provide all the literature and papers for that matter “ Magnetophoresis under different magnetic field gradients”

## Fundamentals of high gradient magnetic separation (HGMS)

Magnetic nanoparticles which are abbreviated as MNPs have emerged as one of the nanomaterials that are most volatile with high environmental and biomedical application potentials. Some of the ways in which magnetic nanoparticles are used for the purposes of separation include MNPs that are surface-functionalized are dispersed initially into solution possessing compounds targeted, hence the magnetic nanoparticles can be attached onto the compounds above-mentioned by non-specific or specific bending. Subsequently, the compounds that are MNP-tagged are directed to a specific solution or withdrawn from the solution in a controlled way through magnetic field applied externally.

This arrangement enables the separation of compounds according to their magnetic properties method referred to as Magnetophoresis that entails the MNPs motion which is controlled by magnetic field externally applied according to the surrounding fluid. There are many benefits involved when using the MNPs in promoting the biological components separation than the convention separation processes. Nevertheless, since MNPs are tiny, their collection from the media surrounding imposed by a huge hindrance because of the excitement of their pathway of magnetophoretic by viscous drag and thermal energy. Hence, the magnetic field of a high gradient is used in order for the MNPs to achieve a huge force of magnetophoresis to overwhelm the opposing forces and energy of randomization and attain reparation in a time scale that is reasonable. This process is referred to as HGMS which is an abbreviation of high gradient magnetic separation (Andreu, 2012).

The LGMS, low gradient magnetic separation is a separation process that was recently implemented by Yavuz who verified the viability of magnetic field of low gradient produced by a permanent magnet in the gathering of 4 nm nanocrystals of superparamagnetic magnetite. The LGMS is more advantageous than the HGMS due to its simplicity and cost-effectiveness and also accelerated the collection of MNP and reduction of separation duration. The current stage of research efforts is directed to the study of the fundamental principles which describe transport the behaviour of MNPs under LGMS (Barbero, 2012).

The morphology of the aggregation of MNP through LGMS has been explained and investigated by incorporating interaction or magnet into the standard DLVO theory which is an abbreviation of Derjaguin-Landau-Verwey-Overbeek. Furthermore, the transient behaviour of aggregation of MNP upon the use of exterior magnetic field has been simulated and studies. Hydrodynamic effect is a phenomenon in which there is emergence of convective flow as a result of the two-way transfer of momentum between the surrounding fluid and the magnetic particles.

## Low gradient magnetic separation (LGMS)

The hydrodynamic effect is noted specifically in the magnetic particles magnetophoresis under inhomogeneous magnetic field gradient. Hydrodynamic effect plays a significant role in governing the dynamic behaviour of the low gradient magnetic separation process. Owing to the momentum transfer between the surrounding fluid and moving magnetic particles, continuous sweeping flow is produced within the whole of the solution of magnetic particle that is subjected to LGMS. Hydrodynamic effect plays a significant role in dictating the low-field-gradient magnetophoresis separation kinetics (Bennelmekki, 2010).

The underlying principles of the hydrodynamically driven low gradient magnetic separation (LGMS) still remains unclear. In order to design magnetic separator, the understanding towards the underlying principles of hydrodynamically driven LGMS is a must. The hydrodynamic effect has been identified to be useful in accelerating the magnetic separation rate of magnetic particles. Real-time magnetic separator is dealing with fluid with wide range of viscosity such as biological fluids like molecules of biologically active compounds, cancer cells, parasites, viruses, and bacteria. Therefore, it is extremely important to understand the underlying principle of hydrodynamically driven magnetophoresis for solution of different viscosity, which is now still remained unexplored by the researchers (Barbero, 2012).

The objectives of this project are:

- To experimentally evaluate the effect of magnetic field and viscosity on the intensity of magnetophoresis induced connection for the LGMS, low gradient magnetic separation.
- To evaluate the effect of magnetic field and viscosity on the intensity of magnetophoresis induced connection for the LGMS, low gradient magnetic separation through simulation.

