Physical and Chemical Stability of Nanoparticles in Ferrofluid Before and After Impregnation: Implications for Magnetic Pore Fabric Studies

Magnetic pore fabrics (MPFs) are a promising approach to explore the 3D pore space of rocks. There exist empirical relationships between the orientation, degree, and shape of MPF with pore space geometry and permeability anisotropy. Nevertheless, the precise nature of these relationships remains elusive. A common assumption in MPF studies is that ferrofluid uniformly fills the pore space, establishing a constant nanoparticle density and magnetic properties in space and time. However, this assumption is challenged by observations of particle sedimentation and time‐dependent magnetic properties, which render the quantitative interpretation of MPFs challenging. This study explores the physical and chemical stability of ferrofluid, mobility of particles after impregnation, and the magnetic properties of impregnated rocks over time. Water‐based ferrofluids are physically more stable than oil‐based ferrofluids, though with higher magnetic variability. In impregnated rock, magnetic nanoparticles display a certain degree of mobility, resulting in changes in MPF degree and shape. When ferrofluid is mixed with epoxy, particles are less mobile, though some changes were observed both during polymerization and aging. The susceptibility of ferrofluid‐epoxy mixtures is lower than for ferrofluid and carrier liquid at the same concentration. Interestingly, the susceptibility of impregnated rock increases over time, regardless of the ferrofluid used for the impregnation. Understanding and controlling these processes will enhance the reliability of MPF interpretations and increase the applicability of the method.

. For the first method, several cores or cubes are typically measured, and heterogeneities between samples can affect the estimate of anisotropy (Adams et al., 2013).With 2D-imaging and 3D-tomography methods, the main challenge lies in the trade-off between sampled volume and resolution.Additionally, physical or flow properties calculated from tomography data largely depend on resolution and processing method, and differ from the experimentally determined properties (Al-Raoush & Willson, 2005;Andrä et al., 2013aAndrä et al., , 2013b;;Dvorkin et al., 2011;Madonna et al., 2012;Peng et al., 2014;Saxena et al., 2017).While this difficulty can be partly overcome by combining local (high resolution on a small volume) and global (low resolution on a larger volume) analyses (Keller & Holzer, 2018;Keller et al., 2013;Louis et al., 2007;Pini & Madonna, 2016), the upscaling of the small volumes sampled using imaging methods to the sample or even formation scales remains a major challenge (example in Keller and Holzer (2018)).
A promising and efficient estimate of pore fabric and permeability anisotropy can be obtained by the magnetic pore fabrics (MPFs) method (Hrouda et al., 2000;Parés et al., 2016;Pfleiderer & Halls, 1990, 1994).After infiltrating the pore space with ferrofluid, measurements of the anisotropy of magnetic susceptibility reflect the average orientation and arrangement of connected pores (Biedermann, 2019;Hrouda et al., 2000;Jones et al., 2006).Ferrofluids are colloidal suspensions of superparamagnetic iron oxide nanoparticles (commonly magnetite with 10 nm nominal diameter) in water-or oil-based carrier liquid, kept in suspension by Brownian motion.Nanoparticles in water-based fluids have an anionic or cationic surfactant to stabilize the suspension by preventing electrostatic attraction and aggregation (ferrotec.com).Because ferrofluids have high magnetic susceptibility compared to rock, MPFs are controlled by the geometry of the ferrofluid-filled pore space.Empirical studies revealed correlations between principal axes orientation, anisotropy degree, and shape of MPFs and pore fabrics or permeability anisotropy (Hailwood et al., 1999;Jones et al., 2006;Nabawy et al., 2009;Pfleiderer & Halls, 1993, 1994).Apparent differences between published empirical relationships are largely explained by the different susceptibilities of the ferrofluids used, and by early studies neglecting distribution anisotropy (Biedermann, 2019(Biedermann, , 2020)).Ferrofluids that are commonly used in MPF studies include oil-based EMG901, EMG905 and EMG909 (from highest to lowest susceptibility), and water-based EMG705 (most common), EMG304, EMG507 and EMG509 (Almqvist et al., 2011;Benson et al., 2003;Biedermann & Parés, 2022;Biedermann et al., 2021;Hrouda et al., 2000;Humbert et al., 2012;Jones et al., 2006;Parés et al., 2016;Pfleiderer & Halls, 1990, 1993, 1994;Pfleiderer & Kissel, 1994;Pugnetti et al., 2022Pugnetti et al., , 2023;;Robion et al., 2014;Zhou et al., 2022).Initially, it was believed that oil-based ferrofluids were more effective in impregnating rock, which was likely a misinterpretation related to differences between the effective susceptibility under standard measurement conditions (1 kHz) and the initial susceptibility listed in the fluids' technical specifications (Biedermann et al., 2021;Robion et al., 2014).An additional complication became evident when a recent study reported that MPFs depend on the age of the sample since impregnation (Biedermann & Parés, 2022), challenging some fundamental assumptions underlying any application of MPFs.These include (a) Uniform filling of the entire connected pore space by the ferrofluid, (b) homogeneous distribution of magnetic nanoparticles within the ferrofluid, and as a result constant magnetic properties throughout the pore space, (c) constant statistical distribution of the magnetic particles over time, and (d) stability of the magnetic properties of the ferrofluid itself.
The aforementioned assumptions are related to the colloidal stability of the ferrofluids, which in turn comprises two aspects: (a) physical stability, meaning that the particles remain dispersed homogeneously in the suspension rather than aggregating (flocculating) and settling, and (b) chemical stability, meaning the absence of dissolution, decomposition or alteration of the particles within the carrier liquid.The chemical stability of iron and its oxides in aqueous solutions depends on pH and redox potential, and can be summarized in a Pourbaix diagram (Figure 1).Note that magnetite (Fe 3 O 4 ) is not stable under atmospheric conditions, which is why it oxidizes to maghemite (γ-Fe 2 O 3 ) and hematite (α-Fe 2 O 3 ) over geologic time (e.g., O'Reilly, 1984, p. 7).Similarly, physical stability depends on numerous factors, most importantly the pH: Fe 2 O 3 is positively charged in acidic aqueous

