Orientation of Magnetic Pore Fabrics
The maximum principal MPF susceptibility (K1,imp) in wood is consistently parallel to the visible orientation of the wood fibres. This confirms observations by Merk et al. (2014), and is independent of wood type, porosity and impregnation method. In particular, the directional impregnation enforced by the flowthrough vacuum method did not create a MPF orientation different from non-directional impregnation methods, e.g., standard vacuum. This suggests that the measured MPF is a true representation of the pore fabric, and the pore fabric did not change during impregnation. In the molasse sandstone samples, the MPF is coaxial to the AMS, indicating that the pore fabric reflects the mineral fabric. The MPF orientation appears independent of impregnation method, making us confident that it images pore fabric, and not impregnation-related artefacts. Because the direction of impregnation does not affect the MPF orientation results, samples can be oriented arbitrarily during the impregnation process, so that no a priori information on the sample and its pore fabric is needed.
Improving Impregnation Methods and Determination of Impregnation Efficiency
The rock samples investigated here show a large variability of impregnation efficiency, with standard vacuum impregnation reaching the highest efficiency with I.E.susc = 76%. Percolation with water-based fluid lead to I.E.susc = 23% and 53% with oil-based fluid. Flowthrough vacuum impregnation resulted in an intermediate impregnation efficiency of 31%, but lead to the most homogeneous ferrofluid distribution. The same rock samples show larger I.E.susc for samples impregnated with oil-based fluid compared to water-based fluid. This supports previous interpretations that oil-based fluid is more suitable to impregnate rock samples Robion et al. (2014), though further investigations are needed to confirm this is the case for all rocks. Because oil is made of larger molecules and has higher viscosity compared to water, it would be expected that water can access smaller pores. Additional forcing may increase impregnation efficiencies; e.g., Locs et al. (2008) impregnated pine wood under pressure (30, 60 and 125 MPa) and report impregnation efficiencies of 96%, and even > 100% since the pressure enlarges and impregnates small fibres that were not previously detected as pores. However, high pressure injection may be unsuitable to study pore fabrics, as it can destroy the pore structure and generate cracks, preventing the characterization of the real pore structure of the sample. Esteban et al. (2006) impregnated rocks at different pressure and reported a change in MPF orientation; however, they did not determine impregnation efficiency, and it is not clear if the changes in MPF are related to different fabrics of different pore sizes or pressure-induced changes. Additional forcing of the ferrofluid migration that has little effect on the pore space itself, is magnetic forcing (Borglin et al. 2000). Comparing the migration of ferrofluid through the sample between percolation and diffusion assisted by magnetic forcing and without additional forcing suggests that future MPF studies will benefit from combining gravitational or pressure forces with magnetic gradients to increase impregnation efficiency, and control the fluid migration path.
Mass- and susceptibility-based estimates of impregnation efficiency differ, because it is the carrier liquid of the colloid that mainly contributes to mass changes, while the magnetic nanoparticles themselves define the susceptibility increase. Thus, I.E.susc is most suitable to describe how many nanoparticles entered the pore space. The impregnation efficiencies reported here are at the lower end or below the threshold of I.E.mass reported elsewhere, while our I.E.susc is similar to or larger than reported elsewhere (Almqvist et al. 2011; Nabawy et al. 2009; Parés et al. 2016; Robion et al. 2014). While previous studies systematically reported I.E.mass > > I.E.susc, our results show smaller deviations (cf. Fig. 6c). This is because rather than estimating the expected susceptibility from the nominal fluid susceptibility, this study takes the frequency-dependence of ferrofluid susceptibility into account. For some samples, especially wood impregnated by percolation methods I.E.mass is still larger than I.E.susc, and this indicates that some filtering occurred, i.e., the carrier fluid entered smaller pores, but the nanoparticles did not.
None of the experiments proposed here achieved impregnation efficiencies close to 100%. Possible explanations include that (1) the porosity determined by helium pycnometry overestimates the porosity accessible by any fluid, i.e., water, oil and ferrofluid; and (2) the ferrofluid suffers from particle aggregation, further decreasing the accessible pore volume. Particle aggregation and sedimentation has been described in particular for oil-based ferrofluid (Biedermann et al. 2021). Unlike for nanoparticles in water-based ferrofluids, no surfactants are applied to particles in oil-based ferrofluids (ferrofluid.ferrotec.com), and this may explain why they are more prone to particle aggregation and sedimentation. In addition to hindering impregnation, particle sedimentation in larger pores may affect MPF orientation, degree and shape, and needs to be investigated further. Particle filtering appeared stronger in wood samples compared to rocks, evident by differences in I.E.mass vs I.E.susc, and may have an additional dependence on mineralogy.
