Magnetite-latex nanoparticle motion during capillary uptake in thin, porous layers studied with UFI‐NMR

penetration with a temporal resolution of 15 ms and spatial resolution of 18 µ m. In the first part, it is shown that a calibration curve between the UFI-NMR signal intensity and the particle concentration exists. In the second part, UFI-NMR is used to study the penetration of a particles inside a thin nylon membrane during capillary uptake, which revealed liquid-particle front splitting and an inhomogeneous buildup of the particle concentration. Both the liquid-particle front splitting and inhomogeneous build up could be


G R A P H I C A L A B S T R A C T A R T I C L E I N F O
The transport of nanoparticles in porous media has received growing attention in the last decades due to environmental concerns in, for example, the printing industry, filtration, and transport of pollutants.Experimental studies on the imbibition of particle dispersions in porous media with sufficiently high spatial and temporal resolution are still challenging.This study shows how Ultra-Fast Imaging (UFI) NMR is an ideal tool for studying Fe 3 O 4 -latex particles penetration with a temporal resolution of 15 ms and spatial resolution of 18 µm.In the first part, it is shown that a calibration curve between the UFI-NMR signal intensity and the particle concentration exists.In the second part, UFI-NMR is used to study the penetration of a particles inside a thin nylon membrane during capillary uptake, which revealed liquid-particle front splitting and an inhomogeneous buildup of the particle concentration.Both the liquid-particle front splitting and inhomogeneous build up could be

Introduction
The transport of nanoparticles and colloids within porous media has received growing attention in the last decades in view of a wide variety of applications ranging from filtration processes (bacteria [1], viruses [2], colloids [3] and drinking water [4,5]), transport of pollutants in soil [6][7][8], transport of biomarkers in wearable electronics [9][10][11] and ink penetration [12][13][14].In most applications, particle transport is directly linked to performance or quality: for example the print quality in paper [15,16] or filtration efficiency of a filter [17,18].A better understanding of liquid and particle transport through porous media is of great importance for improving the performance of these applications.
Important parameters are the particle penetration depth, the deposition rate and the separation of particle sizes.A detailed review of the transport of nanoparticles in porous media is given by Boccardo et al. [19].One way to study these processes is through theoretical models that try to simulate particle transport [20,21].Such models showed that the particle retention was greatly dependent on porosity, flow rate of the carrying fluid and matrix-particle interaction [21].However, because porosity and permeability depend on the particle deposition within the porous media, the application of these models is very difficult.
Besides theoretical models, there are many experimental methods for studying transport of particles in porous media.Most of the experimental studies measure particle retention in columns filled with porous materials [6][7][8]22].In the experiment, a particle suspension is injected and pushed through a porous media (column).Data is gathered by analyzing the residue from the column with a breakthrough curve, which represent the particle concentration in the residue as a function of input liquid volume.These studies allow to determine the deposition rate of the particles within the porous media and showed that the particle recovery rate increased by increasing the fluid velocity [7].Although experimental methods for measuring nanoparticle dynamics are quite abundant for larger time (>1 min) and length scales (> 1 mm), experimental studies on fast penetration (< 100 ms) in thin-porous media (< 100 µm) are still challenging.Some attempts have been made to measure the particle penetration in thin porous media using microscopic techniques, such as scanning electron microscopy (SEM) [23], focused ion beam (FIB) [12] or confocal laser scanning microscopy [24].These techniques can achieve high-spatial resolution, but require a cross-section of the sample resulting in irreversible damage.Using these techniques, only post-mortem images can be made of the particle distributions.These techniques can provide good results on the final distributions, but will not provide information during transport.
Another type of experimental techniques that can cope with the fast measuring time are ultra-sonic liquid penetration (ULP) [25,26], drop adsorption (DA) or scanning automatic absorptometer (ASA) [27] which provide information on timescales as low as 10 ms.However, these techniques are only able to measure the liquid uptake within the porous medium and therefore only information about the effect of particles on the liquid uptake process.With these techniques, no particle distributions can be determined and only limited amount of information can be gained about the particle-matrix interaction.Therefore, a technique that is able to measure particle distributions during transport at sufficient time and length scales would be of great importance.
In a previous study, Ultra-Fast Imaging (UFI) NMR proved an ideal tool to study capillary uptake in thin-porous membranes with a high spatial (18 µm) and temporal (10 ms) resolution [28][29][30].Until now, only the capillary uptake of water-glycerol mixtures was studied, and no studies were performed on the uptake of particle dispersions.The NMR ability to image particles and colloids was already shown in a wide variety of studies [31,32].However, these studies are unable to cope with the high temporal and spatial resolution required to measure capillary uptake within thin, porous media.In this study, it will be shown how the UFI method is able to study the transport of iron oxide nanoparticles during capillary uptake within thin nylon membrane filters.The technique can be easily extended and used to study a wide variety of applications that include penetration of particles and colloids within thin, porous media.
In this study, it is first shown how the iron oxide within the latex particles enables the quantification of the latex particle concentration by the UFI-NMR method.Secondly, it is demonstrated how the UFI-NMR method is able to measure the position of latex particles during capillary uptake with a temporal resolution of 25 ms and a spatial resolution of µm.Furthermore, it is shown how particle concentration profiles within the nylon membranes can be determined.Finally, the UFI-NMR results are compared to scanning electron microscopy images.

