In this study, the complexity of a steady-state flow through porous media is revealed using confocal laser scanning microscopy (CLSM). Micro-particle image velocimetry (micro-PIV) is applied to construct movies of colloidal particles. The calculated velocity vector fields from images are further utilized to obtain laminar flow streamlines. Fluid flow through a single straight channel is used to confirm that quantitative CLSM measurements can be conducted. Next, the coupling between the flow in a channel and the movement within an intersecting dead-end region is studied. Quantitative CLSM measurements confirm the numerically determined coupling parameter from earlier work of the authors. The fluid flow complexity is demonstrated using a porous medium consisting of a regular grid of pores in contact with a flowing fluid channel. The porous media structure was further used as the simulation domain for numerical modeling. Both the simulation, based on solving Stokes equations, and the experimental data show presence of non-trivial streamline trajectories across the pore structures. In view of the results, we argue that the hydrodynamic mixing is a combination of non-trivial streamline routing and Brownian motion by pore-scale diffusion. The results provide insight into challenges in upscaling hydrodynamic dispersion from pore scale to representative elementary volume (REV) scale. Furthermore, the successful quantitative validation of CLSM-based data from a microfluidic model fed by an electrical syringe pump provided a valuable benchmark for qualitative validation of computer simulation results.
Graphic Abstract
We developed a new visualization approach to gain a better understanding of the displacement of one fluid phase by another in porous media. This is based on a recent experimental parameter study with varying capillary numbers and viscosity ratios. We analyse the temporal evolution of characteristic values in this two‐phase flow scenario and discuss how to directly compare experiments across different temporal scales. To enable spatio‐temporal analysis, we introduce a new abstract visual representation showing which paths through the porous medium were occupied and for how long. These transport networks allow to assess the impact of different acting forces and they are designed to yield expressive comparability and linking to the experimental parameter space both supported by additional visual cues. This joint work of porous media experts and visualization researchers yields new insights regarding two‐phase flow on the microscale, and our visualization approach contributes towards the overarching goal of the domain scientists to characterize porous media flow based on capillary numbers and viscosity ratios.
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10 color maps for pores and throatsFigure 1: Transport paths in the porous medium for varying capillary numbers Ca and viscosity ratios M in drainage experiments (i.e., displacement of the fluid-the wetting phase-initially filling the solid with another fluid-the non-wetting phase-entering from the right).Nodes represent pore bodies (diameter =size), links stand for pore throats (edge thickness =width). Experiments capture different time scales that are made comparable in this visualization by considering the time span between (i) the non-wetting fluid entering and (ii) forming an uninterrupted connection from left to right (aka breakthrough). Usage rate U-a normalized measure of how long a pore or throat has been occupied by the non-wetting phase-is mapped to color directly (for U ≈ 0 the duration of the experiment is shown instead). This allows to draw conclusions regarding dominant driving forces of the flow and detect unexpected events. Frames around each experiment depict its representative color used throughout this paper.
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