There is a way of clearing the MNPs progressively at the bottom of the cuvette based on the prediction of MNPS/fluid interacting model as shown in Figure 1 below, where the density gradient of the magnetic flux is the highest. Reasonably, the results of the simulation shows this behaviour due to the incomplete firmness of the magnetic flux density gradient from the magnetic pole, a magnetophoresis force is greatly experienced when the MNPs are situated nearer the magnet to experience thus migration takes place at a high velocity to the origin of magnetism than those situated far away the magnet (Andreu, 2012).
Figure 1: The velocity magnitude (m/s) of Magnetophoresis under different viscosity
The time lapse pictures is shown in the figure 1 above for MNPs solution produced as the simulation results interaction between magnetophoresis in non MNRPs/fluid for the initial 1000 seconds after they are exposed to the process of magnetophoresis. The colour of the simulation results at 0.2Pa. s shows the normalized concentration of the MNPs solution, which range from MNPs viscosity of 0.2Pa.s to 0.002 Pa. s of the MNPs concentration before and after subjecting the solution to the process of magnetophoresis (Barbero, 2012).
Magnetophoretic force of 0.203fN is experienced by MNP in case it is located 1mm away from the face of magnetic pole with a diameter of 30nm and it co rresponds to density gradient ΛB of 93.8 T/m for magnetic flux. In an evaluation, similar particles experiences substantially weaker force of magnetophoresis of 0.038 fN as the distance of separation from the face of magnetic pole upsurges to 10mm with the density gradient of the magnetic flux of 17.5 T/m. Consequently, in case magnetophoresis force is greatly experienced by MNPs, it will travel at a greater velocity, thus it can be separered as well as it be captured from the solution of MNPs at a faster rate (Bennelmekki, 2010). In this situation, MNPs at thebottommost section of the solution are gathered from an setting that is aqueous in nature at faster rate during the beginning of the magnetophoresis process, which is anticipated to produce concentration gradient of particles across the suspension to the topmost (low ΛB) starting at the bottommost (high ΛB) (Berne, 2006).
The interaction of MNPs/MNPs solution is not linked by the suspension of MNPs and this can be deduced by observing the experiment (Pankhurst, 2004, p. 78) . Though, the observation carried out from the experiment is being exposed by the results of the non MNPs/fluid interacting magnetophoresis model simulated, which shows homogeneity in the entire solution of MNPs throughout the duration. As a result, there exists a enormous difference between the magnetophoresis parting kinetic profiles predicted by the model above and the experimentation results acquired. (Birss, 2003). The two main dissimilarities concerning the results from simulation and experiment are articulated below: (1) A longer MNPs collection time of is anticipated by simulation unlike the results of the experiment and (2) in experiment, there was a consistent distribution of MNPs all over the solution as shown in Figure 2, while in the case of simulation model, therewas no consistency distribution of solution. (Borm, 2008).
Figure 2: The concentration profile of Magnetophoresis under one viscosity
For our model system, it was strangely observed that the determination of separation kinetic profile takes place by the failure of the classical non MNPs/fluid interacting magnetophoresis model (Rosensweig, 2005, p. 543). During magnetophoresis, it can be depected that there is a force enhancing the distribution of MNPs in the whole solution and this can be confirmed by the consistency MNPs solution. The force is possibly as a result of the convection of fluid, and is normally depicted as a important task in the mixing or agitation of a solution (Camacho, 2010). Since the adjacent fluid is responsive non-magnetically, momentum must be acquired from the solution of MNPs to start the process of convention. Consequently, this observation has resulted in the fluid/MNPs interaction which initiate the hydrodynamic effect, ought to be the outweighing element in standardizing the MNPs. (Camacho, 2011).