Styrene-Fe 3 O 4 hybrid particles
First, iron oxide nanoparticles were synthetized as described by Lu et al. [33].In a 2 L jacketed glass reactor, iron (III) chloride hexahydrate (FeCl 3 ⋅6 H 2 O, 27.02 g) and iron (II) chloride tetrahydrate (FeCl 2 ⋅4 H 2 O, 9.90 g) were dissolved in water (650 g) at 25.0 • C. Oleic acid (10 g) was dissolved in acetone (60 ml) and added to the reactor and mixed for min.NH 4 OH (25 wt% solution in water, 75 ml) was added dropwise in 10-15 min under N 2 atmosphere to the reactor and mixed for 1 h.After that the temperature was increased to 85.0 • C for 1 h.The reaction mixture was cooled down to 70.0 • C and HCl (2 N solution) was added until pH 2 was obtained.Under the acid pH the nanoparticles coagulated.The nanoparticles were washed with deionized water until the pH of the washing water was 7 and were dried in an oven (at 65.0 • C) for h.
In a next step, polystyrene-Fe 3 O 4 hybrid nanoparticle latexes were synthetized by mini-emulsion polymerization, using 100 ml bottles submerged in a water tank and tumbled end over end at 70.0 • C for 24 h.The mini-emulsion was obtained by sonicating the mixture of the water and organic phases in a Branson Digital Sonifier for 20 min at 80% amplitude and a 0.8 s on and 0.2 s off cycle in an ice bath under magnetic stirring.The compositions of the organic and water phases for each polymerization are summarized in Table 1.Styrene (S), which is the main monomer, is converted to polystyrene in the final latex.methacrylic acid (MAA) is used as comonomer and sodium dodecyl sulfate (SDS) as surfactant, azobisisobutyronitrile (AIBN) is the initiator and hexadecane (HD) is used as costabilizer to keep the stability of the miniemulsion during the polymerization process.Three latexes of 30% S.C. were obtained with Fe 3 O 4 concentrations from 0.5 to 5.0 wt% (based on total dispersed phase).

Liquid solutions
In this study, liquid solutions are made by mixing demineralized water (type I), glycerol, Clariscan and the Fe 3 O 4 -latex particles, see Table 1.Solutions were coded by GxPyFz where x gives the wt% of glycerol, y the wt% of particles and z the wt% of Fe 3 O 4 within the particles.Clariscan (C 16 H 25 GdN 4 O 87 ) is a gadolinium based contrast agent commonly used in medical MRI [34].It is provided in a water like solution with a concentration of 279.3 mg/ml (0.5 M).The Clariscan solution has a pH between 6.5 and 8, a density of 1.349 g/ml and a viscosity of 3.0 mPa.s at room temperature [35].The goal of the Clariscan is to change the T 1 -relaxation time and allow fast imaging by UFI.The concentration of Clariscan was determined based on an earlier described method [29].The glycerol (> 99.0% purity) has a density of 1.26 g/ml and is used to tune the viscosity of the liquid solutions.
For calibration of the signal intensity, four different glycerol contents were used (0 wt%, 25 wt%, 50 wt% and 70 wt%).The actual penetration experiments were only done with mixtures containing 70 wt% (G70) of glycerol and use the particles with 0.5 wt% of iron oxide (F0.5).To study the effect of particle concentration, the particle concentration was varied between 0 (P0) and 8 wt% (P8).Experiments with lower viscosities can be performed but would lower the signal-to-noise ratio.When taking the spatial resolution (14.5 µm) and the measurement time (11.6 ms), an estimate about the maximum penetration speed can be given.When the distance that the liquid moves within the measurement time exceeds the spatial resolution, the decrease in signal-to-noise ratio becomes problematic.Therefore, the penetration speed limit for our experiments is 1.25 µm/s.

Membranes
For the penetration experiments, Whatman nylon-6,6 membranes (from VWR) are used with a typical pore radius of 0.2 µm (nylonmembrane I) and 0.45 µm (nylon-membrane II).The membranes have a thickness of 170 µm and a porosity of 65%.

NMR
In a previous study, it was shown that the UFINMR method was able to measure the absorption of liquids in thin, porous media with a time resolution of 10 ms [29,30].In this study, it will be shown that the same technique can be used to study the transport of Fe 3 O 4 latex particles.This section will start by a discussion of the pulse sequences, followed by a discussion of the signal characterization.Thereafter, the signal characterization will be used to discuss the NMR-signal profiles for four typical imbibition cases: 1) a pure liquid without particles, 2) particle dispersion that during imbibition remains homogeneously mixed, 3) a particle dispersion with particles penetrating slower than the liquid phase, and 4) a particle dispersion with particles not entering the porous material.Finally, the experimental procedure and NMR settings will be described.