Testing Colloidal Stability
Because particle sedimentation within voids and pores may result in an MPF that does not reflect pore space geometry, the first experiment in this study tested how long ferrofluid particles remain in suspension before they aggregate and sediment.Additionally, we tested whether the addition of stabilizing chemicals (oleic acid for oil-based fluids, and LiOH and polyvinylpyrrolidone (PVP) for water-based fluids) would increase colloidal stability.During synthesis, PVP controls the particle size and mineral phase, and thus the magnetic properties of iron oxide nanoparticles (Cooper et al., 2018;Silva et al., 2017).In this study, PVP was added after the particle formation and should only affect agglomeration.LiOH increases pH, and thus improves the thermodynamic stability of iron oxides as opposed to ferric and ferrous iron in aqueous solutions that are thermodynamically stable at low pH (Beverskog & Puigdomenech, 1996;Perry et al., 2019;Pourbaix & de Zoubov, 1974).However, note that some surfactants may desorb at high pH, which then favors particle aggregation (Park et al., 2012).LiOH was chosen here for its small cation size, which also influences the double layer and aids the colloidal stability (Quinson et al., 2019).
Oil-based ferrofluids EMG901 and EMG909 diluted at 1:50 with light hydrocarbon carrier oil were mixed with oleic acid in different proportions, 1:2, 1:5, 1:10 and 1:50.Water-based fluids EMG705 and EMG304 at dilutions of ferrofluid to deionized water of 1:10, 1:25 and 1:50 were tested under four conditions: (a) pure, (b) with added 5 mM PVP, (c) with added LiOH at a pH of 12, and (d) with both 5 mM PVP and LiOH (Table 1).Standard 5 ml glass vials with 2 and 5 ml for oil-and water-based ferrofluids, respectively, were prepared at the Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern.The smaller volume of the oil-based ferrofluid samples is related to the amount of fluid available from the same batch.The vials were closed and wrapped with parafilm to prevent fluid evaporation.All samples were then stored at 20-25°C over ∼8.5 months, with pictures being taken at increasing time intervals, to monitor the stability of each mixture, for example, by  changes in color, or particle sedimentation.Sample preparation and storage under ambient laboratory conditions reflect current practices of MPF studies.