Magnetophoresis is the process through which the particle of magnet move with respect to their fluid surrounding while responding to a magnetic field externally applied. Magnetophoresis process has found numerous applications in the mining industry and mineral processing. Currently, every conventional technology operating on separation driven by magnetophoresis, which is implemented widely for engineering uses, are majorly functioned in the columns of separation described by high gradients of the magnetic field. This procedure is commonly referred to as HGMS, high gradient field separation. The theoretical calculation carried out by the use of magnetic, viscosity, geometry, and fluid flow properties show that the gradient of the magnetic field of the order 10^{4} to 10^{5} T/m is required for effective capture and quick elimination of the magnetic particles dispersed (Camacho, 2010).

In the process of HGMS, the gradient of the magnetic field is normally produced by magnetic field distortion which is normally imposed by the electromagnet through packing materials that are magnetizable which fill the column of bed that is packed. The generated gradient of magnetic field in this method is highly localized and exceedingly intense, which grants specifically near the fibres of steel wool where there is trapping of particles. Nevertheless, this strategy is not appropriate in numerous magnetic nanoparticle applications in solution like biomedical applications since they strictly require no chain formation even under strong fields like hyperthermia treatment or magnetic resonance imaging contrast agent. The approach preferred in such cases is the incorporation of the permanent magnet, which is situated outside the suspension of the particle for a distal motion regulation of the particle in non-contact mode. This approach is referred to as low gradient magnetic separation, which has been applied broadly by chemist and engineers dealing in chemicals to recollect the magnetic receptive materials in the elimination of contaminants like microalgae, toxic organic compound, heavy metals, and dye (Camacho, 2009).

## Role of magnetic particle sizes and concentration in separation kinetics

However, the implementation of LGMS in the real-time application is very technically challenging since MNPs undergoes a magnetic field gradient (ΔB< 100 T/m) that is much lower hence rendering the MNPs isolation to be rapid beyond the possibility bound. Hence new strategies are required so as to bring LGMS into practicability realm. The LGMS strategies should have the ability to incorporate different physical effects which are appropriate to the MNPs magnetophoresis rate of separation that is theoretically expected. The current study presents two kinds of effects that are different which have the ability to promote the separation rate of magnetophoresis of LGMS, these effects include hydrodynamic effect and cooperative effect (Camacho, 2011).

The size of the magnetic particles plays a significant role in controlling the kinetics of LGMS as shown in the equation below:

From the equation above, the magnitude of Fm experienced by a magnetic particle is linearly proportional to the cube of r. Therefore, the balance of force between Fd and Fm shows that the magnetophoretic velocity which influences the time of separation, changes direction with respect to r^{2}. Hence in the process of LGMS, particles with large sizes are separated initially before those particles with smaller sizes when they are under the influence of same magnetic field. There are numerous literatures relating to the efficiency of MS to the size of magnetic particles. Recently, Lin proved that 180mm magnetic particles can be labelled successfully in less than two minutes within a magnetic bioseparator of average magnetic field gradient of about 90T/m (Jiang, 2008).

When a similar experiment was performed by the use of magnetic particles of sizes 30nm, the maximum duration of MS was noted to be 60 minutes, which is approximately 30 times slower compared to the process of MS that used magnetic particles of sizes 180nm. Therefore, the magnetic particles of large sizes are preferential for fast screening or detection applications. Under this situation, the interaction between antigens (from targets) and antibody (from magnetic particles) would result in the formation of magnetic particles. The outcome of the studies above shows the significance of selectin magnetic particles of appropriate sizes for successful implementation of MS process in biomedical diagnosing (Zeisberger, 2012).

Apart from the sizes of the particles, the separation kinetics of magnetic separation process is also dependent on the magnetic particles concentration. This occurrence is endorsed to the corporative nature of the system of magnetic particle in which the magnetic particles tend to collectively move and aggregate towards the source of the magnet upon exposure to an exterior magnetic field. The aggregation of the particles is initiated by the magnetic interaction between the moments of the magnetic dipole by every magnetic particle (Zborowski, 2015).

## Hydrodynamic effects in LGMS

Hydrodynamic effect originates from the interaction between MNPs and fluid which dictates the process of LGMS and it can be investigated from the simulation results of the hydrodynamically interacting magnetophoresis model and the Non-MNP/fluid interacting model. There are two models that have been established to anticipate the kinetic profile separation of magnetophoresis in the experimental setup, these include hydrodynamically interacting and non-fluid/MNPs fluid interacting magnetophoresis models. The predicted results from these two models can then be related with the outcome for the experiments to authenticate the precision of the models and therefore validate the significance of the hydrodynamic interface in the MNPs magnetophoresis of the low gradient (Jiang, 2008).