Pulse sequences 2.4.1.1. Saturation recovery (T 1 ).
To characterize the effect of the Fe 3 O 4 -latex particles on the T 1 relaxation time, measurements are performed with a saturation recovery sequence: Here, m denotes the amount of saturation pulses and α represents the flip angle [36,37].To increase the signal-to-noise ratio, multiple measurements are performed and averaged.The time between two measurements (pulse sequences) is given by the repetition time (t r (s)).

Ostroff-Waugh (T 2 ).
To characterize the effect of the Fe 3 O 4 latex particles on the T 2 relaxation time, measurements of the T 2relaxation times are performed by an Ostroff-Waugh (OW) [37,38] sequence given by (90 where n denotes the amount of echoes measured, α represents the flip angle and 2τ = t e (s) is the echo time.Similar to the saturation recovery sequence, the signal-to-noise will be increased by performing multiple measurements, where the time between two measurements (pulse sequences) is given by the repetition time (t r (s)).

UFI (proton density).
To measure the proton density profiles during penetration, the UFI method was used.UFI can measure proton densities with a spatial resolution of 18 µm and temporal resolution of 10 ms.To achieve these resolutions, the solutions T 1 -relaxation time is decreased by the addition of a contrast agent (Clariscan).anddifferent echoes are summed to have a high enough signal to noise ratio in a reasonable time period.The pulse sequence is given by 90 where Nis the number of repetitions within one measurement.The final signal intensity is built up by a summation of all 2Nmeasured echoes.A detailed description of this UFI method can be found in [29].

NMR signal calibration
Because our NMR equipment is set to measure hydrogen nuclei, the signal originates either from hydrogen nuclei of the liquid solution or from the latex particles.However, because UFI is a T 2 weighted signal and the T 2 -time of the polystyrene within the latex particles was as low as 100 μs, the polystyrene will not contribute to the signal intensity measured by UFI.Therefore, the only signal intensity that is measured is that of the liquid solution.The Fe 3 O 4 within the latex particles will decrease the T 2 -relaxation time of the surrounding liquid, which allows for the detection of the particles.Therefore, this section focuses on the effect of the particles on the NMR-signal of the liquid, with the goal to establish a calibration curve to determine the particle concentration.The signal intensity measured by UFI was determined in an earlier study (Eq. 4 of [29]) and is given by: where ρ stands for the hydrogen density and 2Nis the number of echoes that are used for determining the signal profile.Due to the addition of Clariscan and its effect on the T 1 -time, the following condition is always satisfied: t r /T 1 ≪1.Therefore, the (1 − e − tr/T1 ) factor can be neglected within the UFI signal intensity.When the Fe 3 O 4 -latex particles are introduced to the liquid solution, the Fe 3 O 4 will influence the signal of the surrounding nuclei via the T 2 according to [39,40], with R 2 (ms.wt% − 1 ) being the relaxivity of the Fe 3 O 4 -latex particles and C (wt%) the particle concentration.Another effect that should be considered when introducing latex particles, is the replacement of water by latex particles.As explained before, hydrogen nuclei of the latex particles are invisible for UFI.Therefore, signal will be lost when replacing water molecules by latex particles.Therefore, ρ is replaced by ρ max (1 − aC), where ρ max is the density of visible hydrogen nuclei in a pure liquid.The variable a (wt% − 1 ), called the density change factor, is a constant that represents the decrease in liquid hydrogen nuclei per wt% of latex particles introduced in the suspension.When introducing both relations in Eq. 1, the signal intensity in a UFI experiment becomes: If the signal intensity is taken relative to the signal of a solution ).The relative signal becomes: where it can be seen that S′(0) = 1.Here, it is assumed that the T 2bulk of the solution does not change by introducing latex particles.Once again, this underlines adding particles decreases the measured signal intensity by 2 effects: by decreasing the amount of water molecules and lowering the T 2 -relaxation time.
In Fig. 1, the relative signal intensity S′ is plotted for different concentrations of particles.The relaxation values and a are set to 0.095 ms − 1 wt% − 1 and 0.016 wt% − 1 , respectively.These values correspond to a mixture containing 70 wt% glycerol and particles with 0.5 wt % of iron oxide and are determined in section 3.1.2.For the echo time, 50 µs is used.The signal decrease due to a lowering of the hydrogen atoms is drawn in black-dashed while the T 2 -effect is drawn in orangedashed.The total calibration curve is a combination of both effects and is drawn in blue-solid.The resulting calibration curve allows to extract the particle concentration from the signal.

