Rheological behavior of cement paste with nano-Fe 3 O 4 under magnetic field: Magneto-rheological responses and conceptual calculations Cement and Concrete Composites

The magneto-rheological responses of cement paste with nano-Fe 3 O 4 particles are experimentally investigated. The estimated magneto-dynamic force between two neighboring nanoparticles and equilibrium movement velocity of the nanoparticles in cement-based suspensions are calculated. Results show that the nanoparticles have a potential to move to form magnetic clusters when a magnetic field is applied, which creates a sort of agitation effect breaking down the early C-S-H links between cement particles, and thus the corresponding suspensions exhibit liquid-like behavior immediately after applying the magnetic field. The solid-like property of the studied suspensions becomes more dominant with magnetizing time due to the formation of magnetic clusters and the reconstruction of C-S-H bridges. The rheological properties of paste medium exert significant influences on the magneto-rheological responses of cement paste containing nano-Fe 3 O 4 particles. It is revealed that the calculated magnetic yield parameter and nanoparticle movement velocity are useful relevant indicators to evaluate the magneto-rheological effect of cementitious paste.


Introduction
The engineering application process of concrete includes transporting, pumping and formwork casting. Each process is a significant factor influencing the properties of fresh and hardened concrete. However, for a specific concrete mixture proportion, once the concrete is prepared, its properties cannot be further adjusted nor controlled postmixing. The concrete will be transported, pumped and cast according to its mixture-dependent properties, requiring appropriate processing methods. Many conflicts and contradictions in requirements of fresh concrete performances exist in different operation processes. For example, low thixotropic structural build-up is needed to overcome the major problem in resuming pumping operations after a short interruption (e.g. due to the delay of the concrete truck) [1] and to improve the interface properties during multi-casting process [2]. In contrast, a higher structuration rate of fresh concrete is beneficial for reducing formwork pressure during casting [3,4]. In this context, an innovative casting concept "SmartCast" has been proposed by De Schutter [5,6] to overcome the aforementioned problems. By active rheology control (ARC) and active stiffening control (ASC) of fresh concrete, pumping and casting operations could be better controlled and become more reliable.
Magnetorheological (MR) fluids are kinds of smart materials, consisting of magnetic particles, carrier fluid and additives. In the absence of external magnetic field, the magnetic particles are randomly distributed in the carrier fluid. After the application of an external magnetic field, the magnetic particles align along the direction of the magnetic field and form chain-like or columnar structures, resulting in higher elastic behavior [7,8]. After removing the external magnetic field, the chain-like structures break down and the MR fluid reversibly changes from semi-solid to liquid state. However, due to the significant difference in density between magnetic particles and carrier fluid, particle sedimentation has become a main limitation of industrial applications of conventional MR fluids. One of the potential approaches to improve the stability of MR fluids is using a yield stress carrier fluid [9][10][11][12]. Fresh cement paste is usually regarded as a concentrated suspension with yield stress [13][14][15]. A stable cement-based MR fluid could be obtained using fresh cement paste as the carrier, and meanwhile, the rheological properties of the cement paste would become controllable. Some preliminary results about the effect of magnetic field on the properties of cement-based materials can be found in literature. For example, the pumpability of fresh concrete seems to be somewhat improved by applying an electromagnetic field [16]. By exposing fresh steel chip-reinforced concrete specimen into an alternating magnetic field, the steel chips act as a vibrator and the compaction of concrete can be facilitated [17]. More information about the application of external signals to control concrete properties can be found in Ref. [5]. Nevertheless, there is currently no comprehensive understanding of the MR behavior of cementitious materials, especially at the initiation of the magnetic field.
Ferroferric oxide (Fe 3 O 4 ) is a ferromagnetic material with Fe 2+ and Fe 3+ , and the magneto dipoles can be aligned along the direction of an external magnetic field. The addition of nano-Fe 3 O 4 particles in cementbased materials has attracted extensive interest [18]. The nano-Fe 3 O 4 particles, on the one hand, fill the voids between cement particles, leading to a denser suspension system. On the other hand, the nanoparticles provide nuclei for cement hydration products [19]. As a consequence, the hydration reaction of cementitious materials is accelerated with the addition of nano-Fe 3 O 4 particles, and thus the early age mechanical properties are enhanced [20,21]. Moreover, the Fe available in the cement-based materials because of the addition of nano-Fe 3 O 4 has a potential to form Kuzel salts and Fe-ettringite which accumulate in the pores and voids between cement particles, resulting in an enhanced microstructure and higher electrochemical stability [22]. Mansouri et al. [23] found that the replacement of 2% cement with nano-Fe 3 O 4 particles dramatically reduced the percentage of water adsorption and improved the resistance of chloride ion permeation, providing a potential extension of service life of submerged structures. From a fresh performance point of view, cement paste containing nano-Fe 3 O 4 particles possesses fluid and magnetic properties at the same time. This provides a potential reasonable method to control the rheological behavior of cement paste by applying external magnetic fields.
Our previous publications [24,25] presented some preliminary findings about the rheological behavior of cement paste under external magnetic field. The structural evolution of cement paste under time-varying magnetic fields was also studied. In the current study, the structural build-up of cement paste with nano-Fe 3 O 4 particles under constant magnetic field is experimentally investigated using small amplitude oscillatory shear (SAOS) technique. The magneto-rheological responses illustrated by the relationship between storage modulus, loss modulus and phase angle are discussed. The influences of cement paste medium on the magneto-rheological responses are also examined. The hypothesis concerning the underlying mechanisms is verified by estimating the magneto-dynamic force between two neighboring nanoparticles and the movement velocity of the nanoparticles in cement-based suspensions, based on some conceptual approach.