Testing Stability of Particle Distribution Over Time
Magnetic nanoparticles in mm-sized voids aggregate and sediment over time, and the carrier liquid of both oil-and water-based ferrofluids evaporates (e.g., Biedermann et al., 2021).Conversely, the magnetic fabric of impregnated red silty sandstone has been found to be stable over time in terms of fabric orientation, anisotropy degree and shape, potentially because the relatively small pores of this rock hinder particle motion (Biedermann & Parés, 2022).To immobilize particles in larger pores, and to ensure homogeneous ferrofluid properties throughout the pore space, Pugnetti et al. (2023) proposed the impregnation of rocks with ferrofluid-epoxy mixtures for MPF measurements, inspired by Thorpe et al. (2011)'s approach to stabilize nanoparticles with epoxy resin mixtures.Here, the stability of particle distributions was tested for epoxy-ferrofluid mixtures.Only oil-based ferrofluid mixtures were used because water is immiscible with epoxy.

Ferrofluid-Epoxy Samples
Epoxy-ferrofluid mixtures were prepared from Epo-Tek301 (Epoxy Technology, Inc.) mixed with EMG901 or EMG909 ferrofluid.The epoxy has a pot life time of 1-2 hr.Initial magnetic measurements were performed at least 24 hr after sample preparation, that is, on the fully polymerized epoxy, and repeated over time.For the first set of experiments, ferrofluid-epoxy mixtures at concentrations 1:10, 1:25, and 1:50 were filled into voids of 1 mm diameter and 2 mm height, drilled into transparent polycarbonate cubes (Table 2; CV2 samples, where the sample name indicates the shape CV = circular void, 2 reflecting the ratio of z to x dimensions, followed by the fluid type and concentration, and a lower-case letter to distinguish samples with the same geometry and ferrofluid).The cubes were then stored with their z-axis (cylinder axis) vertical.Due to the uniaxial sample symmetry, susceptibility measurements were made only along the sample x, y and z axes, where z is along the cylinder axis, and x and y are chosen arbitrarily normal to the cylinder axis.For the second set of experiments, ferrofluid-epoxy mixtures at a concentration of 1:10 were poured into specifically prepared half-cylindrical or rectangular molds, and hardened (polymerized) for at least 24 hr (RR and CR samples, where RR = rectangular rod with x = y, CR = circular rod with x = y and ER = elliptical rod with x < y).Circular and elliptical rods were glued together from two half-cylindrical pieces each, because they could not be poured directly.To verify that the thin layer of diamagnetic glue in-between the two half-round pieces has a minimal effect on the measured directional susceptibilities, pre-tests were conducted using rectangular rods, for example, comparing the MPFs of a 1 mm × 1 mm rectangular rod with that of a rectangular rod glued together from two 0.5 mm × 1 mm pieces of the same length.As these results were comparable within measurement uncertainty, the CR and ER samples represent the MPF of true cylindrical and elliptical rods.All rods were cut to specific lengths and mounted on plastic holders to facilitate orientation.RR, CR and ER samples were stored with their y axes vertical.Expected directional susceptibilities and anisotropy parameters were calculated based on the sample shape and the ferrofluid's intrinsic susceptibility and concentration, using Sato and Ishii (1989)'s approximations for self-demagnetization factors in cylindrical, rectangular and elliptical rods.Then, directional magnetic susceptibilities were measured along the x, y, and z directions, subtracting the susceptibility of the holder.Magnetic susceptibilities were measured on an MFK1-FA Kappabridge (AGICO), at 200 A/m and frequencies of 976 (F1) and 15,616 Hz (F3).Repeat susceptibility measurements over 5-6 months were used to monitor changes in mean susceptibility (i.e., average of the three directional susceptibilities) and its frequency-dependence, as well as the orientation of the maximum and minimum susceptibility directions.Because nanoparticles in the size range of 10 nm are superparamagnetic, their susceptibility is expected to depend on frequency, and changes in frequency-dependence may reflect particle aggregation.Biedermann and Parés (2022) observed a decrease in frequency-dependence over time for water-based ferrofluids EMG705 and EMG304, but little change for oil-based ferrofluids.Here, the goal was to investigate whether oil-based ferrofluid mixed with epoxy behaves similarly to oil-based ferrofluid by itself.