Typical NMR signal profiles for different cases
When a particle dispersion penetrates in a thin, porous media, three typical situations can occur.Firstly, the particles and liquid move together as a homogeneous mixture and the particle and liquid front coincide.Secondly, the particles move slower than the liquid leading to a splitting of the particle and liquid front.Thirdly, the particles cannot enter the porous membrane, and a particle layers forms on top of the membrane.Because the measured NMR-signal is a function of the particle concentration (Eq.4), all the above-mentioned cases will have their typical NMR-signal profiles.A better understanding of these NMR-signal profiles will help in understanding the measured profiles during uptake experiments.Therefore, a more theoretical discussion about the NMRprofiles will be given in this section.
In the top of Fig. 2, the different situations are schematically drawn.The figures represent the penetration of liquid (blue) and particles (orange dots) in the nylon membranes (gray).The figures show 50 µm of the droplet on the left followed by the nylon membrane where the interface is marked with a green dashed line.The liquid and particles move from left to right and their corresponding fronts are marked with respectively a black and orange dashed line.The middle figures show the corresponding wt% of liquid (blue-dashed) and particles (red-solid).The lowest figures represent the corresponding NMR-profiles.The NMRprofiles are simulated using MATLAB based on the NMR-system specifications (echo time of 50 μs and a sample rate of 5 MHz), which results in a theoretical spatial resolution of 14.5 µm.To calculate the signal intensities, the calibration curve for a mixture containing 70 wt% glycerol and particles with 0.5 wt% of iron oxide is used (blue-solid line in Fig. 1).The start concentration of particles used in this discussion is 5 wt%, which corresponds to a relative value of 0.65.In the following subsections, we will discuss these potential situations in more detail.

A pure liquid without particles (A).
In Fig. 2A, the reference situation, where only liquid penetrates the nylon membrane is shown.The liquid content is always 100 wt% but drops to 0 after the liquid front.The corresponding NMR-profile shows first the droplet region with a signal intensity of 1, meaning a fully saturated region with only liquid.Within the membrane, the signal intensity of a fully saturated region drops to 0.65 as a consequence of the porosity (65%).Ahead of the liquid front (x > 100 µm), no liquid is found, which results in a signal intensity of zero.From the reference, it can be observed that the NMR-resolution will have a significant effect on the NMR-profiles, which can be observed in the gradual change in signal intensity at the droplet-membrane and liquid front interface.Experimental measurements of this situation can be found in earlier research, where the penetration of water-glycerol mixtures was measured within nylon-and PVDF-membranes [28,29].

Homogeneous movement of liquid and particles (B).
In the second situation (Fig. 2B), the particles move together with the liquid and, therefore, the liquid front (black-dashed line) and particle front (orangedashed line) coincide.In this particular case, the particle concentration was set to 5 wt%.As there is no blocking of particles, at the dropletliquid interface, the particle concentration everywhere in the liquid phase is 5 wt% (Fig. 2B, middle).Because the particles are homogeneously distributed, their effect on the signal intensity will be the same at every position.Therefore, the profile is similar to the reference but lowered with a factor of 0.65 due to the presence of particles.

The particle front lags behind the liquid front (C).
In the third case, a splitting between the particle front and liquid front occurs.In Fig. 2C top, the particles front has reached a depth of 50 µm (orangedashed), while the liquid front has already reached 100 µm (black-Fig. 1. UFI NMR signal as a function of the particle concentration (blue).Shown in orange and black dashed lines are the contributions coming from the decrease in -relaxation and the decrease of hydrogen atoms respectively.dashed line).Fig. 2C middle, shows the particle concentration throughout the sample starting with 5 wt% in the droplet, 10 wt% until 50 µm followed by a region with no particles.The increased particle concentration in the upper part of the membrane can be attributed to the slower movement of the particles, which results in a buildup of particles.From the calibration curve, we know that the signal will be higher in absence of particles, therefore the signal will start to increase again around 50 µm.The corresponding NMR-profile can be seen in the bottom of Fig. 2C, where a clear increase in signal intensity is found beyond 50 µm.When the separation between the particle and liquid front is larger than two times the resolution (29 µm), the signal intensity will increase back to its original intensity found within the reference.In this way, the NMR-profiles could be used to identify a splitting in particleand liquid-front.The position of this particle front is situated at the position where the increase in signal intensity is at half maximum (the orange-dashed line).

Particle cannot enter the porous media (D).
In the last situation, the particles do not enter the porous membrane, while the liquid penetrates (Fig. 2D).In this situation, the particles are clogged and stay at the droplet-membrane interface (green-dashed line), where they will create a dense particle layer.In this example, an arbitrary particle layer with thickness of 20 µm and a particle content of 50 wt% was chosen.Inside the medium only water can be found, which can be seen in the middle figure.The dense particle layer results in a decreased NMR-signal intensity on top of the membrane.Similar to the situation where particles lag behind the liquid front, the signal starts to increase to its original value within the membrane (x > 0 µm), because only liquid is present here.As the particle layer at the top is smaller than 2 times the resolution (29 µm), the signal at the droplet-membrane interface will not reach zero.

Experimental details and setup
The NMR setup used in this study is a GARField-NMR with a magnetic field of 1.46 T and a gradient of 40.3 T/m which is thoroughly described in earlier work [29].The GARField NMR uses a Radio Frequency coil (measurement coil) to record the signal intensity.Fig. 3 shows a schematic representation of the droplet insert, light sensor, measurement coil and a typical sample during the penetration of a particle suspension.Next to the sample, the corresponding UFI signal profile is shown.In this example, the particle suspension penetrates the nylon membrane as described by Section 2.4.3.3where the particle front p(t)(orange-dashed line) lags behind the liquid front l(t)(blue-dashed line).
An experiment starts by jetting a droplet (8-12 µL) on top of a nylon membrane, which triggers a light sensor that will start the UFI pulse sequence.The measurement area is located above the measurement coil and indicated with a black box.The corresponding UFI measurement is a 1D-profile of the situation within this black box.
The settings used for the UFI pulse sequence are t e = 50μs, a window width of 40 μs, and N = 16.These settings result in a theoretical spatial resolution of 14.5 µm.The experimental resolution was determined to be 18 µm.The t r was varied between 10 and 300 ms depending on the speed of the penetration experiment.