Raw materials
Ordinary Portland cement (OPC) CEM I 42.5 N conforming to EN 196-1 [26] is used in this study. The chemical composition and particle size distribution are respectively shown in Table 1 and Fig. 1. The specific gravity of the Portland cement is 3.15. Spherical Iron Oxide nano-Fe 3 O 4 particles (MNPs) with Fe 3 O 4 purity higher than 98% (from US Research Nanomaterials, Inc) are used. The particle size and relative density of the nano-Fe 3 O 4 particles supplied by the manufacturer are 20-30 nm and 4.95, respectively. The curves of magnetization versus magnetic field strength of the cement and nanoparticles, obtained from a vibrating sample magnetometer (VSM), are shown in Fig. 2. The saturation magnetization of Portland cement particles and nano-Fe 3 O 4 particles are 0.59 emu/g and 49.48 emu/g, respectively. The extremely low magnetization value of the cement particles means that the response of pure cement paste to an external magnetic field can be neglected [27,28]. A commercial polycarboxylate ether superplasticizer (PCE) (Mas-terGlenium 51) is used. All samples are prepared using de-ionized water.

Mixing procedure
Five cement pastes were prepared as the medium and the nano-Fe 3 O 4 particles content was fixed at 3% by weight of the cement paste (i.e. cement + water). A mass of 20 g of cement was used for each sample. The mixture proportions of the cement pastes with nano-Fe 3 O 4 particles are shown in Table 2. The cement paste was mixed using a rotational rheometer (MCR 52, Anton Paar) with a helix geometry, which provides repeatable initial state of paste samples with same mixture proportion. The details of the geometric parameters of the helix geometry and the mixing procedure can be found in Ref. [25].

Testing methods
A rotational parallel plate rheometer (MCR 102, Anton Paar) with magneto-rheological device (MRD) was used for the rheological test. The diameter of the plate is 20 mm and the gap between the upper and lower plates is fixed at 1 mm. A homogeneous magnetic field vertical to the plates can be applied to the sample by inputting specific current. During the rheological tests, the temperature of all samples was controlled at 20 ± 0.5 • C. Rheological tests were repeated three times using fresh samples.
The testing protocol for evaluating the structural build-up of the cement pastes is presented in Fig. 3. The magnetic field was applied to the sample at the beginning of the oscillatory time sweep test, and the field strength used in this study included 0 T and 0.5 T. During the strain sweep test, the shear strain logarithmically swept from 0.0001% to 10% at constant frequency of 2 Hz. The strain amplitude and frequency during the time sweep test were 0.001% (within the linear viscoelastic region (LVER)) and 2 Hz, respectively.
Moreover, an additional flow curve test was conducted using fresh  samples to measure the rheological parameters of cement pastes in the absence of magnetic field. The key parameters during the shear curve test are as follows. During the pre-shearing process, the shear rate and duration were respectively 100 s − 1 and 30 s. Afterwards, the shear rate logarithmically decreased from 100 s − 1 to 0.1 s − 1 within 100 s, and the shear stress and shear rate were recorded every second.

