Fluid flow modeling using fuzzy boundary conditions is one of the viable areas in biofluid mechanics, drug suspension in pharmacology, as well as in the cytology and electrohydrodynamic analysis of cerebrospinal fluid data. In this article, a fuzzy solution for the two immiscible fluid flow problems is developed, which is motivated by biomechanical flow engineering. Two immiscible fluids, namely micropolar and Newtonian fluid, are considered with fuzzy boundary conditions in the horizontal channel. The flow is considered unsteady and carried out by applying a constant pressure gradient in the X-direction of the channel. The coupled partial differential equations are modeled for fuzzy profiles of velocity and micro-rotation vectors then the numerical results are obtained by the modified cubic B - spline differential quadrature method. The evolution of membership grades for velocity and microrotation profiles has been depicted with the fuzzy boundaries at the channel wall. It is observed that Micropolar fluid has a higher velocity change than Newtonian fluid, and both profiles indicate a declining nature toward the interface.

The Momentum Conserving Scheme for Two-Layer Shallow Flows

This paper confronts the numerical simulation of steady flows of fluid layers through channels of varying bed and width. The fluid consists of two immiscible fluid layers with constant density, and it is assumed to be of a one-dimensional shallow flow. The governing equation is a coupled system of two-layer shallow water models. In this paper, we apply a direct extension of the momentum conserving scheme previously used for solving the one layer shallow water equations. Computations of various steady-state solutions are used to demonstrate the performance of the proposed numerical scheme. Under the influence of a given flow rate, the numerical steady interface is generated in a channel topography with a hump. The results obtained confirm the analytic steady interface of the two-layer rigid-lid model. Furthermore, the same scheme was used with an additional artificial damping to simulate the maximal exchange flow in channels of varying width. The numerical steady interface agreed well with the analytical steady solutions.

Discovery of Dynamic Two-Phase Flow in Porous Media Using Two-Dimensional Multiphase Lattice Boltzmann Simulation

The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

Integrated impedance sensing of liquid sample plug flow enables automated high throughput NMR spectroscopy

A novel approach for automated high throughput NMR spectroscopy with improved mass-sensitivity is accomplished by integrating microfluidic technologies and micro-NMR resonators. A flow system is utilized to transport a sample of interest from outside the NMR magnet through the NMR detector, circumventing the relatively vast dead volume in the supplying tube by loading a series of individual sample plugs separated by an immiscible fluid. This dual-phase flow demands a real-time robust sensing system to track the sample position and velocities and synchronize the NMR acquisition. In this contribution, we describe an NMR probe head that possesses a microfluidic system featuring: (i) a micro saddle coil for NMR spectroscopy and (ii) a pair of interdigitated capacitive sensors flanking the NMR detector for continuous position and velocity monitoring of the plugs with respect to the NMR detector. The system was successfully tested for automating flow-based measurement in a 500 MHz NMR system, enabling high resolution spectroscopy and NMR sensitivity of 2.18 nmol s1/2 with the flow sensors in operation. The flow sensors featured sensitivity to an absolute difference of 0.2 in relative permittivity, enabling distinction between most common solvents. It was demonstrated that a fully automated NMR measurement of nine individual 120 μL samples could be done within 3.6 min or effectively 15.3 s per sample.

High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

Numerical modeling of immiscible contaminant fluid flow in unsaturated and saturated porous aquifers is of great importance in many scientific fields to properly manage groundwater resources. We present a high-resolution numerical model that simulates three-phase immiscible fluid flow in both unsaturated and saturated zone in a porous aquifer. We use coupled conserved mass equations for each phase and study the dynamics of a multiphase fluid flow as a function of saturation, capillary pressure, permeability, and porosity of the different phases, initial and boundary conditions. To deal with the sharp front originated from the partial differential equations’ nonlinearity and accurately propagate the sharp front of the fluid component, we use a high-resolution shock-capturing method to treat discontinuities due to capillary pressure and permeabilities that depend on the saturation of the three different phases. The main approach to the problem’s numerical solution is based on (full) explicit evolution of the discretized (in-space) variables. Since explicit methods require the time step to be sufficiently small, this condition is very restrictive, particularly for long-time integrations. With the increased computational speed and capacity of today’s multicore computer, it is possible to simulate in detail contaminants’ fate flow using high-performance computing.