# SIF1006 Practical Physics I

## Question:

Discuss the influence of viscosity on magnetophoresis induced magnetic convection for low gradient Magnetic Separation (LGMS).

Based on the prediction of MNPS/fluid interaction model (Figure 1 below), where the magnetic flux density gradients are highest, there is a way to gradually clear the MNPs from the bottom.

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The simulation results show that this behavior is due to the incompatibility of the magnetic flux density curve from the magnetic pole. This means that MNPs located closer to the magnet experience a greater magnetophoresis force. Therefore, migration takes place at a faster velocity to the origin magnetism (Andreu (2012)).

Figure 1: Magnetophoresis’ velocity magnitude (m/s), for different viscosities

The figure 1 shows time lapse images of MNPs solution that was produced by simulation results interaction between magnetophoresis and non MNRPs/fluid during the initial 1000 seconds following their exposure to the process.

The simulation results are shown in a colour of 0.2Pa.

s indicates the normalized concentration of MNPs solution. This ranges from MNPs viscosity at 0.2Pa.s up to 0.002Pa.s.

MNP experiences 0.203fN magnetophoretic power when it is 1mm away the face of magneticpole with a diameter (30nm) and it corresponds to density gradient LB of 93.8T/m for magnetic flux.

An evaluation showed that similar particles experience a substantially lower force of magnetophoresis (0.038 fN) as the distance between the face of magneticpole and magnetic pole rises to 10mm, with a magnetic flux density gradient of 17.5T/m.

In other words, MNPs will experience a stronger magnetophoresis force and travel faster, so it can be seperated as well as taken from the solution of MNPs more quickly (Bennelmekki 2010, 2010).

The MNPs located at the bottom of the solution are taken from an environment that’s aqueous. This is expected to cause a concentration gradient of particles to the topmost (low-low LB) and starting at the bottommost(high LB) (Berne 2006).

The suspension of MNPs doesn’t cause an interaction between MNPs/MNPs solution. This can be determined by observation of the experiment (Pankhurst 2004 p.78).

The experiment observation is being revealed by the simulation of non-MNPs/fluid interactions magnetophoresis models, which show homogeneity across the entire MNP solution.

There is a significant difference between the predicted magnetophoresis parting profile kinetic profiles and the experiment results.

Below are two major differences between the simulation and experimental results: (1) Simulated results show a slower collection time for MNPs, whereas experiment results showed a more consistent distribution of MNPs, as shown in Figure 2; (2) simulation results predict a shorter simulation run time.

Figure 2: Magnetophoresis concentration profile at one viscosity

Our model system revealed that the failure to use the classical non-MNPs/fluid interconnected magnetophoresis (Rosensweig (2005), p. 543).

The consistency MNPs solution can confirm that magnetophoresis is enhanced by a force.

It could be caused by fluid convection and is often depicted in terms of an important task in mixing or agitating a solution (Camacho 2010, 2010).

The fluid in the vicinity is non-magnetically responsive, so momentum must be gained from the solution MNPs to initiate the convention process.

This observation leads to the conclusion that fluid/MNPs interactions, which cause the hydrodynamic effect and initiate standardization of MNPs, must be the outweighing element.

The dye tracing experiment was performed while MNPs were experiencing magnetophoresis to track the movement of the solution.

Also, a black solution was used for a control experiment. It was found that there was slow and gradual diffusion of dye from the bottommost to the end. (Faraudo 2010).

The dye moved quickly upward in some other MNPs solutions. As shown in the figure, it did so until it was completely filled under magnetophoresis.

Figure 3: Magnetophoresis dye motion under different viscosities. (Dye experiment).

The first row of images shows dye motion when it is exposed to an outside magnetic field. These images were taken during controlled experiment.

The convection occurs during magnetophoresis. Unexpected dye movement can be seen in the MNPs after exposure to an external magnetic force (Andreu (2012), p.89).

Convective flow promotes mixing and homogenizing as well as increases MNPs’ diffusion in the solution.

The harder convective flux of magnetophoresis makes homogenization of dye faster. (Furlani 2007, 2007).

Additionally, the solution homogeneity was established as time passes by the drop in light intensity standard deviation (Heinrich 2007).

Figure 4: Evolution in light intensity standard deviations in the entire solution to MNPs (calculated at about 85 000 pixels) over time.

ImageJ (Birss (2003), p. 56) was used for the investigation of the image.

A low light intensity standard deviation means that there is not much dispersion of sunlight, which leads to consistent dye spreading in the solution. (Oberteuffer (2006), p. 218)

The lines are continually introduced to guide your eyes.

Concentrated solutions have a tendency to increase the dye homogenization rate.

Concentrated MNPs solutions exhibit magnetophoresis because of their strong convection.

It was found that the concentration of MNPs in the solution is what determines the convective motion.

It is not widely known that fluid convection in magnetophoresis is caused by fluid/MNPs interaction. This extraordinary characteristic is what is being presented (Oberteuffer (2006), p. 67).