Rheological properties of cement pastes without magnetic field
The storage modulus (G ′ ) and loss modulus (G ′′ ) obtained during the oscillatory strain sweep test are used to evaluate the viscoelastic behavior of the cement pastes in the absence of external magnetic field. The storage modulus, related to the energy stored in each cycle, describes the elastic behavior of the system. The loss modulus characterizes the viscous property of the paste, which is proportional to the energy dissipated in each measuring cycle. A typical oscillatory strain sweep testing result of the cement paste with w/c of 0.4 and nano-Fe 3 O 4 of 3 wt% is displayed in Fig. 4. At relatively low shear strain, the storage modulus and loss modulus showed plateau behavior (LEVR), and the storage modulus was higher than the loss modulus, indicating that the solid-like property of the cement paste dominates the liquid-like property. At shear strain higher than a critical strain, the storage modulus and loss modulus started to decline, indicating the breakage of C-S-H links between cement particles. The crossover point between the storage modulus and loss modulus at shear strain of ~2% represents the beginning of viscous property domination under oscillatory amplitude sweeping. The aforementioned critical strain can be determined by the point where the storage modulus deviates 10% from the plateau [29,30]. The elastic stress at the critical strain is defined as elastic limit yield stress, which can be calculated by Eq. (1). The magnitude of the elastic limit yield stress can be used to characterize the intensity of C-S-H contacts between cement particles.
where τ c,ys is the elastic limit yield stress (Pa), γ c is the critical strain (%), and G' is the storage modulus at critical strain (Pa). Fig. 5 shows a representative flow curve of the cement paste with w/ c of 0.4 and nano-Fe 3 O 4 content of 3%. With the decrease of shear rate, the measured shear stress first slowly decreased and then dramatically decreased. This indicates that the cement paste showed noticeable shear thinning behavior at the selected shear rate region, which is consistent with [31][32][33]. At extremely low shear rates (e.g. less than 1 s − 1 ), a slight increase in shear stress was observed from the inserted enlarged view in Fig. 5. This can be explained by the competition between attractive particle interactions and hydrodynamic forces. At extremely low shear rates, the attractive forces between solid particles dominate the repulsive ones and hydrodynamic forces. Agglomerates and clusters between    particles, especially nano-Fe 3 O 4 magnetic particles, are formed, leading to a slightly higher measured shear stress. Furthermore, the interparticle contacts might exert a significant resistance to the shear flow at low shear rates [34]. As a result, the slight increase in shear stress at low shear rates was recognized.
The main properties of the cement pastes obtained from the oscillatory strain sweep test and shear curve test are summarized in Table 3. Plastic viscosity at linear low shear rate region (η pl ) was selected to characterize the dynamic rheological behavior. The stiffness of cement paste was expectedly increased with the decrease of water content (i.e. w/c). At fixed w/c, both the elastic limit yield stress and the viscosity at low shear rates were increased after adding 0.2% PCE. The slight increase in stiffness of cement paste with low PCE addition can be found in Refs. [35,36]. This unexpected aberration in this study can be explained by the potential deagglomeration of nanoparticle clusters. At w/c of 0.35, some nano-Fe 3 O 4 particles might aggregate to clusters in the cement paste due to the low water content. After adding small dosage of PCE (0.2%), the large nano-Fe 3 O 4 clusters could be broken to small clusters or individual nanoparticles, improving the dispersion of the solid particles, and thus requiring more water to coat the surface of the nano-Fe 3 O 4 particles. As a result, free water with lubricating effect was decreased. Besides, the addition of PCE increases the viscosity of the interstitial solution and thus the adhesion between particles. Consequently, the stiffness of the cementitious paste increased with the addition of 0.2% PCE. With the continuous increase of PCE content, the stiffness of cement paste was significantly decreased, as reflected by the decrease in the storage modulus at linear viscoelastic region. Remarkably, the critical strain exhibited an increasing behavior with the addition of PCE, which is consistent with [37,38]. As a result, the elastic limit yield stress of cement pastes with PCE was higher than that of cement pastes without PCE. It should be mentioned that the high viscosity of Mix. 0.35 + 0.4%PCE at low shear rates could possibly be attributed to the increase of shear thinning intensity due to the presence of PCE, showing a high resistance to the shearing.