Characterization of the particles
To characterize the particles, particle size distributions were measured for both the hybrid iron oxide latex particles and the iron oxide particles themselves.Additionally, STEM images of the hybrid iron oxide latex particles are provided which depict both the complete particles and individual iron oxide nanoparticles.
Fig. 4 shows the particle size distributions of the Fe 3 O 4 -polystyrene latex particles containing 0.5 wt% (black), 2.5 wt% (orange) and 5 wt% (blue) of Fe 3 O 4 .The particle size distribution was measured by capillary hydrodynamic fractionation (CHDF).A CHDF-3000 (Matec Applied Science) was used with an operating flow of 1.4 ml/min at 35.0 ºC and detector wavelength at 220 nm.The carrier fluid was 1X-GR500 (Matec).The samples were diluted to 0.5% S.C. using the carrier fluid and the samples were analyzed using the Matec software v.2.3.The small population observed around 40 nm which is marked with a star, is an artifact coming from the signal of the emulsifier, which is not separated from the particles due to its small size.Furthermore, the particles containing 5.0 wt% of iron oxide (blue line) show a small peak around 150 nm which probably comes from an artefact as the measurement was performed three times and the peak was only observed once.
Scanning transmission electron microscopy (STEM) images of the latex particles containing 7.5 wt% of iron oxide (E in Table 1) are shown in Fig. 5a.In this image, latex particles appear as light gray while iron oxide appears white.The figure shows individual iron oxide latex particles embedded within the latex particles.Using these images, a particles size distribution was obtained for the iron oxide particles which are shown in Fig. 5b.

Characterization of the membrane samples
To characterize the membrane samples, the pore size distributions were measured, as depicted in Fig. 6a.The data was obtained using mercury intrusion porosometry (MIP).The pore radius deduced from these measurements were 0.42 µm for nylon-membrane I and 0.53 µm for nylon-membrane II, which showed a slight deviation from the specified values of the supplier.Furthermore, Fig. 6b presents a scanning electron microscopy (SEM) image of the top surface of the nylon membrane II.

Characterization of the liquid solutions
The liquids used in the penetration experiments of Section 3.2 are given in Table 2, together with their physical parameters.For the complete set of liquids used in signal calibration in Section 3.1, we refer to Appendix C. The viscosities of the solutions were measured using an  5 wt% (black), 2.5 wt% (orange) and 5 wt% (blue) of Fe 3 O 4 respectively.The small population observed around 40 nm which is marked with a star, is an artifact due to the signal of the emulsifier, which is not separated from the particles due to its small size.
Anton Paar MCR302 rheometer (20 • C), while the surface tension was determined using the Wilhelmy plate method.
The measured data reveals that an increase in particle concentration leads to an increased viscosity and decreased surface tension, see Table 2.The T 1 and T 2 times of the liquid solutions are measured using a saturation recovery and OW sequence respectively.

NMR-characteristics of latex particles
Before particles can be followed during imbibition experiments, their NMR characteristics were studied by determining their relaxation characteristics and effect on the signal intensities within the setup.The goal of this section is to select the proper Fe 3 O 4 latex particle and make particle calibration curves.The section starts by determining the relaxation behavior of latex particles containing varying Fe 3 O 4 -content.Thereafter, the effect of the latex particle concentration on the T 2relaxation time is studied in order to get values for R 2 and a (Eq.4).The relaxation measurements will be used to determine the calibration curves and select the Fe 3 O 4 -latex particles for the imbibition experiments.

Effect of Fe 3 O 4 -content on the relaxation behavior
To characterize the effect of the iron-oxide within the latex particles, the relaxation characteristics of particles containing different amounts of iron-oxide were measured.All solutions contained 70 wt% water and

Table 2
The liquids used in the imbibition experiments and their physical properties.30 wt% solid content, from which 0.1 wt% to 7.5 wt% was iron oxide.T 2 -and T 1 -decay curves were measured using an OW-sequence and saturation recovery sequence.Figures of the decay curves can be found in Appendix A, Fig. 14.The curves show that increasing the iron-oxide content decreases both the T 1 -and T 2 -relaxation times.In Fig. 7, the inverse relaxation times are plotted as a function of the Fe3O4 content, which shows a linear relationship between both.From this linear relationship, the relaxation rates R 2 and R 1 were determined to be 1.5 ms − 1 wt% − 1 and 0.034 ms − 1 wt% − 1 .Based on this finding, the particles containing 0.5, 2.5 and 5 wt% of Fe3O4 were selected for further observation.The particles containing 0.1 wt% showed a T 2 -relaxation time with too low effect to make them clearly visible, whereas the one containing 7.5 wt% decreased the T 2 -relaxation time too much in order to have sufficient signal for UFI measurements.