Fluid convection can be explained macroscopically by using the concept of magnetic bostancy (Holman (2008)).

Figure 5: An object will be immersed in a low-magnetization fluid volume. The body is exposed to an external magnetic field. This will cause the body to reach a region of high magnetic flux density.

If the surrounding fluid is responsive magnetically to the object, then the negative magnetic force will drive it to a location where the magnetic flux density of the object is lower.

The concept of magnetic buoyancy can be illustrated by the motion molecules that aren’t magnetic in nature being immersed into a solution MNPs (Morimoto (2008), p. 126).

The fundamental principle of buoyancy can be used as an orientation. An analogy can be drawn between magnetophoresis of MNPs in experiment conditions and natural convection above a horizontal heatingplate (Jiang (2008)).

Thermal contact between a fluid and a hot horizontal surface causes it to heat up. Fluids with lower density experience lower gravitational forces per unit volume and a higher temperature.

According to Khajeh (2013), gravitational buoyancy forces the fluid’s bottom to rise.

MNPs in the bottom of the solution are constantly depleted because they tend to gravitate towards the section that has a higher magnetic flux density (captured on cuvette walls) due to magnetophoretic collection (Bennelmekki 2010, p. 658).

This results in a temporary drop in concentration of MNPs, and consequently decrease in volumetric magneticization of the bottom portion of the solution (Kowalczyk 2011).

The lower magnetic force per unit of volume experienced by this MNPs solution section is subsequently compared to the upper section.

Thus, MNPs whose magnetization volume is lower are solved by magnetic buoyancy. This forces the fluid at its upper section to move down in order to replace it.

Convective current is thus produced during magnetophoresis in the solution MNPs. This is consistent in Figure 3 (Latham and 2009).

The importance of magnetophoresis induced conection is governed by magnetic buoyancy as well as viscous force.

A new concept, the magnetic Grashof numbers, Grm, has been developed to allow for an improved measurement of these binary forces when magnetophoresis is activated.

Lc denotes the characteristic length of the fluid and n the fluid’s kinematicviscosity. T?

T? is the fluid’s bulk temp, Ts is temperature of the heating plates, and volume per unit weight is represented by V. (Barbero 2012, p. 543). Five segments were used to classify the classical Grashof number for natural convection. They include the force of gravity and fluid kinetic viscosity, length features and volume per units mass as well the transportation driving force.

Table 1 shows a failure in the Grashof numbers as stated over head (Lightfoot 2007).

Similar to the magnetic Grashof, Grm is usually defined based upon the five segments of Grashof number (Latham, 2009 p. 78).

Accordingly, Grm is as follows:

MNPs solution kinetic viscosity, represented by n, is the MNPs density, Lc is the characteristic length, and C is the concentration of MNPs solution.

Bulk concentration of MNPs. cs is the MNPs concentration on the surface next to the magnet. Lc is the characteristic length. M is the magnetization per MNPs solution mass.

Magnetroporesis induced convection will be noted if Grm is greater than unity (Louie (2012)).

Table 1: A breakdown of the classic Grashof number in five parts, to facilitate the analogous derivation the magnetic Grashof amount (Morimoto (2008)).

Grm being a function ofRL, its magnitude decreases in relation to the magnet pole separation distance due to rapid decay of LB. As shown in the figure below.

Figure 6: Diagram of the distance between magnet pole and magnetic Grashof number for solution of MNPs at different concentrations of MNPs (Obaidat 2013).

The existing study’s experimental setup helps to determine the magnetic Grashof number.

Grm is superior to unity.

As a result of inevitable convection in magnetophoresis, Thi affects the dynamic performance (Pankhurst 2004,).

According to the calculation, Grm can be less than unity if the concentration MNPs exceeds 90Kmg/L.

For any engineering application that involves LGMS, convection induced via magnetophoresis will be essential (Tang, 2013,).

Conclusion

These experiments show that even when an MNPs concentration of 10 mg/L is extremely low, the interaction between MNPs/MNPs is not significant, hydrodynamic driven phenomenon is still not trivial.

This scenario will allow LGMS to be implemented for large engineering projects. This is due to the slow decay of LB and the distance from the magnetic field that causes poor separation performance.

In conclusion, the fluid/MNPs/interaction (also referred to as the interaction hydrodynamic) regulates the magnetophoretic conducting of a solution containing MNPs. This interaction should be considered in modeling magnetic separators and the process of magnetophoresis.

The LGMS process’ kinetics is affected by the characteristics of particles as well as the concentration, as demonstrated in the experiment.

It is necessary to categorize the LGMS process by the ratio of the typical separation between particles with the magnetic Bjerrum duration, which is dependent on the dispersion content.

The time taken for particles to separate at different concentrations can be summed up in a single curve that can be described using a power law.

A description of the driving mechanisms behind low gradient magnetophoresis separation has been given. It is based on a simple, but very useful concept called the magnetic Bjerrumlength.

The results of this experiment are likely to be useful in biomedical as well as technological applications of low-grade magnetophoresis.

References

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