There are numerous assumptions that have been made during the model development, these assumptions include that the gradient of the magnetic flux density flux's vertical component in the whole of the solution of MNPs that is being subjected to magnetophoresis, are more dominant than the horizontal components, The MNPs motion does not result in perturbation of fluid flow such that the fluid surrounding persist constantly in the whole of magnetophoresis, the migration of magnetophoresis of MNPs is the solution does not result from motion that is slinking that obeys Stokes' law. The shape of MNPs are spherical and are made of core of a magnet bordered by a PEG layer that is non-magnetic, the interaction between MNPs/MNPs is negligible because of the nature of non-interaction of the particles, and lastly, the MNPs distribution is uniform in the whole of the solution before the magnetic field is applied (Khajeh, 2013).

There are four forces acting on the MNPs under an externally applied magnetic field which govern the MNPs motion in the MNPs solution. These forces include the Brownian force which induces the MNPs diffusion along the gradient of concentration of MNPs that initiates from thermal motion, viscous drag force which is as a result of resistance brought by the relative MNPs in solution movement, magnetic force which is as a result of the moment of magnetic dipole response in MNPs to the magnetic field applied externally, and gravitational force (Kowalczyk, 2011). The behaviour of MNPs in terms of transport in the fluid in the entire magnetophoresis caused by the combination of fluid advection and diffusion effects can be expressed by the equation of drift-diffusion shown below:

Where:

D = diffusivity of MNPs in solution

u = magnetophoretic MNPs velocity

c = MNPs solution concentration

The relationship between the applied strength of the field of the magnet and the mass magnetization of MNPs can be determined through fitting the curve of magnetization which is acquired from VSM to the equation below:

## Models to predict magnetophoresis in LGMS

Where:

L = [L(x) = coth (x) - 1/x]; Langevin function

M = magnetic moment strength for a single magnetic dipole

Ms = magnetization saturation per unit MNPs mass

The force of magnet acting on an MNP can be determined as a function of distance along the vertical or axial direction from the pole of the magnet as shown below:

The experienced force of viscous drag by MNP that is under low Reynold number environment or in motion in a viscous fluid can be formulated by Stroke’s law, which is formulated by:

Where u_{z}, u_{y}, an u_{x} are z, y, and x in equation (2.5) are the MNPs magnetophoretic velocity components respectively. However, e_{z} and e_{x} are the unit vectors aiming to the z and x directions (Watarai, 2002).

The equation 2.6 below can be used in predicting the transient behaviour and produce a kinetic profile of the magnetophoresis separation process.

This section discusses the process of modelling the magnetophoresis kinetics in the presence of conventional magnetism. Before the formulation of the different model deliberated in this section, it is critical to evaluate the model of conventional magnetophoresis as well as its disadvantages. By considering then situations in both (a) and (b) in Figure 1 above where the interaction of antiparticle magnetic dipole-dipole can be ignored. The assumption made is that the system is composed of non-interacting particles (Faraudo, 2010).

This model describes actual time LGMS successfully with a constant gradient of the magnetic field which has anticipated the separation of magnetophoresis accurately times done with a Figure 1a arrangement using systems that are diluted with less interaction between particles. As denoted by the analytical, simulation, and experiments theory, the process of separation, in this case, continues as shown in part (a). The movement of the particles are in a radial direction toward the system's walls, and a region which is clear is established in the system's centre whose particle front is advancing toward the wall. The limitation of this process is that it fails to anticipate the time of separation of magnetophoresis with setup portrayed in the part (b) of the figure above, which resembles a gradient of the magnetic field that is inhomogeneous (Faraudo, 2013).

In a LGMS with one magnet, as portrayed in parts (b), equation (1.2) denotes that the velocity of magnetophoresis of the particles will reduce with the vertical shift from the magnet z, because the gradient of magnetic field and strength of magnetic field decreases due to increase in z as shown in part (c). This situation denotes that, as time elapses, any particle will become inhomogeneous that was originally homogeneous distribution, with lower concentration at the bottom and a higher concentration at the top (Friedman, 2005).