Effect of particle concentration on the relaxation behavior
To determine the relaxation characteristics as function of the particle concentration, relaxation times were determined for liquid mixtures containing varying particle concentrations.Because the addition of Clariscan will ensure that the T 1 -relaxation time will not influence the signal intensity (Eq.1), only the T 2 decay will be discussed in this section.Information about the effect on the T 1 -relaxation time can be found in Appendix B. This study was performed on solutions containing a varying glycerol content (0 wt%, 25 wt%, 50 wt% and 70 wt%) with the particles containing 0.5 wt%, 2.5 wt% and 5 wt% of iron oxide.A list of all solutions can be found in Appendix C. T 2 -relaxation times of the solutions were determined by an Ostroff-Waugh pulse sequence with an echo time of 50 μs.The measured decay curves for the solution containing 70 wt% glycerol, 0.005 M Clariscan and 0 -8 wt% of particles are given in Appendix B, Fig. 15.Fig. 8 shows the inverse T 2 relaxation time and maximum signal intensity as a function of particle concentration (particles with 0.5 wt% of iron oxide) for a mixture containing 70 wt% of glycerol.These dispersions will be used for penetration experiments in Section 3.2.It is obviously, increasing the particle concentration increases the inverse T 2 -relaxation time, as expected from Eq. 2. The expected linear relationship between 1/T 2 and the particle concentration is observed.Furthermore, the maximum signal intensity depends linearly on the particle concentration.Using these data, a value for the density change factor a (0.016 wt% − 1 ) and relaxivity R 2 (0.042 ms.wt% − 1 ) can be found.Values for a and R 2 corresponding to all possible combinations of glycerol content and iron oxide content can be found in Appendix D.

Calibration curves
In this section, the previous measured relaxation characteristics will be used to construct calibration curves that couple the signal intensity with the particle concentration in UFI-NMR experiments.These calibration curves allow to determine particle density profiles during capillary uptake.
In this section, calibration curves are determined for solutions containing 70 wt% glycerol and iron oxide contents of 0.5, 2.5 and 5 wt%.Calibration curves for other combinations of glycerol and iron oxides contents can be found in Appendix D. To test the theoretical model, signal intensities of all liquid mixtures were measured by UFI-NMR.Fig. 9 shows a comparison between the measured signal intensities (dots) and the predictions (lines) using the theoretical model.
The graph shows the calibration curve for different Fe 3 O 4 latex particles, containing 0.5 wt%, 2.5 wt% and 5 wt% of Fe 3 O 4 .As expected, with increasing the Fe 3 O 4 content, the signal drop is steeper with increasing the particle concentration.It is seen that the measured signal intensities (points) coincide very well with the theoretical signal intensities (lines) found by Eq. 1.The type of Fe 3 O 4 -content that should be used will depend on the type of experiment.The advantage of using a lower iron oxide content, such as 0.5 wt%, is the large range of particle  concentrations that can be probed.However, the signal differences are smaller and therefore harder to discriminate.Therefore, when small particle concentrations should be discriminated, particles with a higher Fe 3 O 4 content are recommended.The downside of the larger signal differences is the smaller range of particle concentrations that can be probed.While with a 0.5 wt% Fe 3 O 4 content, solution with a particle concentration of 15 wt% still provide enough signal (black line), the particles with 2.5 wt% (orange line) and 5 wt% (blue line) can only be used to probe particle concentrations up until 7.5 wt%, where the signal enters the noise level.In the subsequent study, we performed all measurements on dispersion with particles containing 0.5 wt% Fe 3 O 4 .