Magneto-rheological responses of cement paste with nano-Fe 3 O 4 3.2.1. Evolution of viscoelastic properties
The developments of storage modulus and loss modulus of the cement paste with w/c of 0.4 and nano-Fe 3 O 4 particles of 3 wt% are shown in Fig. 6. In the absence of magnetic field, the storage modulus was always higher than the loss modulus, indicating that the solid-like property dominates the liquid-like behavior during the entire timesweep test. Both storage modulus and loss modulus increased over time, but the storage modulus showed relatively high increase rate. This points to a gradual enhancement of the solid-like property, probably due to the multiple effects of flocculation, thixotropy and slight chemical hydration reactions [38,39]. Strong inter-particle interaction forces, dominating the Brownian motion and inertial forces [38,40], lead to formation of flocculated structures. This is reflected by the remarkable increase in the storage modulus at very early age. Furthermore, C-S-H links and bridges between cement particles are continuously formed with the progress of cement hydration. As a result, the rigidity and stiffness of the cement-based suspensions are consolidated, exhibiting a gradual increase in storage modulus with nearly constant increase rate.
In the presence of an external magnetic field, it can be observed that the cement paste containing nano-Fe 3 O 4 particles showed obvious magneto-responses, as applying magnetic field evidently affected the evolution of the storage modulus and loss modulus. More specifically, the storage modulus showed a slight increase immediately after applying the magnetic field and then dramatically increased with magnetization time. This can be explained by the formation of magnetic clusters of nano-Fe 3 O 4 particles under magnetic field [41]. The increase rate of the storage modulus slowed down after about 150 s, nevertheless reaching G' values that are significantly higher than that obtained without magnetic field. The linear increase of storage modulus represents the enhancement of C-S-H connections between flocculated structure due to chemical hydration of cement particles [37,42]. The equivalent increase rate of the storage modulus at steady state indicates that applying the external magnetic field has negligible influence on the intensity of C-S-H links between cement particles.
The loss modulus of cement paste containing nano-Fe 3 O 4 particles also showed distinct evolution trends in the absence and presence of the external magnetic field. Without the magnetic field, the loss modulus slightly increased with increasing magnetization time. In the presence of the external magnetic field, however, the loss modulus increased first and then gradually decreased. Moreover, the loss modulus of the cement  Note: G' (LEVR) is the storage modulus at linear viscoelastic region. γ c is the critical strain. τ c,ys is the elastic limit yield stress. η pl is the viscosity at linear low shear rate region. paste was even higher than the storage modulus at very early age. This can be attributed to the micro-movement of the nanoparticles under external magnetic forces, which will be discussed through the relationship between storage modulus, loss modulus and phase angle.