Impregnated Rock Samples
Natural rock samples were the same Swiss molasse sandstones as those used to test multiple impregnation methods by Pugnetti et al. (2022).These sandstones were collected in Schüpfheim, LU, Switzerland, consist mainly of quartz and feldspar, and possess porosities of 20 ± 5%.Field observations showed both parallel and cross-bedding, and the samples investigated here were selected for their homogeneous parallel bedding (Pugnetti et al., 2022).Standard-sized cores of 25.4 mm diameter and 22 mm height were drilled with their cylinder axis (z-axis) normal to bedding, and x and y oriented arbitrarily in the bedding plane, as no lineation was macroscopically visible.One core each was impregnated with EMG901, EMG909, EMG705 and EMG304 and MPFs were measured on the MFK1-FA, using a 15-position measurement scheme (Jelinek, 1977), at 200 A/m and 976 Hz.Principal susceptibilities (k 1 ≥ k 2 ≥ k 3 ) were calculated from a best-fit ellipsoid to the directional measurements.Furthermore, MPFs were characterized by their mean susceptibility k mean = (k 1 + k 2 + k 3 )/3, the degree of anisotropy P = k 1 /k 3 , and the shape U = (2k 2k 1k 3 )/(k 1k 3 ) (Jelinek, 1981).All samples had been impregnated using the magnetic flowthrough method of Pugnetti et al. (2023), and initially had their maximum susceptibility k 1 parallel to the impregnation direction along the sample z-axis.This is likely related to an artifact of the impregnation method and reflects the path of the ferrofluid through the sample, rather than the pore fabric.Nevertheless, the simple MPF of those samples was an advantage for the present study, investigating whether the magnetite nanoparticles in the ferrofluid are mobile after impregnation.After the initial MPF measurement, each sample was placed next to a 1.3 T magnet, with the magnetic gradient along the sample x-axis.Repeat measurements of the MPF were performed over 8-9 months to identify any changes in fabric orientation, shape, and anisotropy degree.

Colloidal Stability
During the preparation of the ferrofluids and ferrofluid-epoxy mixtures, different behaviors were observed: For example, foam developed for all samples of EMG705, but none of the other ferrofluids.For EMG705, foam appeared independent of whether or not LiOH or PVP was present, and the foam formation was strongest at a pH of 12, and for the highest concentration of ferrofluid to carrier, 1:10.Pipetting an accurate amount was hardest for EMG901, drops of which tended to remain in the pipette tip, and could only be partially removed by repeatedly taking up and releasing small volumes of the EMG901-carrier liquid mixture.Additionally, all EMG901 samples left marks on the walls of the glass vials, while the glass appeared clean for the other three fluids.This may be explained by the higher viscosity of EMG901 compared to the other fluids, which is however not confirmed by the fluids' technical specifications.The viscosities of EMG901 and EMG304 are both reported as <10 mPa*s, while those for EMG909 and EMG705 are reported as <5 mPa*s.Other possible explanations include that another compound was present in EMG901, which upon contact with oleic acid reduces the ferrofluid dispersibility, or that the higher concentration of magnetic nanoparticles in EMG901 compared to EMG909 leads to stronger magnetostatic interactions and faster flocculation.Finally, particles may dissolve due to the oleic acid, which could be faster in EMG909 compared to EMG901 because of its lower particle: liquid ratio.While EMG901_1_50_OlS showing the lowest amount of deposited material on the walls may suggest a dependence on concentration, the other three EMG901 samples show a similar amount of deposited material, so that no clear conclusion about oleic acid influencing dispersibility or dissolving particles can be drawn.Once sedimented, the thickness of the particle layer remains constant, suggesting that the particles have at least some stability.At the same time, dispersed particles are surround by a larger amount of fluid and oleic acid than those in the sedimented layer, so that some degree of initial dissolution cannot be excluded.
Further differences between samples were observed over time (Figure 2, Figure S1 in Supporting Information S1, Table S1 online supplementary).Most of the oil-based ferrofluids displayed a segregation into two layers, where the lighter color and higher transparency likely indicated a depletion of magnetite nanoparticles in the top, and the darker and more opaque appearance of the bottom layer a concentration of particles.Subsequently, the top layer increased in thickness, and became more transparent and lighter.Note that the thickness of the top layer shows no correlation with the oleic acid concentration.These segregated layers further developed into a clear layer of sedimented particles underneath a light brown transparent fluid, where the fluid became more transparent as the experiment progressed.Note that the thicker particle layer for EMG901_1_2_OlS compared to EMG909_1_2_ OlS is related to the higher concentration of magnetite nanoparticles in the EMG901 series.Similarly, the thicker particle layer of EMG901_1_2_OlS and EMG909_1_2_OlS compared to EMG901_1_50_OlS and EMG909_1_50_OlS, respectively, relates to the lower particle concentrations in the samples with higher amounts of oleic acid.The two exceptions to this general behavior for the oil-based ferrofluids are EMG909_1_10_OlS and EMG909_1_50_OlS, where sedimented particles appeared with the prior phase separation.43 days after the experiment started, all EMG901 and EMG909 samples had largely sedimented.For EMG901, the sedimentation process was slowest for EMG901_1_10_OlS, and for EMG909, the slowest sedimentation occurred for EMG909_1_5_OlS.
While the oil-based ferrofluids had largely sedimented, no visible changes were observed in the water-based ferrofluids (cf., Figure 2; Table S1), other than the foam disappearing for all EMG705 samples except those diluted at 1:10 and pH = 12.Thus, the particle settling in water-based ferrofluids was significantly slower compared to oil-based fluids.No changes were observed for EMG304, or EMG705 diluted with water or water and PVP.For EMG705 at pH 12, the development of color gradients indicated deterioration of colloidal stability.These color gradients became stronger over time, until a layer of sedimented particles appeared.Note that none of the water-based ferrofluids displayed the phase separation typical for the oil-based ferrofluids.