Measuring particle concentration profiles during imbibition
In this section, it will be shown that the UFI-NMR method can be used to study particle transport during imbibition.This is done by comparing two imbibition experiments on a nylon 0.45 membrane.One experiment is performed with a solution containing no particles (G70P0) while the other one contains 5 wt% of particles (G70P5F0.5).Both solutions contain 70 wt% of glycerol to slow down the penetration and increase the signal-to-noise ratio.The section starts by comparing the measured UFI-NMR signal intensity profiles for both experiments.Thereafter, the calibration curves in Fig. 9 will be used to determine particle concentration profiles, which in the final part will be compared to SEM-images.
Fig. 10a, shows the liquid profiles for the G70P0 liquid.Similar profiles were also measured in a previous study, with the penetration of a glycerol mixture inside PVDF and nylon membranes [28,29].The liquid profiles can be divided in three main regions which by moving from left to right are: the droplet (S = 1), membrane (S ≈ 0.65) and tape (S = 0).In the case of no particles, Fig. 10a, the droplet (x < 0) has signal intensity 1, referring to a fully saturated region.Inside the membrane (0 < x < 170), the volume percentage of liquid drops, because of the membrane porosity.This results in a decrease in signal intensity equal to the porosity of the membrane, which in this membrane is around 65%.The tape (170 < x) has signal intensity of 0 because of the absence of liquid.
Fig. 10b, shows the liquid profiles for the penetration of the G70P5F0.5 liquid.The liquid profiles are shown in a wide range of timesteps, indicated with a green color map.Here, profiles are measured for longer times than in Fig. 10a, because particles keep penetrating after the liquid had reached the bottom of the membrane.The addition of particles will affect the measured liquid profiles (blue arrows).For comparison a liquid profile of a fully saturated membrane containing the G70P0 is added (orange).As expected, the signal inside the droplet decreases from 1 to 0.65, in correspondence with the black calibration curve in Fig. 9. Inside the membrane, the signal intensity drop appears in the upper part of the membrane (0 < x < 100) while, in the bottom part of the membrane (x > 100) the signal intensity increases again.These profiles correspond to case C from Fig. 2, the situation that the particle front lags behind the liquid front.A clear signal increase is only observed behind 100 µm, which indicates that the splitting before this distance is not large enough to be picked up by our setup.The particle's final penetration depth can be determined to be 100 µm, the position where the signal intensity starts to increase again.After the liquid has reached the bottom of the membrane, the droplet keeps spreading, allowing more particles to enter inside the membrane.The increase in particle concentration within the membrane can be observed by the decrease in signal intensity (black arrows).Besides the signal increase within the membrane, also a slight signal decrease on top of the membrane is observed, which is probably due to a buildup of particles that are unable to penetrate inside the medium.
Using the black calibration curve in Fig. 9, particle density profiles can be calculated for every signal profile shown in Fig. 10b.However, before this can be done, the effect of porosity on the signal intensity  should be taken into account.This is done by dividing the signal profiles of Fig. 10b (green) by a profile of a fully saturated membrane (orange) containing only liquid.This will result in signal intensity profiles that are completely determined by the particle concentration, for which the calibration curve can be used to determine the particle concentration profiles.Fig. 11, shows the particle concentration profiles that correspond to the signal profiles shown in Fig. 10b.However, there are still some limitations when determining the particle concentration profiles.First, the particle concentration can only be determined behind the liquid front, where the signal intensity has reached its maximum and is not affected by the limits in resolution.If concentrations are determined too close to the liquid front, the incline due to the resolution limit will result in an overestimation of the particle concentration.Therefore, particle concentrations are determined until 20 µm behind the liquid front.For the same reason, particle concentration profiles are only shown until 175 µm.However, some profiles still have the problem of an overestimation near the end of the particle concentration profiles.The resolution problems will also lead to difficulties in determining particle concentrations near the droplet-membrane interface.
The particle concentration profiles in Fig. 11 show that the particle concentration inside the droplet and top part of the membrane varies around 5 wt%, in line with the initial concentration of the droplet.This shows that the particles are not hindered by the interface and move together inside the porous medium.This small decline observed at the droplet-membrane interface is probably due to difficulties in determining the particle concentration around interfaces, as it will become more homogeneous through time.During penetration, it is observed that the particle concentration will start to decrease around 100 µm.However, the particle concentration does not decrease towards 0, which suggest that some particles penetrate deeper than 100 µm.Another explanation may originate from the NMR-resolution.If the experimental resolution is 18 µm, a complete signal recovery would require that the particles are at least 36 µm separated from the end of the membrane.In practice, this distance to require complete signal recovery can be somewhat higher.However, our measurement, shows that particles are able to penetrate up to 100 µm and the sample is around 170 µm in thickness.Therefore, there are probably particles that do penetrate a little further than 100 µm.
After the liquid has reach the end of the membrane, the continuous spreading of the droplet in lateral direction will keep bringing particles into the membrane.Because the lateral penetration of liquid takes place beyond the measurements area, this movement cannot be observed within the UFI measurement, see Fig. 3.However, the additional particles that are brought in are observed by an increase in the particle concentration, which is marked by black arrows in Fig. 11.It is seen that the particle concentration does not increase homogeneously throughout the medium.The concentration increases first inside the membrane, at 100 µm, which is the depth the particles could penetrate during the process of vertical liquid penetration.Followed by a particle concentration increase that will travel towards the droplet-membrane interface.The final profiles show that the particle concentration has increased to 12 wt% within 330 s To verify these findings, SEM-images of the samples cross-section were taken after penetration.Fig. 12 a and b show the SEM-images, corresponding to the samples used for the experiments shown in Fig. 10a (no particles) and Fig. 10b (5 wt% of particles).In samples without particles (reference), the membranes texture is homogeneous throughout the whole cross-section.No particles are visible and only nylon fibers can be seen.The situation is completely different after the penetration of a dispersion containing 5 wt% of particles (Fig. 12b).Based on the texture, three different regions can be distinguished.The top, which looks denser and completely different than the reference sample, the middle, appearing even denser (between white dashed lines) and the bottom with a similar texture as the reference sample.12b, reveals that there are some particles beyond the dense particle layer (red arrows).This is probably the reason for the non-zero particle concentration found beyond 100 µm in Fig. 11.Both droplets also contained 70 wt% of glycerol.The white line marks the particle penetration depth and the red lines refer to particles that were able to penetrate behind the final particle penetration depth.relaxation data with S = S max exp( − t/T 2 ) and S = S max (1 − exp( − t/T 1 )), the relaxation data and maximum signal intensities can be extracted.For the T 2 -decays, fits were made on the first 32 echoes.The reason for choosing only the first 32 echoes is because UFI uses the first 32 echoes to build up a liquid profile [29].Therefore, the relaxation characteristics of these first 32 points are most relevant and are used for fitting.In both measurements, the relaxation time and maximum signal intensity decreases when increasing the particle concentration, marked by a red arrow.The determined relaxation times and maximum signal intensities can be used to determine the relaxation rates (R 1 , R 2 ) and required for Eq. 4. The value for R 2 is determined in section 3.1.2Fig. 8 while the value for R 1 is determined within this section Fig. 16.
In this section, relaxation parameters are determined for Fe 3 O 4 -latex particles with an iron oxide content of 0.5 wt% in a solution containing 70 wt % glycerol and 0.005 M Clariscan.However, this procedure was repeated to determine the relaxation characteristics of the Fe 3 O 4 -latex particles in varying glycerol contents (0, 25, 50 and 70 wt%) and with varying iron oxide contents (0.5, 2.5 and 5 wt%).