Time Evolution of the Impregnation Process
Impregnation is a process that proceeds over time, and in particular the diffusion cell experiments have shown that long durations are needed to impregnate samples by water-ferrofluid diffusion. The experiments were running for up to six months (4300 h for BE1) before the samples became unstable and experiments had to be discontinued. Even longer times would have been necessary to reach equilibrium, despite the relatively large porosity of 19% for BE1. Mazurek and Rufer (2018) reported an equilibration time for pore-water diffusion of ~ 3000 h. The slower process for ferrofluid is related to the larger particle size, and may be decelerated further by particle aggregation. Because particle aggregation worsens over time, and due to the increased risk of sample deterioration, we do not recommend long-term diffusion or immersion impregnation for MPF studies. One way to accelerate diffusion is by adding magnetic forcing. The magnetic diffusion in the agarose gels was significantly faster than the non-forced diffusion, and resulted in a more homogeneous impregnation throughout the sample.
While large efforts have been made to study empirical correlations between MPFs and pore shapes or other anisotropic properties, or to improve our understanding of how MPFs arise (Benson et al. 2003; Biedermann, 2019, 2020; Biedermann et al. 2021; Hailwood et al. 1999; Hrouda et al. 2000; Jezek and Hrouda 2007; Jones et al. 2006; Louis et al. 2005; Pfleiderer and Halls, 1993, 1994; Robion et al. 2014), relatively little is known about the ferrofluid impregnation process itself. Valuable insights on this process and its evolution over time were obtained here from impregnating transparent TEOS and agarose gel samples. The TEOS experiments illustrate how cracks developed with time control the speed of the ferrofluid impregnation process; the ferrofluid quickly fills the cracks, and then diffuses more slowly into the surrounding pore space. The agarose experiments allow investigation of an additional effect, the influence of the fluid already present in the pores on the time evolution and shape of the impregnation front. Similar experiments could help understand further factors influencing the impregnation process in future studies.
Sample and Fluid Properties Affecting Impregnation Efficiency
An advantage of the MPF method that has been put forward is its potential ability to capture pores with throats down to 10 – 20 nm (Almqvist et al. 2011; Esteban et al. 2006; Humbert et al. 2012; Parés et al. 2016; Robion et al. 2014). At the same time, the centre of the samples is not always impregnated (Almqvist et al. 2011; Robion et al. 2014), and Robion et al. (2014) state that ‘depending on the pore throat geometry this [10 nm] threshold is probably much higher’. A higher threshold of impregnatable pore throat size is also confirmed by the spatial variation in impregnation efficiency observed here (cf. Figure 7b), differences between I.E.mass and I.E.susc that indicate that the carrier liquid was more successful entering the pore space than the nanoparticles (cf. Figure 6), and the observation of particle aggregation, e.g. in the diffusion cell (cf. Figure 10). In our attempt to better define porosity and size thresholds above which impregnation is likely successful, we have identified additional factors that control impregnation.
Sample properties that may influence the impregnation efficiency include porosity, pore throat size, pore shape, tortuosity and connectivity, wettability (i.e., mineralogy), and pore fluids already present in the samples. Ferrofluid properties that likely affect impregnation outcomes are viscosity, particle size, and whether the particles have a neutral or electrically charged surface. Oil-based fluids have been considered more efficient at impregnating rocks compared to water-based fluid (Robion et al. 2014). Our results show that water-based fluid is more successful in some samples, e.g. wood and agarose gel, while oil-based fluid leads to more efficient impregnation in others, e.g. molasse sandstone, thus highlighting the influence of sample properties. Particle aggregation and filtering is observed mainly for oil-based ferrofluid impregnating wood, as shown by lower I.E.susc compared to I.E.mass. This confirms findings by Biedermann et al. (2021), who reported particle aggregation and sedimentation of oil-based ferrofluid inside voids of synthetic samples. Related differences between the nominal 10 nm nanoparticle size and the effective hydrological diameter of clustered particles limits ferrofluid impregnation to larger pores than previously reported.