Particle Motion in Ferrofluid-Epoxy Samples
For the cube samples with cylindrical voids filled with epoxy-ferrofluid mixture (CV2), a prolate anisotropy was expected based on self-demagnetization (i.e., shape of the void; cf., Table 2), with the maximum susceptibility along the cylinder axis, and anisotropy degree depending on the type and concentration of ferrofluid.Conversely, voids filled with EMG901 show highly oblate fabrics, and lower-than-expected anisotropy degrees (Figure 3, Table S2).Voids filled with EMG909 possess a range of anisotropy shapes, from oblate to prolate, and anisotropy degrees that vary around those expected.There is variability with time, but no clear time-dependence that is observed in all samples.The data suggest that the ferrofluid-epoxy mixtures were heterogeneous from the beginning, or that the magnetic nanoparticles had settled between the sample preparation and the first measurement.The epoxy-ferrofluid mixture does appear darker at the bottom.Most samples showed an increase in mean susceptibility at the beginning of the experiment, followed by a decrease.
The epoxy rods show a similar behavior for all samples in that the mean susceptibility decreases over time (cf., Figure 3).For the epoxy rods made from EMG909, the data group around two main trends, where the two groups correspond to two sets of samples made from the same ferrofluid at a different time.Hence, it is not only the age of the sample itself, but also the age of the ferrofluid at the start of the experiment that controls the susceptibility.The anisotropy degree and shape vary slightly at the first 1-2 weeks of the experiment.This variation is small compared to the variability between samples.The anisotropy degree of the EMG901 rods of dimensions 2 × 2 × 10 mm varies around that expected, though the measured shapes are less prolate than expected.This suggests an inhomogeneous particle distribution within the rods.As k x /k y increases slightly at the start of the experiment, this could be explained by gravitational settling of the magnetic nanoparticles or aging and shrinking of the epoxy resin, leading to a larger extension of the strongly magnetic part of the rod along x (full width) than y (concentrated at the bottom, which would also explain the darker color).The data further suggest that the particle settling already started before the first measurement, and it cannot be excluded that most of this process occurred during solidification of the epoxy and continued at a slower rate afterward.For the EMG909 rods, the measured anisotropy is larger than that expected, and surprisingly, k x /k y increases over time.This cannot be explained by the shape of the volume with the highest particle concentration.One possible explanation could be related to the lower particle concentration of EMG909 compared to EMG901, so that between-particle distances within a given horizontal plane remain constant throughout the experiment, while vertical distances decrease due to particle settling, allowing magnetic interactions along the y-axis before the onset of interactions along x.In general, between-sample variability is larger than time-variation also for the EMG909 samples.
Hysteresis and remanence data show some variability between samples, and a decrease in M s and initial susceptibility as the sample age (Figure 4).There is no clear relationship between sample age and H cr .Note that given the very weak remanences of <40 nA/m, some variability is expected from the VSM's sensitivity to sample positioning (Kelso et al., 2002).

