F16FerroFluid

Introduction

A ferrofluid is an oil-based liquid containing iron based nano-particles. In the absence of an external magnetic field, the particles within the ferrofluid are not magnetized and the fluid behaves as a conventional liquid and follows Newtonian motion. However, when a magnetic field is applied to the fluid, the particles become magnetized and align with the magnetic field. This allows the metallic particles to interact and link together which theoretically causes the ferrofluid to become more viscous. Viscosity is the measure of the flow rate of a fluid. In the simplest case flow rate is expected to have a linear relationship with the viscosity, meaning as the viscosity increases the flow rate of the ferrofluid will decrease. The experiment performed observed the flow rates of a ferrofluid out of a small circular opening in a cylinder. The cylinder containing the ferrofluid was placed inside of a solenoid producing a uniform magnetic field. This magnetic field will cause the nano particles in the ferrofluid to align and clump; this will make the viscosity increase. The relationship between the viscosity and the flow rate is an inverse linear relationship.

By measuring the flow rate as a function of the applied magnetic field a relationship between the strength of the magnetic field and the flow rate of the fluid under a constant pressure can be obtained. For a linear relation between flow and magnetic field, the slope of the resulting linear relationship would give the ferrofluid viscosity.

Theory

A ferrofluid is an oil-based liquid containing metallic nanoparticles. In this experiment the flow rate of ferrofluids through an orifice while exposed to a magnetic field was observed. This flow rate is defined as:

When in the presence of a magnetic field the nanoparticles align and this alignment is expected to cause an increase in the viscosity of the fluid. As viscosity increases, this will show a decrease in flow rate as seen in the equation:

Where pressure P is the pressure difference , radius R, and length of the orifice L remain the same. The only variable that is able to affect the flow rate is the viscosity ŋ. As ŋ is expected to increase with the magnetic field the flow rate is expected to decrease linearly. This can be seen below from the data collected by previous MXP students, as well as other papers read.

Experimental Setup

Figure 1: A diagram of the experimental set up. 1: The scale to measure mass of ferrofluid 2: Cup used to catch ferrofluid 3:Solenoid 4:Pipe filled with ferrofluid 5:Opening to allow ferrofluid to flow and is centered in the solenoid 6: Resistor in series with solenoid 7: leads to DVM used to measure voltage across resistor and DC Power Supply 8: Air pressure sensor 9: DVM and Power source used to for pressure sensor 10: Air tank reservoir 11: Leads to Nitrogen tank and regulator

Results

3 trials were run for each data point. The error for each point was taken to be

with Q the flow rate, M the total mass(always 10 grams for us), sigma mass taken to be .1 g for our scale, t the total time for the trial, and sigma t the human error component, taken to be 100 milliseconds. After averaging, you then divide by the square root of N, with N being 3. As one can see, the shorter the flow time, the more uncertainty in measurements. This can be seen in the data below. The total flow time for 0 PSI was about 13 seconds, 10 PSI ~4 seconds, 25 PSI ~2.5 seconds.

Figure 2. Depicts flow rates at four magnetic field strengths ranging from 0 to 393.5 Gauss with no applied pressure

Figure 3. Depicts flow rates at seven magnetic field strengths ranging from 0 to 789 Gauss with a constant pressure of 10 PSI applied.

Figure 4. Depicts flow rates at seven magnetic field strengths ranging from 0 to 789 Gauss with constant pressure of 25 PSI applied.

Conclusion

It was found that there was no correlation between field strength and ferrofluid viscosity while the opening was at the center of the solenoid. The slopes may appear to be negative, but the scales are zoomed in, and the slopes easily fall within the margin of error of the experiment.

While the results are not what was expected, there are several theories as to why the data we got was not fitting with the papers that were read beforehand. The primary hypothesis is that the experiment should be conducted at the edge of the solenoid, not the middle. This would do two things to the ferrofluid. One, it would produce a magnetic differential, which we believe is more important than actual field strength. With a magnetic differential, the forces in the stronger magnetic field would “pull” the ferrofluid from the weaker to the stronger part of the B-field, thus decreasing flow rate. Also, one would see edge effects of the solenoid. This would cause the chains created by the ferrofluid to bend, and not be parallel to the flow of the ferrofluid, thus decreasing flow rate.Secondly, a couple of the papers that this experiment was based off of simply mention “magnetic fluid,” of which there are two types: ferrofluid and magnetorheological (MR) fluid. Ferrofluid is spherical nano-particles, while MR fluid is shaved iron filings on scales of micrometers. It is believed that MR fluid, because of the asymmetry of the particles, as well as the size, may have a larger impact on the flow rate of the fluid it is in when applied to a magnetic field. It is unknown if a field differential or simply a large static field must be applied to see this effect.

This experiment could be improved upon in several ways. The foremost of which is having a solid base and structure, as ours was suspended by two ring stands. Also, if a large container of ferrofluid could be permanently set on top of the solenoid, instead of having to pour it in every time, this is believed to help. The issues with these are time and money being spent to better the project, as well as expertise to do it correctly.