## Conclusion

Since the experienced magnetic force by MNPs is proportional directly to the gradient of magnetic field, MNPs situated auxiliary from the magnet undergoes a substantial deficit in pulling by the magnet, and the model anticipates extraordinary ineffective an slow separation of magnetophoresis. Despite that, for the MNP aggregate of 200nm which is 1.5cm from the magnet, the time of separation is hypothetically determined to be 43 minutes which is three times longer when compared to the experimental observation (Friedman, 2005).

In the model above, the assumption made is that the fluid is continuous and persist without alteration by MNPs motion in the entire process of magnetophoresis. In this model, the assumption of stagnant motion has been relaxed in the sense that the flow of fluid could be produced within the solution of MNPs because of fluid/MNPs interaction. The MNPs magnetophoresis is also expressed by the equation of drift-diffusion comparable to the non-fluid/MNPs interaction magnetophoresis model (Krishnan, 2010). The convective MNPs solution motion is determined by Navier-Stokes and continuity equations:

f_{m} = volumetric force of magnet acting on the solution of MNPs

p = absolute pressure

? = MNPs solution density

u = velocity vector of the MNPs solution

By the inclusion of Navier-Stokes equation into this model, momentum transfer as a result of the interaction of fluid/MNPs has been included accordingly. The above equation governs the transfer of momentum within the solution of MNPs by joining its spatial profile of fluid flow to the viscosity and the forces that are external are enacted on it, majorly gravitational and magnetic forces. Moreover, the solution of MNPs is assumed to be a fluid that is incompressible, which is operated under the pressure of the atmosphere. The final term in the equation (2.7) denotes the force of magnet acting on the unit solution of MNPs volume due to the application of a magnetic field externally (Latham, 2009). The magnetization volume of MNPs solution, denoted by M, depending on the MNPs concentration denoted by c, in the solution:

M = cM _{p, m}

Where c.M _{p, m} = Magnetization mass of MNPs

2.4 Effect of Viscosity on Magnetic Separation

It has been established that colloids have a tendency to aggregate in the presence of polyallylamine hydrochloride (PAH) in the previous study. This aggregation is as a result of electrostatic forces put in place by bridges of polymer developing between the particles, and these are found to produce forces. The velocity measured as a function of the concentration of PAH with the magnet in position produced a graph shown in the figure below:

## References

The results in figure 5 above shows aggregates velocity produced as the function of the concentration of PAH, where the extraction of velocity was done through drawing a linear fit to the first section of the curve of transmittance. It is observed that initially, the velocity escalates with the increase in the concentration of PAH, apparently as a result of the large aggregates formation. Nevertheless, the velocity has significantly decreased at 5 g/L and it can be noted that it is smaller than that noted in the PAH presence at 10g/L (Martinez, 2012). This observation explains the effects of viscosity of magnetophoresis which can be clarified by the fact that for the high concentration of PAH molecules fully cover each particle, hence prevention of extra aggregation. However, the solution viscosity escalates with the concentration of PAH, hence minimizing the velocity equation 3.1 below:

Where:

η=viscosity of the surrounding liquid at room temperature = 0.8 × 10−3 Pa s

R = Radius of each particle

Δ? = difference in density between the surrounding liquid and the particle

Uz = particle velocity in the z-direction

f= constant = 6 π

dB/dz = magnetic field gradient

χ=susceptivity of the particles

μ=permeability of water

The numerical simulations can be used to depict the trajectory of magnetic particles towards the permanent magnet. The simulations can be used in determining the collection volume with a time-dependent shape and size, which determines the number of particles that can be captured from the fluid in a specific moment. The viscosity of the fluid strongly determines the velocity of the magnetic particles towards the magnet, hence the collection volume after a specific moment. In high-viscous fluids, the balance between magnetic force and drag leads to the low velocity of the particles, which in practical solution may regulate the collection volume.

Therefore, the impact of viscosity is of critical significance. In this research, the viscosity range was selected to reflect the viscosity of the healthy human synovial fluid and the reduction by an order of magnitude observed in the OA-affected synovial fluid. The viscosity variation shows the significant practical impact on the time-of-flight. A particle positioned I mm away from the magnet reaches the surface after a few seconds when in water, however, the same particle may need 1000s when in glycerol (Wang, 2012).