MPFs in Impregnated Rock Samples
The mean susceptibility of impregnated samples increases over time (Figure 5, Table S3), an observation that confirms results by Biedermann and Parés (2022), who reported a 2.5-3-fold increase in the mean susceptibility of red silty sandstone samples impregnated with EMG905 over 4 years.Interestingly, for samples impregnated with EMG909, EMG705 and EMG304, the mean susceptibility reached a plateau after an initial increase that lasted about a week.Five weeks after impregnation, the mean susceptibility started a second increase, which became slower over time.For both water-based ferrofluid a second plateau was reached ∼5 months after impregnation.Conversely, the susceptibility of EMG909 was still increasing ∼8 months after impregnation.The sample impregnated with EMG901 showed a different behavior in that the first plateau between 1 and 4 weeks was absent, though also these samples experienced a slower susceptibility increase during a similar time period.After 8-9 months, the experiment was discontinued, and at that time, the mean susceptibility of the samples impregnated with water-based ferrofluids had increased by 15% compared to k mean right after impregnation.For samples impregnated with oil-based ferrofluids, k mean had increased by 20%-25%.
Normalized principal susceptibilities show a decrease in k 1 (parallel to z), and an increase in the susceptibility along x.This is expected from the geometry of the experiment setup, that is, the magnetic gradient acting along x.Despite this, k 1 remained parallel to z throughout the experiment.The directional susceptibility changes are   associated with a P-value that decreases over time, and a U value that becomes less prolate.The one exception is the sample impregnated with EMG705; it is the only sample where k 3 right after impregnation was parallel to x instead of y, and the resulting switch of k 2 and k 3 as the susceptibility along x increased led to a more complex variation of U over time.Changes in the anisotropy shape U are most prominent during the first 2 weeks after impregnation, while the variation of P as a function of time starts to slow down after ∼2 months.

Discussion
A homogeneous spatial distribution of magnetic nanoparticles in ferrofluids during and after impregnation, and constant magnetic properties are essential prerequisites for MPF studies.This involves the physical, chemical and magnetic stability of each particle, and the absence of particle mobility.Particle stability and mobility, as well as interaction of ferrofluid with rock will be discussed here.

