Advances and benefits of fractal models to predict streaming potentials in partially saturated porous media

<p>Understanding streaming potential generation in porous media is of high interest for hydrological and reservoir studies as it allows to relate water fluxes to measurable electrical potential distributions in subsurface geological settings. The evolution of streaming potential <span>stems</span> from electrokinetic coupling between water and electrical fluxes due to the presence of an electrical double layer at the interface between the mineral and the pore water. Two different approaches can be used to model and interpret the generation of the streaming potential in porous media: the classical coupling coefficient approach based on the Helmholtz-Smoluchowski equation, and the effective excess charge density. Recent studies based on both approaches use a mathematical up-scaling procedure that employs the so-called fractal theory. In these studies, the porous medium is represented by a bundle of tortuous capillaries characterized by a fractal capillary-size distribution law. The electrokinetic coupling between the fluid flow and electric current is obtained by averaging the processes that take place in a single capillary. In most cases, closed-form expressions for the electrokinetic parameters are obtained in terms of macroscopic hydraulic variables like permeability, saturation and porosity. In this presentation we propose a review of the existing fractal distribution models that predict the streaming potential in porous media and discuss their benefits compared against other published models.</p>

Bacterial Adhesion of Streptococcus mutans to Dental Material Surfaces

The aim of this study was to investigate and understand bacterial adhesion to different dental material surfaces like amalgam, Chromasit, an Co-Cr alloy, an IPS InLine ceramic, yttrium stabilized tetragonal polycrystalline zirconia (TPZ), a resin-based composite, an Au-Pt alloy, and a tooth. For all materials, the surface roughness was assessed by profilometry, the surface hydrophobicity was determined by tensiometry, and the zeta potential was measured by electrokinetic phenomena. The arithmetic average roughness was the lowest for the TPZ ceramic (Ra = 0.23 µm ± 0.02 µm), while the highest value was observed for the Au-Pt alloy (Ra = 0.356 µm ± 0.075 µm). The hydrophobicity was the lowest on the TPZ ceramic and the highest on the Co-Cr alloy. All measured streaming potentials were negative. The most important cause of tooth caries is the bacterium Streptococcus mutans, which was chosen for this study. The bacterial adhesion to all material surfaces was determined by scanning electron microscopy. We showed that the lowest bacterial extent was on the amalgam, whereas the greatest extent was on tooth surfaces. In general, measurements showed that surface properties like roughness, hydrophobicity and charge have a significant influence on bacterial adhesion extent. Therefore, dental material development should focus on improving surface characteristics to reduce the risk of secondary caries.

The strain-generated electrical potential in cartilaginous tissues: a role for piezoelectricity

The strain-generated potential (SGP) is a well-established mechanism in cartilaginous tissues whereby mechanical forces generate electrical potentials. In articular cartilage (AC) and the intervertebral disc (IVD), studies on the SGP have focused on fluid- and ionic-driven effects, namely Donnan, diffusion and streaming potentials. However, recent evidence has indicated a direct coupling between strain and electrical potential. Piezoelectricity is one such mechanism whereby deformation of most biological structures, like collagen, can directly generate an electrical potential. In this review, the SGP in AC and the IVD will be revisited in light of piezoelectricity and mechanotransduction. While the evidence base for physiologically significant piezoelectric responses in tissue is lacking, difficulties in quantifying the physiological response and imperfect measurement techniques may have underestimated the property. Hindering our understanding of the SGP further, numerical models to-date have negated ferroelectric effects in the SGP and have utilised classic Donnan theory that, as evidence argues, may be oversimplified. Moreover, changes in the SGP with degeneration due to an altered extracellular matrix (ECM) indicate that the significance of ionic-driven mechanisms may diminish relative to the piezoelectric response. The SGP, and these mechanisms behind it, are finally discussed in relation to the cell response.

Non-invasive Electroarthrography Measures Load-Induced Cartilage Streaming Potentials via Electrodes Placed on Skin Surrounding an Articular Joint

Objective We aimed to demonstrate that electroarthrography (EAG) measures streaming potentials originating in the cartilage extracellular matrix during load bearing through electrodes adhered to skin surrounding an articular joint. Design Equine metacarpophalangeal joints were subjected to simulated physiological loads while (1) replacing synovial fluid with immersion buffers of different electrolyte concentrations and (2) directly degrading cartilage with trypsin. Results An inverse relationship between ionic strength and EAG coefficient was detected. Compared to native synovial fluid, EAG coefficients increased ( P < 0.05) for 5 of 6 electrodes immersed in 0.1X phosphate-buffered saline (PBS) (0.014 M NaCl), decreased ( P < 0.05) for 4 of 6 electrodes in 1X PBS (0.14 M NaCl), and decreased ( P < 0.05) for all 6 electrodes in 10X PBS (1.4 M NaCl). This relationship corresponds to similar studies where streaming potentials were directly measured on cartilage. EAG coefficients, obtained after trypsin degradation, were reduced ( P < 0.05) in 6 of 8, and 7 of 8 electrodes, during simulated standing and walking, respectively. Trypsin degradation was confirmed by direct cartilage assessments. Streaming potentials, measured by directly contacting cartilage, indicated lower cartilage stiffness ( P < 10−5). Unconfined compression data revealed reduced Em, representing proteoglycan matrix stiffness ( P = 0.005), no change in Ef, representing collagen network stiffness ( P = 0.15), and no change in permeability ( P = 0.24). Trypsin depleted proteoglycan as observed by both dimethylmethylene blue assay ( P = 0.0005) and safranin-O stained histological sections. Conclusion These data show that non-invasive EAG detects streaming potentials produced by cartilage during joint compression and has potential to become a diagnostic tool capable of detecting early cartilage degeneration.