Relationship between G ′ , G ′′ and phase angle
In the presence of an external magnetic field of 0.5 T, the representative evolutions of storage modulus (G ′ ), loss modulus (G ′′ ) and phase angle of the cement paste with w/c of 0.4 and nano-Fe 3 O 4 particles of 3 wt% are shown in Fig. 7.
At the initiation of the external magnetic field, i.e. t 0 , the loss modulus was higher than the storage modulus and the phase angle was close to 80 • . This indicates that the cement paste showed almost totally liquid-like behavior immediately after initiation of the external magnetic field, which is consistent with our previous study [25] as well as with Nair and Ferron [43]. This can be attributed to the displacement and movement of magnetic nanoparticles in cement paste medium under external magnetic field. Without the external magnetic field, the magnetic nanoparticles can be regarded as randomly distributed in cement paste medium. When the magnetic field is applied, the nano--Fe 3 O 4 particles will be magnetized and the magnetic dipoles have a potential to form chains and/or clusters in a very short time. During their displacement to form the magnetic clusters, the nanoparticles create a sort of mechanical micro-agitation, destroying the C-S-H bridges between cement particles, as schematized in Fig. 8 (a). Moreover, some possibly entrained water in the agglomerated cement clusters is released, which increases the content of free water. As a result, a more dispersed state is obtained after initiation of the external magnetic field. It should be noted here that most probably not all the nano-Fe 3 O 4 particles will contribute to the formation of the clusters, due to the resisting viscoelastic properties of the cement-based medium.
With increasing magnetization time, the cement paste gradually transitions from viscous state to elastic state, where the capacity of energy stored gradually increases and simultaneously part of the mechanical energy dissipates. This is reflected by the rapid increase in storage modulus, the decrease in phase angle and the slight increase in loss modulus. This could be explained by the particles distribution, as depicted in Fig. 8 (b). On the one hand, part of the remaining nanoparticles in the interstitial solution try to move to join the clusters under the magnetic force, and meanwhile, the cement particles disturbed by the moving nanoparticles will try to reach new equilibrium positions, resulting in a slight increase in the loss modulus. On the other hand, the interactions between the magnetic clusters are improved, and new bridges and links between cement particles are gradually re-formed due to the colloidal interactions and cement hydration, which enhances the elastic property. At t 1 , the storage modulus was equal to the loss modulus and the phase angle was 45 • , indicating that the elastic-solid property starts to dominate the viscous-liquid property.
When the elastic-solid property reaches a threshold (t 2 ), the number of nanoparticles contributing to the clusters reaches the maximum, and the cement particles arrive at their final equilibrium positions, as represented in Fig. 8 (c). Therefore, the energy dissipation becomes limited, and the loss modulus reaches a maximum. With the continuous magnetization, the solid-like behavior evolves and the loss modulus starts to decline. After a sufficiently long period of magnetization (e.g. t 3 ), the cement-based suspensions possess enough elastic property and the deformation energy is hardly dissipated. This is reflected by the slight decrease in phase angle and loss modulus. Since the C-S-H links and bridges gradually evolve over time, as shown in Fig. 8 (d), the storage modulus gradually increases with magnetization time. Overall, for the cement paste containing nano-Fe 3 O 4 particles, the application of an external magnetic field improves the liquid-like properties at very early age, and enhances the solid-like properties after enough long period of magnetization.  Fig. 6 was modified to Fig. 9 (b) to keep same coordinates with Fig. 9 (a). Under zero magnetic field, the reduction in w/c significantly increased the magnitude of storage modulus, indicating higher stiffness of cement paste with lower water content. This can be attributed to the higher solid fraction and particle contacts. Furthermore, the cement paste with lower w/c showed a faster flocculated structural formation. Indeed, shorter time was required for the cement paste with w/c of 0.35 to reach a stable state of storage modulus, which is in agreement with [37]. Under an external magnetic field of 0.5 T, both cement pastes exhibited pronounced magneto-rheological behavior but with different intensities. The difference of the storage modulus at steady increase state obtained between 0 T and 0.5 T decreased with the reduction of w/c. Certainly, the storage modulus after magnetization for 300 s increased about 2.2 times and 1.2 times for the cement paste with w/c of 0.4 and 0.35, respectively. All the specific time points, including t 1 when storage modulus is equal to loss modulus, t 2 when loss modulus reaches a peak and t 3 when loss modulus starts to be stabilized, were shortened with the w/c of the cement paste medium decreasing from 0.4 to 0.35.