A second study investigates the effect of viscosity on the collection volume (intensity of induced convection) of the magnetic particles on the collection time. To determine the intensity of the induced convection at a given time experimentally, the permanent magnet is allowed to collect particles from a volume of solution with a known concentration. The number of particles collected is indirectly deduced from the number of particles uncollected which remain in the solution. The simulation results show that more than 120,000 particles can be collected after 120 seconds in a fluid with the viscosity of a healthy-knee synovial joint.

The dry experiment can be performed to visually trace the motion of a fluid during the process of magnetophoresis. Initially, 300mg/L of concentrated methylene blue was carefully introduced to the bottom of a cuvette containing 3mL if the solution of MNPs by the use of the syringe. The MNPs solution was then subjected to the magnetophoresis and the movement of the dye in the solution can then be captured. Since the molecules of the dye are highly positively charged and MNPs have an average zeta potential of -10mV, it is assumed that some of the molecules of the dye may adhere to the MNPs as a result of the electrostatic interaction. The figure below shows the magnetophoresis experimental setup:

Nevertheless, since the molecules of MB are available in excess, there should be a substantial quantity of free suspended molecules of dye which can trace the motion of the fluid within the solution of MNPs for visualization of magnetophoresis. This procedure was performed by the use of MNPs solution with the following concentration; 100Mg/L, 50Mg/L, 20Mg/L, 10Mg/L and 5Mg/L. The motion of the dye in the solution with different MNPS concentration under magnetophoresis can then be compared (Saunders, 2009).

Initial and Boundary Conditions: The assumption made is the MNPs concentration is uniform in the entire solution and the fluid is stagnant at the beginning of the magnetophoresis. There is no application of slip boundary conditions along the MNPS solution boundaries where the velocity of the fluid is always zero. The pressure at the surface of the MNPs solution is set equal to be equal to the atmospheric pressure. All boundaries are assumed to be rigid and hence there is no flow of MNPs across the boundaries. It was noted that the MNPs solution concentration exponentially decays with time under an external magnetic field and conforms the equation below:

When the above equations are plotted as shown below, the results show a perfect fit of data into the linear equation which passes through the origin with the regression coefficient being greater than 0.99.

This has illustrated clearly that the concentration profile is confirming the first order kinetics in the equation (2.9). This phenomenon is as a result of the limitation of the UV-vis spectrophotometer in the detection of the low concentration of MNPs solution in the duration of the experiment. Just like the MNPs solution concentration, MNPs outlet also exponentially decays with time as shown in the figure above.

Numerical Simulation: Chemical Reaction Engineering Modules and Computational Fluid Dynamics were employed in the work of computation to solve this model in two-dimensional space. Navier-Stokes and Continuity equations are found in Laminar flow Physics while drift-diffusion equations are contained in Transport of Diluted Species physics are both employed in this section. A 1*3 cm rectangle was constructed to represent the solution of MNPs filled in the disposable cuvette. The rectangular domain was then filled with 230 boundary elements and 3874 quadrilateral meshes as shown in the figure below:

Time-dependent solver was used in solving the model in the time span of 0 to 4000 minutes and time step as long as 10 seconds was adopted. The solution of the model was not able to converge under the default solver setting due to the highly non-linearly contributed by the magnetophoresis induced convection. This problem was manually solved by assigning the scaling factors to some critical dependent variables in this model. The absolute tolerance for the concentration of MNPs to halt the iteration was set as 0.0005. The simulated results are produced by COSMOL Multiphysics according to the model of hydrodynamically interacting magnetophoresis (Rebollo, 2011).

In the model of hydrodynamically interacting magnetophoresis, convection induced by magnetophoresis in governing the behaviour of MNPs in terms of movement under the field of the magnet. This is the major reason for the non-fluid/MNPs interacting magnetophoresis model failure to illustrate the process of real-time magnetophoresis. This model was established to anticipate the kinetic profile of the separation of the solution of MNPs going through low gradient magnetophoresis (Pankhurst, 2004). In the hydrodynamically interacting magnetophoresis model, the assumption made is that the fluid is constant and persist without alteration by MNPs motion in the entire process of magnetophoresis. In this model, the assumption of stagnant motion has been relaxed in the sense that the flow of fluid could be produced within the solution of MNPs because of fluid/MNPs interaction (Prakash, 2009).