Fig. 2 .
Fig. 2. Representation of four different archetypical situations that can occur during particle penetration.From left to right these four situations (top row), corresponding fluid and particle distributions (middle row) and resulting NMR signal profiles (bottom row) are shown.The four situations are A) pure liquid penetration, B) homogeneous movement of liquid and particles, C) splitting between particle and liquid front and D) particles cannot enter the porous media.

Fig. 3 .
Fig. 3. Schematic picture of the measurement insert.Shown are the droplet insert, the light sensor to trigger the NMR, the sample with droplet and the RF coil to measure the signal.A signal profile that corresponds with the 3-dimensional situation is shown in the indent.

Fig. 4 .
Fig. 4. Particle size distribution of Fe3 O 4 -polystyrene latex particles containing 0.5 wt% (black), 2.5 wt% (orange) and 5 wt% (blue) of Fe 3 O 4 respectively.The small population observed around 40 nm which is marked with a star, is an artifact due to the signal of the emulsifier, which is not separated from the particles due to its small size.

Fig. 5 .
Fig. 5. a) STEM image of the Fe 3 O 4 latex particles containing 7.5 wt% iron oxide (E) latex appears as light gray while Fe 3 O 4 appears white.B) Particle size distributions of the Fe 3 O 4 particles, determined from STEM images.

Fig. 6 .
Fig. 6. a) Pore size distribution measured by mercury intrusion porosometry for nylon membrane I and nylon membrane II.b) SEM image of the top surface of nylon membrane II.

Fig. 7 .
Fig. 7. Inverse relaxation times as a function of the Fe 3 O 4 -content in the latex particles cores.a) T 1 and b) T 2 .

Fig. 8 .
Fig. 8. Inverse -relaxation time (black) and maximum signal intensity (red) in function of particle concentration for a dispersion containing 70 wt% of glycerol and particles with 0.5 wt% of Fe 3 O 4.

Fig. 9 .
Fig. 9. Calibration curves for the signal intensity in function of the particle concentration for varying Fe 3 O 4 contents but with the same glycerol content of 70 wt%.Calibration curves, predicted from the previously obtained values of R 2 and a, are shown as lines.The data points mark measured UFI-NMR signals from the particle dispersions.

Fig. 10 .
Fig. 10.UFI-NMR signal profiles measured for different times during the penetration of a 70 wt% glycerol mixtures with no particles (a) and with 5 wt% of Fe 3 O 4latex particles that contain 0.5 wt% of Fe 3 O 4 (b) inside nylon membrane II.A green color map is used to mark the specific time of each profile.Note the huge time difference in timescales of both figures.

Fig.
Fig.12b, reveals that there are some particles beyond the dense particle layer (red arrows).This is probably the reason for the non-zero particle concentration found beyond 100 µm in Fig.11.

Fig. 12 .
Fig. 12. SEM-images of the cross section of a nylon membrane after the penetration of a droplet containing no particles (a) and containing 5 wt% of particles (b).Both droplets also contained 70 wt% of glycerol.The white line marks the particle penetration depth and the red lines refer to particles that were able to penetrate behind the final particle penetration depth.

Fig. 13 .
Fig. 13.SEM images of the top (a), middle (b) and bottom (c) part of the cross-section shown in Fig. 12b.

Fig. 16 .
Fig. 16.Inverse T1-relaxation time and maximum signal intensity in function of particle concentration for a solution containing 70 wt% of glycerol and Fe3O4-latex particles with 0.5 wt% of iron oxide. .

Table 1
Composition of the latex particles in grams.The different components are: Fe 3 O 4 , styrene as the main monomer, Methacrylic acid (MAA) as comonomer, hexadecane (HD) as costabilizer, Azobisisobutyronitrile (AIBN) as initiator and sodium dodecyl sulfate (SDS) as surfactant.