Effect of cement paste medium on magneto-rheological responses
From the above results, it can be concluded that the cement paste with w/c of 0.4 showed more obvious magneto-rheological response than that with w/c of 0.35. This can be attributed to the relatively high stiffness of the cement paste with high solid concentration. According to Table 3, it can be seen that the elastic limit yield stress and viscosity of the cement paste with w/c of 0.35 (5.99 Pa and 10.65 Pa.s) were higher than that of cement paste with w/c of 0.4 (4.52 Pa and 7.21 Pa.s). This means that under a magnetic field with same strength, the cement paste with w/c of 0.35 exerts higher movement resistance to the nano-Fe 3 O 4 particles to form magnetic clusters than the cement paste with w/c of 0.4. Therefore, the interactions between the formed magnetic clusters are lowered with the decrease of w/c. Overall, for the same nano-Fe 3 O 4 particles concentration and without superplasticizer, the cement paste with higher solid fraction shows lower response to an external magnetic field. Fig. 10 shows the influence of PCE dosage of cement paste medium on the evolution of storage modulus under w/c of 0.35 and nano-Fe 3 O 4 content of 3 wt%. It should be mentioned that under zero magnetic field, the storage modulus of the cement paste with 0.2% PCE was higher than that of the cement paste without PCE (as can be seen by comparing Figs. 9 (a) and Fig. 10). This is in agreement with the oscillatory strain sweep test results in Table 3. Viewed as a whole, all the cement pastes with PCE seemed to exhibit unapparent responses to the external Fig. 7. Evolution of G ′ , G ′′ and phase angle for the cement paste under magnetic field of 0.5 T. magnetic field with 0.5 T. This can be explained by the high elastic limit yield stress and viscosity of the cement paste, as can be clearly found in Table 3. For the cement paste with 0.6% PCE, the storage modulus obtained under 0.5 T was slightly higher than that collected under zero magnetic field, especially after a longer period of magnetization (as can be seen from the inserted enlarged view in Fig. 10). This means that the cement paste with 0.6% PCE showed slight magneto-rheological response and magnetic clusters could be formed under the magnetic field. The slight increase of the storage modulus between 0 T and 0.5 T is probably due to the highly flowability of the suspension. Nevertheless, further research is required to study the interactions between nanoparticles and superplasticizer in cement-based suspensions under external magnetic field.

Validation: conceptual calculations
Under sufficiently strong magnetic field, the nano-Fe 3 O 4 particles in cement-based suspension have a potential to move to form magnetic clusters. In order to start moving after applying the magnetic field, the magneto-dynamic force between adjacent nano-Fe 3 O 4 particles should be higher than the resistance induced by the viscoelastic stress of the suspension. In this part, the estimated magneto-dynamic force and the   equilibrium movement velocity of the nanoparticles in the tested cement-based suspensions are tentatively calculated. It should be mentioned here that our aim is not to obtain the real numerical values of the magnetic force or movement velocity of nanoparticles in cement paste. Instead, hopefully the calculated parameters could provide some useful indicators for the rheological responses of a cementitious paste to an external magnetic field.