To monitor the movement of solution in MNPs, the dye tracing experiment was carried out while it is experiencing the process of magnetophoresis. A solution black in color was also used in conducting a control experiment and it was noted that there was a slow and a gradual diffusion of the dye from the bottommost until the solution was entirely coloured (Faraudo, 2010). There was fast upward movement of dye in other solutions of MNPs Some solutions of MNPs, the dye moved relatively fast upward until it is filled entirely under magnetophoresis as shown in the figure below
Figure 3: Captured dye motion of Magnetophoresis under different viscosities (Dye experiment)
The first row images show the the movement of dye motion exposed to an exterior magnetic field as used in controlled experiment. During magnetophoresis, it can be said that the convection is produced and this can be illustrated by unexpected dye movement in the MNPs after exposing it to external magnetic field (Andreu, 2012, p. 89). The process of mixing and homogenizing the is encouraged by the convective flow as well as enhancing MNPs diffusion inside the solution. In addition, the homogenization of dye is faster when the concentration of MNPs is higher due to the tougher convective flux in magnetophoresis (Furlani, 2007).
Furthermore, the drop in the light intensity standard deviation in the entire solution of MNPs, as shown in the figure below, additionally established the solution homogeneity as time lapses (Heinrich, 2007).
Figure 4: Evolution of light intensity standard deviation in the entire solution of MNPs (calculated from about 85 000 pixels) with time.
The investigation of the image was carried out by the use of ImageJ (Birss, 2003, p. 56]). The lower the light intensity standard deviation results when there is little dispersion of light, thus leading to a consistent spreading of the dye in the solution (Oberteuffer, 2006, p. 218). Lines are continuously introduced to guide the eyes. Additionally, it can be noted that the rate of dye homogenization upsurges when the solution is concentrated. Therefore, MNPs solution which is highly concentrated has a vigorous convection thus magnetophoresis is experienced. (Helseth, 2007).
The observation done shows that the convective motion relies on how concentrated is the solution MNPs. This exceptional characteristic of magnetophoresis, in which fluid convection is induced as a consequence of the fluid/MNPs interaction in the process entirely is not well acknowledged and is the objective of the subsequent argument (Oberteuffer, 2006, p. 67). Macroscopically, the occurrence of fluid convection during the MNPs magnetophoresis can be rationalized by the use of the concept of magnetic buoyancy (Holman, 2008)
Figure 5: Immersing an object in a low magnetization fluid volume shown to an exterior magnetic field, the body will end up to a region having high density of magnetic flux. The object will undergo a negative magnetic force which drives it to a position where the magnetic flux density is relatively lower in case the neighbouring fluid has a responsive magnetically unlike the immersed fluid and the magnetic buoyancy is simply the opposite force (Israelachvili, 2008).
This concept of magnetic buoyancy is illustrated by the movement molecules not magnetic in nature are immersed in a solution of MNPs (Morimoto, 2008, p. 126). By taking the fundamental the principle of buoyancy as a orientation, there is an analogy that can be drawn between the magnetophoresis of MNPs under the experiment conditions and the natural convection of a fluid above a horizontal heating plate (Jiang, 2008). When a fluid is thermally in contact with a hot horizontal plate, the temperature of the layer of fluid in the vicinity of the contacted surface increases, and the density of the fluid decreases and experiences lower gravitational force per unit volume compared to the fluid surrounding. Therefore, the bottom layer of the fluid is driven upwards by the force of gravitational buoyancy (Khajeh, 2013).
MNPs at the bottom of the solution are continuously depleted since MNPs tend to be attracted towards the section with higher magnetic flux density (captured on the cuvette wall) because of the magnetophoretic collection (Bennelmekki, 2010, p. 658). This condition results in a temporary reduction in the concentration of MNPs and hence decrease of volumetric magnetization of the bottom section of the solution (Kowalczyk, 2011). Subsequently, the magnetic force per unit volume experienced by this section of MNPs solution is relatively lower than that of the upper section of the MNPs solution. Consequently, the solution of MNPs with lower magnetization volume is driven upwards by the force of magnetic buoyancy so that the fluid at the upper section moves down to replace it. In this way convective current is produced in the solution of MNPs during magnetophoresis, which is consistent with the experimental observation in Figure 3 (Latham, 2009).