The MNPs magnetophoresis is also controlled by the equation of drift-diffusion comparable to the non-fluid/MNPs interaction magnetophoresis model (Prakash, 2009). The convective MNPs solution motion is determined by Navier-Stokes and continuity equations. By the inclusion of equation of Navier-Stokes into this model, transfer of momentum as a result of the interaction of fluid/MNPs has been included accordingly. The Navier-Stokes and continuity equations govern the transfer of momentum within the solution of MNPs by joining its spatial profile of fluid flow to the viscosity and the forces that are external are enforced on it, majorly gravitational and magnetic forces (Rebollo, 2011). Moreover, the solution of MNPs is assumed to be a fluid that is incompressible, which is effective under the pressure of the atmosphere. The final term in the Navier-Stokes and continuity equations denotes the force of magnet acting on the unit solution of MNPs volume due to the application of a magnetic field externally (Pankhurst, 2004).

Under the effect of an externally magnetic field produced by a cylindrical permanent magnet of 1.5cm in length and 1.4cm in diameter with the magnetization of 1.45T, the MNPs suspended were attracted towards the bottom of the solution by the force of the magnet, which reduced the concentration of MNPs in the solution in tandem with progression time. The figure below shows that the expected normalized separation kinetic profiles of the MNPs solution almost collapse into the single curve, despite the initial concentration of particles used:

This observation shows that the effects of concentration majorly the MNPs/MNPs interaction, are important in regulating the kinetics of magnetophoresis under LGMS. Logically, the interaction of MNPs/MNPs is more intense in a highly concentrated solution of MNPs as a result of the higher frequency of collision, which consequently results in the formation of larger aggregates within a shorter duration (Morimoto, 2008).

Larger aggregates are expected to be more magnetically responsive, and hence attain a higher velocity of magnetophoresis and accelerate the MNPs collection under magnetophoresis. Such concentration dependence on the separation of the kinetic profile has been noted in the previous study, in which there was the application of intensive interaction of MNPs systems. Nevertheless, the interdependence of the separation kinetic profile on the concentration of MNPs shows that the concentration of MNPs range used in this study is still far below the critical concentration of MNPs in which the interactions between antiparticles begin to become crucial (Martinez, 2012).

The magnetic interaction between MNPs is relevant only when the aggregate parameter, N* is larger than unity according to the theory developed by Andreu and coworkers. It can be concluded that the magnetic interaction between reversible aggregates and MNPs is negligible since the values of N* are below unity within the range of concentration of 10mg/L to 100mg/L considered in the current research. Since the final objective of this research is to study the nature of the fluid/MNPs interaction under LGMS, this system of MNPs is ideal and appropriate for the present investigation because of the fact that the interaction of MNPs/MNPs is insignificant and can be omitted (Martinez, 2012). Coincidentally, the measured separation kinetic profiles at different positions in the entire solution of MNPs also collapsed into a single curve as shown in the figure below:

From the figure above, it can be observed that the MNPs were distributed uniformly in the whole of MNPs solution during the real-time process of magnetophoresis due to the concentration of MNPS at different positions are similar within the entire experimental time scale. In this instance, the solution of MNPs in the cuvette remains homogeneous while experiencing magnetophoresis (Lim, 2013). The captured time-lapse, while the MNPs solution is experiencing magnetophoresis, is shown in the figure below:

The observation made in this experiment provides the first evidence which suggests the significance of hydrodynamic effect associated with magnetophoresis.

In the non-magnetophoresis interaction of MNPs/fluid, the time-lapse images for the results of the simulation shown in the figure below predict the progressive clearing of MNPs at the bottom of the cuvette, where the gradient of magnetic flux density is the highest.

Logically, the results of the simulation displays this behaviour due to the spatial resolution of the gradient of magnetic flux density from the magnetic pole, which causes the MNPs that are positioned closer to the magnet to experience a much greater force of magnetophoresis and hence migrate at a faster velocity to the source of magnet compared to those situated further away from the magnet. For example, an MNP located 1mm away from the magnetic pole with a diameter of 30mm face experiences the magnetic flux density gradient of 93.8T/m, which corresponds to the force of magnetophoresis of 0.203 fN. The same particle experiences considerable weaker magnetophoresis force of 0.038fN as the distance of separation from the magnetic pole face increases to 10mm with the gradient of the magnetic flux density of 17.5T/m (Leun, 2004).