Magneto-dynamic force between nano-Fe 3 O 4 particles
In the absence of an external magnetic field, the nano-Fe 3 O 4 particles can be regarded as randomly distributed in cement paste medium. Assuming that all the nanoparticles have the same constant dipole moment under magnetic field, that is, neglecting the mutual magnetic induction between the nanoparticles, the interaction energy between two spherical particles can be expressed as Eq. (2) [11]: where U ij is the interaction energy (J), m is the dipole moment (Am 2 ), μ 0 is the magnetic permeability of the medium (N/A 2 ), r ij is the center distance between two magnetic nanoparticles (m), and θ is the angle between the center line and the magnetic field direction, as shown in Fig. 11. In case of cement paste as the medium, μ 0 can be considered equal to the value of vacuum (4π × 10 − 7 N/A 2 ). When the centers of two nanoparticles align along the direction of the magnetic field, i.e. θ = 0, the magneto-dynamic force shows the maximum value: where the dipole moment m is related to the nature of the nanoparticles and the magnetic field strength, which can be expressed as: where d is the average particle size of the nanoparticles (m). ρ and M are the density (kg/m 3 ) and the magnetization per unit mass (Am 2 /kg) of the magnetic nanoparticles, respectively. It is to be mentioned that the calculated magnetic force is only intended as a representative measure for the effect of the applied magnetic field on two magnetic nanoparticles, instead of the real evolving force while moving in the paste. Indeed, nanoparticles in cement-based suspensions will experience mutual magnetic forces from surrounding particles. With the given expression, an estimation value is obtained that can be used as a quantitative parameter in further evaluation of the magneto-rheological behavior of the cement paste including magnetic nanoparticles.
Comparing the magneto-dynamic force to the resistance force induced by the viscoelastic stress of the suspension, a dimensionless parameter defined as magnetic yield parameter [9] can be obtained: Assuming that all the nanoparticles are arranged in the voids between cement particles as cubic order with same inter-particle distance (h (m)), as presented in Fig. 12, the volume fraction of the nanoparticles with average particle size of d in a cubic cell is defined as: Thus, the center distance between two neighboring magnetic nanoparticles is expressed as: Substituting Eq. (7) in the above Eq. (5), the magnetic yield parameter can be modified as follows: where τ vs is the viscoelastic stress of the suspension (Pa). The volume fraction of the nanoparticles in the voids between cement particles (φ MNPs ) can be calculated by the following equation: where φ C is the volume fraction of cement (%). V MNPs and V total are the volume of nanoparticles and total paste (kg/m 3 ), respectively. Theoretically, when Y M * > 1, the magneto-dynamic force is higher than the resistance force, magnetic chains or clusters can be formed and the suspension will show significant magneto-rheological response, while Y M * < 1 means that the suspension prevents the formation of clusters structure [11]. It can be clearly seen that the magnitude of the modified magnetic yield parameter depends on the concentration and physical properties of the nanoparticles as well as the viscoelastic stress of the suspension. Fig. 11. Schematic diagram of two magnetic nanoparticles in a homogeneous magnetic field.

Movement velocity of magnetic nanoparticles
For a spherical particle settling in a Bingham plastic fluid under gravitational force, He et al. [44] derived the viscous drag equation which can be expressed as: The equilibrium velocity of the spherical particle can be calculated by equating the gravitational and buoyant force to the viscous drag equation. In the case of nano-Fe 3 O 4 incorporated cement paste under an external magnetic field, the magnetic force plays a comparable role to the gravitational force. When the magnetic force is higher than the resistance induced by the viscoelastic stress of the suspension (Y M * > 1), similarly, the magnetic nanoparticles in equilibrium can be considered to move at constant velocity in the interstitial medium. Assuming that the flow behavior induced by magnetic field follows Bingham law, the equilibrium velocity can be estimated by equalizing magnitude the magneto-dynamic force and the drag force: Or in an explicit way as: where v is the movement velocity of nanoparticles (m/s), τ pl and η pl are the Bingham yield stress (Pa) and the plastic viscosity (Pa.s) of the suspension, respectively. It can be seen that the estimated movement velocity of a magnetic nanoparticle in cement-based suspensions is dependent on the properties of the nanoparticles (particle size, density, concentration and magnetic properties) and the Bingham yield stress and plastic viscosity of the paste. Again, the conceptual velocity estimation is considered as an indicator representing the movement between two neighboring nanoparticles, not the actual evolving velocity while moving in the suspension.