Mechanistic 3D finite-difference simulation of borehole spontaneous potential measurements

The quantitative interpretation of borehole spontaneous potential (SP) measurements via Nernst’s equation often relies on limiting assumptions such as shallow mud-filtrate invasion, negligible streaming potentials, and uniform borehole symmetry. To overcome these limitations while honoring the governing physics of coupled mass transport associated with SP phenomena, we have developed a 3D finite-difference algorithm to simulate borehole SP measurements acquired across water-bearing rocks that incorporates electrochemical, membrane, and electrokinetic SP. The algorithm is based on a mechanistic description of nonequilibrium thermodynamics that enables its coupling with a fluid flow simulator to quantify the effects of continuously varying properties within permeable formations due to mud-filtrate invasion. Numerical modeling of SP measurements acquired under complex petrophysical and geometric conditions enables uncertainty quantification in the estimation of formation-water resitivity, location of bed boundaries, or detection of permeable beds while accounting for shoulder-bed effects, borehole deviation, and borehole eccentricity. Our results indicate that for well trajectories with a relative dip of less than 30°, the assumption of perpendicular beds does not entail significant errors in SP-related calculations, thereby reducing CPU time by a factor of at least 1.76. In vertical wells, SP provides the best resolution possible because deviated wells or dipping beds result in more extended and pronounced shoulder-bed effects. Furthermore, electrokinetic effects can be neglected for commonly used pressure overbalance ranges. In cases in which electrokinetic contributions are not negligible, we conclude that they are more significant when the rock permeability is in the two-figure millidarcy range. Finally, the simulation algorithm enables hypothesis testing to determine the origin and conditions under which SP shale-baseline shifts may occur. The latter shifts can signal vertical variations in salt concentration, which are crucial in the estimation of water saturation and detection of aquifer compartments.

Open-source hydrogeophysical modeling and inversion with pyGIMLi 1.1: Recent advances and examples in research and education

&lt;p&gt;Hydrogeophysics is interdisciplinary by definition. As researchers strive to gain quantitative information on process-relevant subsurface parameters while integrating non-geophysical measurements, multi-physical geoscientific models are often developed that simulate the dynamic process and its geophysical response. Such endeavors are associated with considerable technical challenges due to coupling of different numerical models, which represents an initial hurdle for students and many practitioners. Even technically versatile users often end up with individually tailored solutions at the cost of scientific reproducibility.&lt;/p&gt;&lt;p&gt;We argue that the reproducibility of studies in computational hydrogeophysics, and therefore the advancement of the field itself, needs versatile open-source software. One example is pyGIMLi - a flexible and computationally efficient framework for modeling and inversion in geophysics. The library provides management for structured and unstructured 2D and 3D meshes, finite-element and finite-volume solvers, various geophysical forward operators, as well as a generalized Gauss-Newton based inversion framework.&lt;/p&gt;&lt;p&gt;In this contribution, we highlight some of the recent advances and use cases in research and education since its 1.0 release in 2017 (R&amp;#252;cker et al., 2017) including:&lt;/p&gt;&lt;ul&gt;&lt;li&gt;generalized modeling and inversion frameworks for conventional, joint, time-lapse and process-based inversion&lt;/li&gt; &lt;li&gt;geostatistical regularization operators for unstructured meshes (Jordi et al., 2018)&lt;/li&gt; &lt;li&gt;improved constraints in the presence of petrophysical parameter transformations demonstrated by an estimation of water, ice, and air in partially frozen systems (Wagner et al., 2019)&lt;/li&gt; &lt;li&gt;3D visualization leveraging upon PyVista (Sullivan and Kaszynski, 2019)&lt;/li&gt; &lt;li&gt;simulation of electrical streaming potentials&lt;/li&gt; &lt;li&gt;complex-valued forward modeling and inversion of induced polarization&lt;/li&gt; &lt;li&gt;forward modeling with anisotropic parameters&lt;/li&gt; &lt;li&gt;availability for Mac OS&lt;/li&gt; &lt;li&gt;improved API and documentation&lt;/li&gt; &lt;/ul&gt;&lt;p&gt;Since the library is freely available and platform-compatible, it is also well suited for teaching. We demonstrate examples from Master level university courses and public outreach, where learners can interactively change model and acquisition parameters to study their influence on a hydrogeophysical process simulation. Finally, we would like to use this opportunity to discuss future developments with the community.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Jordi, C., Doetsch, J., G&amp;#252;nther, T., Schmelzbach, C., &amp; Robertsson, J. O. (2018). Geostatistical regularization operators for geophysical inverse problems on irregular meshes. &lt;em&gt;Geophysical Journal International&lt;/em&gt;, 213(2), 1374&amp;#8211;1386. &lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;R&amp;#252;cker, C., G&amp;#252;nther, T., Wagner, F.M., 2017. pyGIMLi: An open-source library for modelling and inversion in geophysics, &lt;em&gt;Computers and Geosciences&lt;/em&gt;, 109, 106-123. &lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Sullivan, C., &amp; Kaszynski, A. (2019). PyVista: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit (VTK). &lt;em&gt;Journal of Open Source Software&lt;/em&gt;, 4(37), 1450. &lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Wagner, F. M., Mollaret, C., G&amp;#252;nther, T., Kemna, A., &amp; Hauck, C. (2019). Quantitative imaging of water, ice and air in permafrost systems through petrophysical joint inversion of seismic refraction and electrical resistivity data. &lt;em&gt;Geophysical Journal International&lt;/em&gt;, 219(3), 1866&amp;#8211;1875. &lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;/p&gt;