A systematic investigation of all mentioned parameters and their effect on impregnation results is difficult, given the limited ranges in properties of available samples, or co-variation of several properties. Nevertheless, the collection of samples investigated here allows to identify some patterns. No clear correlation was observed between impregnation efficiency and porosity, indicating that porosity is not the controlling factor (Fig. 12a). There is no clear evidence that samples with higher porosity show a more homogenous impregnation efficiency, or a higher impregnation depth. Wood and rock samples with similar porosities (WC and Swiss Molasse, ~ 20% porosity) display different impregnation efficiencies, with rock being more easily and homogeneously impregnated, probably due to their larger pore sizes (10–20 μm for molasse compared to 10—1000 nm for wood). Note that the minimum pore size identified depends on the resolution of the method used, and the 10 μm for molasse is overestimated. The correlation between I.E.susc and pore size (Fig. 12b) suggests that size largely controls the impregnation process, with larger pores being impregnated more easily. This is especially evident for samples WC whose pore size is similar to the nanoparticle size, resulting in very low impregnation efficiency. In addition to the control of pore size, we expect lower impregnation efficiencies when long and narrow pore throats are clogged by particles or particle aggregates.
Percolation experiments were performed with water- and oil-based ferrofluid using the same impregnation conditions. These show that the oil-based fluid is more successful impregnating the rock, while for wood, both ferrofluid reach similar impregnation efficiencies in WA, and water-based ferrofluid results in higher impregnation efficiency in WB and WC. This suggests that the material the sample is made of also plays an important role. Wettability describes the ‘preference of a solid to be in contact with one fluid rather than another (Abdallah et al. 2007). The relevance of wettability for MPF studies is two-fold: wettability influences the impregnation process, and it also influences the distribution of ferrofluid inside the pore space when another pore fluid is present. Minerals have different wettability, and quartz and mica have been described as water-wet (Abdallah et al. 2007; Liu and Buckley 1999), while carbonates are reported as water-wet (Abdallah et al. 2007) or oil-wet (Almqvist et al. 2011; Zhang et al. 2006), but wettability also depends on other factors such as pH. Wood is acidic and therefore interacts mainly with basic liquids (Mantanis and Young 1997). The water-based fluid EMG705 has a pH of 8–9, while that of the oil-based fluid EMG909 is not specified (ferrotec.com). While wettability certainly plays a role in impregnation, it cannot explain the observed difference between impregnation results for wood vs rock with water- and oil-based ferrofluid. Another factor is the interaction of the magnetic nanoparticles with the mineral surface by electrostatic forces: silicate surfaces are negatively charged at pH > 2 (Abdallah et al. 2007), and this may hinder impregnation of water-based ferrofluid, where the nanoparticles have an anionic coating to prevent aggregation (ferrotec.com). Conversely, carbonates may be positively charged at pH < 9.5 (Abdallah et al. 2007), which may facilitate the impregnation of water-based ferrofluid with anionic surfactants. Surfactants in general may influence the ferrofluid wetting properties, as they change the surface tension (Latikka et al. 2018). More work will be necessary to investigate these effects in detail, especially concerning the limitations they put on impregnation for specific sample mineralogy.
Water-based ferrofluid is able to migrate through the water-saturated pores of agarose while this is not possible for oil-based ferrofluid, because the latter is not miscible with water. Therefore, in addition to pore size and wettability, the pore fluid already present affects impregnation. This is similar to reservoir rocks whose saturation with hydrocarbons or water affects transport and is important in hydrocarbon exploitation (Abdallah et al. 2007).
To summarize, wood samples are more easily impregnated with water-based ferrofluids while rock samples with oil-based ferrofluids, and pore size is a limiting factor for impregnation efficiency, more so than porosity itself. Sample wettability, the stability of the ferrofluid over time (chemical and physical properties; e.g., evaporation of carrier liquid affects viscosity) and its interaction with the sample (e.g. particle aggregation and filtering) may influence the ability of the fluid to migrate through the sample.
Influence of Cracks
Cracks affect the mechanical and physical properties of rocks, and may mask any MPF anisotropy due to the pore fabric itself (Humbert et al. 2012). Given the large volume and aspect ratio of cracks compared to pores, it is likely that they outweigh any pore fabric anisotropy. The presence of cracks and fractures also affects the impregnation process itself, shown here by the impregnation of monolithic TEOS gel, where cracks developed after polymerization. These cracks can be viewed as analogies to natural rock samples, where permeability is often controlled by cracks or fractures (Sagar and Runchal 1982). Because the cracks are filled prior to the surrounding pores, their MPF contribution could be corrected for based on the time dependence of MPF results. When measuring the MPF right after impregnation started, and again after a longer time, the difference tensor may indicate the pore fabric. More work is needed to develop such a method and investigate if the different constrictions on nanoparticle motion in pores and cracks may be observed as frequency dependence. One approach for future work would be to measure the MPF of samples with and without cracks and to compare the results to each other. This work would benefit from controlling the crack orientation and geometry.