Discussion
According to our hypothesis, the moving magnetic nanoparticles immediately after application of the external magnetic field destroy the early C-S-H links between cement particles and then agglomerate to form chains or clusters. The intensity of C-S-H bridges between cement grains can be characterized by the smallest critical strain with several hundredths of % [39]. Given the rapid response time of cement pastes with nano-Fe 3 O 4 to a magnetic field, the elastic limit yield stress corresponding to the end of the linear viscoelastic region (without magnetic field) is selected as the viscoelastic stress of the paste in Eq. (8) to calculate the magnetic yield parameter. When the magneto-dynamic force overcomes the contacts between cement particles, the cement paste is postulated to exhibit slight flow behavior due to the micro-agitation effect of the moving nanoparticles. In other words, the shear rate of the flowing paste induced by the magnetic force is regarded to be small-scale. In this case, the viscosity at linear low shear rate region is selected for the calculation of the movement velocity of the nanoparticles. For the Bingham yield stress in Eq. (12), it could be selected from the following calculations. Based on Eq. (8), the critical magnetic yield parameter (i.e. Y M * = 1) is derived as: At zero movement velocity, the critical Bingham yield stress can be derived as: For reasons of consistency, having a zero velocity in the case of Y M * = 1, the term τ pl in Eq. (12) is thus assumed to be one third of the elastic limit yield stress where the breakage of C-S-H bridges occurs. Based on the aforementioned assumptions and selections of relevant parameters, the estimated magnetic yield parameter and movement velocity of nanoparticles for all the cement pastes under magnetic field of 0.5 T are listed in Table 4.
For the cement paste with w/c of 0.4 and nano-Fe 3 O 4 particles of 3 wt%, it can be clearly seen that the magnetic yield parameter is much larger than 1 and the movement velocity of the nanoparticles is sufficiently large compared to the estimated average distance between neighboring nanoparticles (h). This indicates that the nano-Fe 3 O 4 particles can move to connect with each other in a very short time if a magnetic field with 0.5 T was applied. The calculated parameters provide a valuable evidence for the fast movement of nano-Fe 3 O 4 particles in the cement paste under the magnetic field of 0.5 T. Reducing w/c resulted in a decrease in the magnetic yield parameter and the movement velocity, indicating that it is more difficult for nanoparticles to form magnetic clusters. The magnetic yield parameter of cementitious paste with 0.2% PCE was lower than 1, indicating that the nano-Fe 3 O 4 particles are hardly to move in the paste medium under the magnetic field with 0.5 T. For cement paste with higher PCE content, taking 0.6% as an example, the magnetic yield parameter was slightly higher than 1. This indicates that some nano-Fe 3 O 4 particles were able to break down the C-S-H bridges between cement particles and the cement paste could exhibit rheological response to the external magnetic field. All the calculated parameters are in good agreement with the experimental results. The calculated magnetic yield parameter and movement velocity are useful indicators to describe the extent of magneto-rheological responses of cement paste containing nano-Fe 3 O 4 particles.

Conclusions
In the present study, the magneto-rheological responses of cement paste with nano-Fe 3 O 4 particles as well as the influences of cement paste medium were investigated. Conceptual equations about magnetodynamic force and movement velocity of nanoparticles dispersed in cement paste were derived. Based on the results and discussion, the following conclusions can be reached: (1) Applying an external magnetic field promotes nano-Fe 3 O 4 particles to form chains or clusters, creating a sort of mechanical micro-agitation effect. This action probably destroys early C-S-H bridges between cement particles, further releasing entrained water in agglomerated cement clusters. Therefore, cement paste containing nano-Fe 3 O 4 particles shows liquid-like behavior immediately after initiation of the external magnetic field. (2) After longer magnetization period, cement paste with nano-Fe 3 O 4 particles gradually transitions from viscous state to elastic state, most probably due to the improvement of interactions between magnetic clusters and the regeneration of C-S-H bridges between cement particles. The cement paste containing magnetic nanoparticles under an external magnetic field shows enhanced stiffness compared to the paste without magnetic field owing to the presence of magnetic clusters. (3) Without superplasticizer, the magneto-rheological responses of cement paste containing nano-Fe 3 O 4 particles are weakened with the decrease of w/c. At fixed w/c, the cement paste with low dosage of PCE shows negligible magneto-rheological responses due to the high elastic limit yield stress and viscosity of the cement paste. (4) The estimated magnetic yield parameter and the movement velocity of the nanoparticles in cement-based suspensions under magnetic field can be used as relevant indicators to describe the extent of magneto-rheological responses of cement paste containing nano-Fe 3 O 4 particles.

Declaration of competing interest
The authors declared that we have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.