Therefore, MNPs that experience a greater force of magnetophoresis will move at a higher velocity and hence can be separated and captured from the solution at a faster rate. In this scenario, MNPs at the bottom section of the solution is collected much more rapidly from the aqueous environment as magnetophoresis starts, which is anticipated to develop a particle concentration gradient across the suspension to the top from the bottom. The outcome serves as the best indication in which the continued homogenization of the suspension of MNPs is not related to the interaction of MNPs/MNPs. Nevertheless, the simulation model of MNPs/fluid interaction magnetophoresis results contradicts the observation of the experiment, which shows homogeneity in the whole of the MNP solution in the entire duration (Leun, 2004).

There exists a big difference between the results of the magnetophoresis separation kinetic profiles acquired from the experiment and the results predicted by interacting magnetophoresis of MNP/fluids. The two primary difference the simulation and experimental results are as flows:

- The predicted collection time of MNPs was substantially longer than the results from the experiment. This observation shows that the failure of the classical model of non-fluid/MNPs interaction magnetophoresis in the prediction of the separation kinetic profile for the model system.
- MNPs were always distributed homogeneously in the whole of the solution in the experiment, while apparent non-consistency was noted in the results of the simulation model, which is indicated by the dependency location of the separation kinetic profile shown in the figure below:

This observation shows that the failure of the classical non-fluid/MNPs interaction magnetophoresis model in the prediction of the separation kinetic profile for the model system. The homogeneity of the solution of MNPs indicates that there is the driving force that distributes the MNPs in the entire solution during magnetophoresis. This driving force is possibly contributed by the fluid convection which is normally portrayed as a critical role in the mixing or agitation of a solution. This surrounding fluid must acquire momentum from the MNPs solution to initiate convection under magnetophoresis because the fluid surrounding is responsive non-magnetically (Jiang, 2008).

Hence there should be some type of interaction between fluid and MNPs so that the momentum from the moving MNPs can be transferred to the fluid surrounding and result in the occurrence of convection. Consequently, this finding has led to the belief that the hydrodynamic effects, which originates from the interaction of MNPs/fluid, maybe predominating factor in homogenizing the suspension of MNPs and later accelerates the MNPs magnetophoretic capture.

The dye experiment conducted to trace the motion of the fluid in the solution of MNP, while it is experiencing magnetophoresis. A control experiment was also conducted through the use of the blank solution. It was noted that that for the case of the control experiment, the dry injected at the bottom of the solution slowly diffused and filled up the entire solution gradually as a result of the thermal energy without any magnetophoresis occurring. For all other solution of MNPs, the dye moved upward relatively faster and then filled up the solution at a much faster rate under magnetophoresis (Birss, 2003).

The sudden migration of the dye in the solution of MNPs after its exposure to an external magnetic field further shows that convection is produced in the solution of MNPs during magnetophoresis. This convective flow induces the process of mixing and enhances further the dispersion of MNPs inside the solution and homogenized the suspension. Furthermore, the decline in the standard deviation of light intensity in the solution of MNPs as displayed in the figure below confirmed further the homogenization of the solution as time advances (Camacho, 2010).

From the figure above, the lower the light intensity standard deviation, the smaller the dispersion of light intensity and therefore, the more uniform the distribution of dye in the solution of MNPs. Additionally, it can be noted that the rate of dye homogenization increases with the MNPs solution concentration. Hence, according to this evaluation, convection is more vigorous in MNPs solution that is more concentrated when experiencing magnetophoresis, which is consistent with the displayed time-lapse images. From this observation, it can be presumed that convective motion, which takes place during the MNPs magnetophoresis, is also dependent on the MNPs concentration (Faraudo, 2010).

This exceptional feature of magnetophoresis, in which fluid convection is induced as a result of the interaction of MNP/fluid in the process, is not well recognized and is the aim of the following the discussion. Macroscopically, the occurrence of fluid convection during the MNPs solution magnetophoresis can be rationalized by the use of the concept of magnetic buoyancy. The magnetic buoyancy is the exerted force on an object that is immersed in the fluid, in which the fluid surrounding has higher volumetric magnetization than the object itself under the magnetic field applied externally. This concept of magnetic buoyancy has been demonstrated by the migration of non-magnetic particles, which are immersed in the solution of MNPs, in the contradictory direction to the source of the magnet when the solution of MNPs is subjected to magnetophoresis (Khajeh, 2013).

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