Recommendations for Future Work
The ferrofluids used in this study were comparable to other MPF experiments (Almqvist et al. 2011; Benson et al. 2003; Parés et al. 2016; Robion et al. 2014), and some of the results can therefore be related to previously published results. This work confirmed that the central part of the cylindrical samples is difficult to impregnate when using percolation or standard vacuum impregnation methods, resulting in large spatial variability of impregnation efficiency and associated artefacts in MPF orientation, degree and shape (cf Fig. 7). Conversely, vacuum flowthrough impregnation provides more uniform impregnation efficiencies. We have not observed any evidence for artificial fabrics introduced by this directional method, and therefore suggest that more work is done to investigate directionally forced impregnation methods. This could be complemented by testing impregnation along three perpendicular axes, to further evaluate potential preferred directions introduced by the forced impregnation.
Full impregnation of the entire pore space as defined by helium pycnometry is not achieved by any method, because the He atom is smaller than water or oil molecules, or magnetic nanoparticles. Impregnation efficiency is heterogeneous throughout the sample, so that bulk weight or susceptibility changes alone may not be sufficient to determine the impregnation efficiency. Susceptibility-derived impregnation efficiencies on sub-samples provide the most accurate estimate how much ferrofluid entered the pore space, and if there are variations with position in the sample. Care has to be taken when comparing measured susceptibilities of ferrofluid-impregnated samples with the susceptibilities reported in the fluids’ technical specifications, because ferrofluid susceptibility is frequency-dependent (Biedermann et al. 2021). Here, the fluid susceptibility at measurement conditions was determined by direct measurement, taking into account self-demagnetization. Weight changes have to be interpreted with caution, as the largest proportion of the weight is related to the carrier fluid, and not necessarily associated with magnetic nanoparticles in the sample. Differences between I.E.susc and I.E.mass may indicate particle aggregation, and impregnation behaviour as well as magnetic properties may change as particles agglomerate. The results in this study suggest that impregnation efficiencies < 10% mostly lead to insignificant MPFs. To avoid artefacts associated with filtered particles at the sample surface, we recommend to either compare the MPFs of sub-samples, or to cut off the surface that was in direct contact with the ferrofluid prior to MPF measurements.
Particle aggregation appears to worsen over time, so that long-term impregnation experiments such as diffusion are not suitable. Additionally, despite oil-based ferrofluids being preferred due to higher impregnation efficiency in rocks compared to water-based ferrofluids (Robion et al. 2014), they appear more prone to particle aggregation and associated filtering. Possible particle aggregation is particularly important in samples with pore sizes that can be accessed by 10 nm particles, but not by larger aggregates. Particle aggregation appears to be slower for water-based ferrofluid, which may be associated with their anionic coating, repelling particles from one another. At the same time, the anionic coating may cause electrostatic repulsion with negatively charged silicate surfaces, which may explain why some rocks are more easily impregnated by oil-based ferrofluids, despite their higher viscosity. Therefore, additional considerations will need to be made other than whether the pore throats allow a 10 nm particle to pass mechanically. These include wettability, electrostatic interactions, and potential chemical reactions between ferrofluid and sample. We have been able to partially impregnate samples with pores slightly above 100 nm in size, but not samples with 10 nm pore size, and therefore believe that 100 nm is a more realistic threshold for pores that can be invade by ferrofluid.
Because of the many factors influencing ferrofluid impregnation, no general recommendation that works for all samples can be made. Nevertheless, the results shown here indicate that a ferrofluid with properties similar to the fluid of interest is most suitable. For example, water-based ferrofluids are preferable for groundwater migration studies, while oil-based fluids are likely more suitable for hydrocarbon migration applications. In addition to impregnation properties that depend on pore size, wettability and potential interaction between a ferrofluid and the rock, practical aspects are also important. Water-based ferrofluid is more difficult to handle than oil-based ferrofluid in vacuum impregnation experiments, because the water boils off at room temperature, when the vacuum pressure is ~ 80 kPa or stronger. However, water-based ferrofluid can be used as long as the vacuum can be controlled, as was done here for the vacuum flowthrough impregnation.