Physical, Chemical, and Magnetic Stability of Ferrofluids
A comparison between the data presented here and that published in Biedermann and Parés (2022) shows that the colloidal and magnetic stability of ferrofluids do not necessarily correlate with each other.In particular, the oil-based ferrofluids that showed low colloidal stability both here and in an earlier study investigating MPFs in synthetic samples (Biedermann et al., 2021), displayed the lowest variation in susceptibility and hysteresis properties over time (Biedermann & Parés, 2022).Because the thickness of the layer of sedimented particles remained constant for several months after sedimentation, we interpret that the nanoparticles are not dissolved, though dissolution of a small portion of particles prior to sedimentation, oxidation or alteration to hydroxides at the surface cannot be excluded.The deterioration of colloidal stability is interpreted here as a result of decreasing physical stability, that is, particle flocculation.Because particle sedimentation affects MPF orientation, shape and degree, it is the lower physical stability, rather than the magnetic stability that is relevant for MPF studies.
The difference between oil-and water-based ferrofluids could be explained by the fact that the particles in both water-based ferrofluids were manufactured with an anionic surfactant to increase colloidal stability, which is absent in the oil-based ferrofluids.Changes to or deterioration of the surfactant likely results in changes to the spin structure at the nanoparticle surface, affecting magnetic properties.Similarly, the formation of hydroxide species at the particle surface likely affects the magnetic properties.Thus, initial variations in magnetic properties in water-based ferrofluids are associated with changes in the surfactant, while (part of) the surfactant still hinders particle aggregation and sedimentation.Hence, the physical stability of these ferrofluids is larger than their magnetic stability, because of the surfactant.Conversely, for oil-based ferrofluids, which are not affected by changes due to the dissolving surfactant, the magnetic properties remain stable even when the particles aggregate.
The water-based ferrofluids diluted with deionized water or deionized water and PVP remained physically stable over the entire duration of the experiment, much longer than the 3-month period stated by the manufacturer.However, this long physical stability is accompanied by large changes in magnetic susceptibility and hysteresis properties, particularly for EMG304, already within the 3-month period (Biedermann & Parés, 2022).If the variation of magnetic properties over time can be controlled and corrected for, water-based ferrofluids may thus be preferable to oil-based ferrofluids in MPF studies.An additional complexity when studying impregnated rock samples is the potential interaction of the ferrofluid with certain minerals, which may lead to different time-variation of both colloidal stability and magnetic properties compared to the pure ferrofluid.Increasing pH led to the deterioration of colloidal stability for EMG705, but not EMG304.Hence, the attempt to stabilize the ferrofluid was not successful.Interestingly, the time until the onset of the particle sedimentation did not correlate or predict the time until complete particle settling.Even though sedimentation started later in EMG705 at pH 12 and with PVP, the process was then faster than without PVP.
While increasing the pH to 12 was not successful at improving ferrofluid stability, it is interesting to note that EMG705, which has a higher pH initially compared to EMG304, displays higher stability of magnetic properties over time.It is not clear whether this may be related to different surfactants or directly associated with pH.In any case, the potential pH-sensitivity of ferrofluid may lead to different impregnation results depending on the properties of the pore water.Both silicates and carbonates may lead to alkaline pore water (Al Mahrouqi et al., 2017;Lacroix et al., 2014).

Motion of Particles Over Time
The changes in P and U after impregnation indicate that at least part of the magnetic nanoparticles remain mobile in the pore space of the rock.The small changes in MPF degree and shape observed in the epoxy-ferrofluid samples suggest that not all particle motions are prevented by the epoxy.Similar to particle mobility in rocks, this may be associated with pores in the polymerized epoxy.Magnetic particles or aggregates are expected to be less mobile with a higher ratio of particle or aggregate size to pore size.Therefore, larger aggregation or smaller pores hinder particle mobility.Larger pores and pore throats are beneficial for the impregnation process, but the enhanced particle mobility after impregnation may lead to MPFs that are not representative for pore space geometry.
The magnetic properties of ferrofluid mixed with epoxy differ from those of ferrofluid in the carrier liquid at the same dilution: saturation magnetization and susceptibility are lower, while coercivity is comparable to older ferrofluid samples.This supports the interpretation that epoxy hinders motion of the particles to some extent, that is, the high magnetic responsiveness of the nanoparticles in the fluid is a composition of particle rotation and Néel relaxation, resulting in high susceptibility and very low coercivity, whereas the magnetic response in the epoxy-ferrofluid mixtures is mainly due to Néel relaxation (Figure 6).Similarly, the evaporation of the carrier liquid would decrease magnetic responsiveness.

