We investigate how diffusion-limited mixing of a layered solute concentration distribution within a porous medium impacts bulk electrical conductivity. To do so, we perform a milli-fluidic tracer test by injecting a fluorescent and electrically conductive tracer in a quasi two-dimensional (2D) water-saturated porous medium. High resolution optical- and geoelectrical monitoring of the tracer is achieved by using a fluorimetry technique and equipping the flow cell with a resistivity meter, respectively. We find that optical and geoelectrical outputs can be related by a temporal re-scaling that accounts for the different diffusion rates of the optical and electrical tracers. Mixing-driven perturbations of the electrical equipotential field lines cause apparent electrical conductivity time-series, measured perpendicularly to the layering, to peak at times that are in agreement with the diffusion transport time-scale associated with the layer width. Numerical simulations highlight high sensitivity of such electrical data to the layers’ degree of mixing and their distance to the injection electrodes. Furthermore, the electrical data correlate well with time-series of two commonly used solute mixing descriptors: the concentration variance and the scalar dissipation rate.

我们研究了多孔介质中分层溶质浓度分布的扩散限制混合如何影响体积电导率。为此，我们通过在准二维（2D）水饱和多孔介质中注入荧光和导电示踪剂来执行毫流体示踪剂测试。示踪剂的高分辨率光学和地电监测是通过使用荧光测定技术并分别为流动池配备电阻率仪来实现的。我们发现，光和地电输出可以通过时间重新定标来关联，该时间重新定标说明了光和电示踪剂的不同扩散速率。等电位磁力线的混合驱动扰动会导致明显的电导率时间序列，垂直于分层进行测量，在与与层宽相关的扩散传输时间尺度一致的时间达到峰值。数值模拟突显了这种电数据对各层混合程度及其与注入电极的距离的高度敏感性。此外，电数据与两个常用溶质混合描述符的时间序列有很好的相关性：浓度方差和标量耗散率。