In conjunction with the case of natural convection, the importance of magnetophoresis induced convection is dictated by viscous force and magnetic buoyancy (Camacho, 2011, p. 456). A new concept known as the magnetic Grashof number, Grm, is familiarized to have an improved measureable classification of these binary forces under the setting of magnetophoresis prompted convection (Leong, 2015).The ratio of buoyancy force to the viscous force is done by the Usually the Grashof number, which is given as follows:
Where Lc is the characteristic length and n is the kinematic viscosity of the fluid, T? is the bulk temperature of the fluid, Ts is the temperature of the heating plate, and volume per unit mass is represented by V. (Barbero, 2012, p. 543) The classification of classical Grashof number for a natural convection system was done in five segments and this include the force of gravity, fluid kinetic viscosity, length features, volume per unit mass and transportation driving force. Table 1 displays a failure of the Grashof number as specified over head (Lightfoot, 2007). Similarly, the magnetic Grashof number, and the definition of Grm is normally done based on the five segments of the Grashof number split (Latham, 2009, p. 78). Therefore, Grm is given as follows:
Where MNPs solution kinetic viscosity is represented by n, r is the MNPs solution density, Lc is characteristic length, c? is bulk concentration of MNPs, cs is MNPs concentration of the surface adjacent to the magnet, c is concentration of MNPs solution, and M is magnetization per unit mass of MNPs solution. The magnetophoresis induced convection is noteworthy if Grm is larger than unity (Louie, 2012).
Table 1: Breakdown of the classical Grashof number into five parts in order to facilitate the analogous derivation of the magnetic Grashof number (Morimoto, 2008).
Because Grm is a function of rΛ, its magnitude decreases with respect to the separation distance from the magnet pole due to the rapid decay of ΛB as shown in the figure below:
Figure 6: The plot of distance from magnet pole against magnetic Grashof number of the solution of MNPs at different concentration of MNPs (Obaidat, 2013)
The experimental arrangement in the existing study assist in determining the magnetic Grashof number. The solution of Grm is superior unlike unity. Thi is as a result inevitable convection induced by magnetophoresis, which affects the dynamic performance of the process of magnetophoresis in this experiment (Pankhurst, 2004).
Additionally, based on the calculation, Grm is fewer compared unity only when the concentration MNPs is less compared to 90Kmg/L. Therefore, convection induced through magnetophoresis will always be important for any type of engineering application that involves LGMS (Tang, 2013).
Conclusion
From the experiments above, it is clear that even in an MNPs which isextremely diluted, with 10 mg/L with is concentrated, in which the interaction of MNPs/ MNPs is insignificant, this phenomenon that is hydrodynamic driven is still nontrivial. By taking advantage of this scenario, it is likely to overcome one of the most substantial problems in the implementation of LGMS for large scale engineering applications, which is the tremendously fast decay of ΛB with distance from the magnet that results in the poor separation performance of LGMS.
In conclusion, the fluid/MNPs/ interaction (which is referred as the interaction of hydrodynamic) is the significant fundamental interaction that regulates the magnetophoretic conduct of a solution of MNPs that is experiencing magnetophoresis and it should be considered in the modeling of the design of magnetic separators and the magnetophoresis process.
The kinetics of the LGMS process is dependent not only on the characteristics of the particles but also on concentration as shown in the experiment. There is need of the kinetics of the LGMS process to be categorized by the ratio between the typical separation between particles and the magnetic Bjerrum length, which depends on the dispersion concentration. The times of separation for different concentrations and particles collapse in a single curve which can be described by a simple power law. In summary, a characterization of the driving mechanisms have been provided behind the process of low gradient magnetophoresis separation based in a simple but useful concept (the magnetic Bjerrum length). There are hopes that the results attained in this experiment will be significant in the biomedical and technological applications of low gradient magnetophoresis.
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