Susceptibility Increase in Rock Versus Decrease in Epoxy
The most prominent change in the magnetic properties of impregnated rocks is the increase in susceptibility, which occurred independently of the type of ferrofluid.The observed susceptibility increase confirms results by Biedermann and Parés (2022), who measured Triassic red silty sandstones impregnated with EMG909 and found a 2.5-3-fold increase in mean susceptibility over 4 years.Several studies have found empirical correlations between the presence of oil and enhanced susceptibility (Abubakar et al., 2020;Badejo et al., 2021;Gadirov et al., 2018;Rijal et al., 2012), andAbubakar et al. (2020) proposed the reduction of hematite, or the aggregation of particles as possible causes.Initially, aggregation of nanoparticles is likely to increase susceptibility due to collective behavior; however, as the aggregates increase in size, a decrease is expected as they start behaving as a bulk material (Dearing et al., 1996;Eyre, 1997;Hrouda, 2011;Stephenson, 1971;Worm, 1998).Transitions between iron oxides are slow at room temperature unless facilitated by microbial processes (Emmerton et al., 2013;Gendler et al., 2005;Machel, 1995).Moreover, a susceptibility increase was observed here independent of whether oil-or water-based ferrofluid was used to impregnate samples.This indicates that the susceptibility increase over time may be related to the magnetic nanoparticles rather than the carrier liquid.Possibly, the magnetite particles had a (partially) oxidized shell initially, causing lattice strain and therefore suppressing susceptibility (van Velzen & Zijderveld, 1995).The reduction of the oxidized shell over time would release the lattice strain, resulting in a susceptibility increase.This cannot, however, explain the decrease in susceptibility for the epoxy-ferrofluid mixtures.Potential reasons for susceptibility decreases are (a) oxidation of the magnetite nanoparticles, (b) particle aggregation leading to SD instead of SP behavior, and (c) aging of the epoxy resin, adding more and more constraints on the particle motion.More work will be needed to investigate the underlying processes in detail, and investigate if the presence of certain minerals, or a combination of a specific ferrofluid with certain minerals enhance or hinder the susceptibility increase.Note that an alternative explanation for the change in P and U of the MPFs of impregnated rocks, in addition to the particle motion, could be associated with new minerals developing in the applied field and thus mimicking the field direction.

Implications for Impregnation Experiments and MPF Interpretation
The results presented here have implications for MPF studies in several ways: (a) the physical stability of ferrofluid, and particle aggregation may hinder the impregnation process in that larger particles are more likely to be filtered, clog the pore throats, and then prevent further impregnation; (b) the difference between physical and magnetic stability poses a challenge to determining whether or not a given fluid is suitable for impregnation; (c) epoxy may stabilize the magnetic particles physically, however, this is also associated with changes in magnetic properties, making the quantitative interpretation of MPFs more difficult; (d) we cannot support earlier statements that oil-based ferrofluid are more suitable than water-based ferrofluids (Robion et al., 2014), because of their lower physical stability; and (e) care needs to be taken when calculating impregnation efficiency, considering changes in mean susceptibility of impregnated samples and ferrofluid itself over time.

Conclusions
This study aimed to examine the physical and chemical stability of magnetic nanoparticles in ferrofluid, and thereby questioning the basic assumption in MPF studies that ferrofluid in an impregnated rock is characterized by constant properties throughout the pore space and over time.The physical stability of oil-based ferrofluids deteriorates relatively quickly while water-based ferrofluids exhibit a more pronounced variation of magnetic properties over time.Both physical and magnetic stability are crucial factors for MPFs.Physical stability, or the absence thereof with particle aggregation and settling influences the impregnation process as well as the distribution of magnetic nanoparticles in the pores.Changes in magnetic properties affect the determination of the impregnation efficiency and the MPF-degree versus pore space anisotropy relationship.Hence, researchers applying the MPF method need to be careful and control the ferrofluid properties at the time of measurement, and potential particle mobility by, for example, storing samples in different orientations between impregnation and measurement.Alternatively, if MPF measurements are conducted shortly after impregnation, the time-dependence is minimal.By accounting for these precautions, MPFs can unfold their full potential and provide reliable and time-efficient information on pore space geometry.

Figure 1 .
Figure 1.The thermodynamically most stable species in equilibrium for iron, as a function of pH and redox potential (Pourbaix diagram), modified after Perry et al. (2019).The pH conditions for EMG304 and EMG705 were taken from the fluids' technical specifications.

Figure 2 .
Figure 2. Schematic sketch of processes in oil-and water-based ferrofluid samples over time.

Figure 4 .
Figure 4. Hysteresis loops, initial susceptibility and remanence curves for representative epoxy ferrofluid samples, compared with the ferrofluid samples measured by Biedermann and Parés (2022).

Figure 5 .
Figure 5. Changes in mean susceptibility and magnetic pore fabrics over time.

Figure 6 .
Figure 6.Schematic sketch of processes contributing to the magnetic response of magnetic nanoparticles in ferrofluid and ferrofluid-epoxy mixtures.

Table 1
Sample List and Preparation for Testing the Stability of Ferrofluid and Added Chemicals

Table 2
Overview of Epoxy-Ferrofluid Samples and Their Expected Magnetic Properties