Effects of External Magnetic Field on Abrupt Contraction Flow in Ferrofluid

John McDonald and Ryan Madden

Methods of Experimental Physics

Introduction

The flow rate of a ferrofluid is measured under varying pressure, of 0 to 1.5 PSI, and magnetic field strength, of 0 to 1000 Gauss. The rheological response of ferrofluids in contraction and expansion flows is examined when a magnetic field is applied longitudinal and transversal. It is observed that the pressure, needed to produce the flowing of the ferrofluid, is proportional to the applied magnetic field. The ferrofluid volumetric flow rate, the pressure applied and magnetic field strength are the desired variables of this experiment. Ferrofluid is a suspension of ferromagnetic nano-sized particles dispersed in a liquid. In the presents of no magnetic field the particles have a zero magnetic moment and the ferrofluid behaves like a conventional suspension of particulates and like an ideal fluid. When an external magentic field is present the particles become magnetized and attract each other forming chainlike aggregates aligning in the direction of the magnetic field (H).

Experimental Set up and Measurements

The apparatus is shown in figure 2. The flow cell is surrounded by a solenoid. The ferrofluid drip mass (ΔM) is collected by an electric scale, over a time interval (Δt) of 10 seconds. The ferrofluid consists of oxide iron (Fe3O4) particles, 10 nm diameter, submerged in a hydrocarbon oil. The density (ρ) is 1210 Kg/m3. The Magnetic field (H) is calculated with the current through the solenoid. The pressure (P) applied to move the particle chains is measured with electronic pressure gauge. The volumetric flow rate (Q) is calculated with equation 1. v

Theory

The theoretical pressure (P) needed to obtain a certain volumetric flow rate (Q) at a given magnetic field (H) is equation 2.

Where η is the viscosity. θ0 is the half-apex angle. Ms is the saturation magnetization of the particles. Ï• the volumetric fraction of particles in the fluid. Rinf is the cutting radius. R0 is the radius of the orifice. μ0 is the permeability of free space.The theoretical graph at three different pressure is shown below. This plot shows our theoretical flow rate versus magnetic field strength for different pressures. Indicating a drop in flow rate as magnetic field strength increases. Notice the overall trend should remain the same for any pressure

The figure blow shows the therictical pressure needed to produce a flow at a given magentic feild. Our measurement data is the dotted line and shows the same relation. Examine the plot of pressure vs magnetic field strength and notice the pressure required to create a flow is a linear increasing function of magnetic field strength.

Data and Analysis

Our data plots show the expected trend as flow rate decreases with increasing magnetic field strength. We examine a strong linear behavior in the flow rate dependence.

Conclusion

The desired effect for this experiment is a quadratic relationship between volumetric flow rate and magnetic field at given pressure. When the pressure was at zero this effect was observed. However, as the pressure increased to 6.8 and 10.3 kPa the trend turned linear. This is an unknown effect and does not follow the theory. The pressure could have been to high for the magnetic field range used in this experiment. The theory was first applied to magnetorheological fluids in Kuzhir and Bossis’ work [3]. MR fluid should be used in future experiments. This will allow for a true review and analysis of Kuzhir and Bossis’ theory. A Helmoholtz Coil should be used to observe the fluids motion and behavior in a magnetic field. Conducting this experiment in a semi-vacuum would help reduce the factor on temperature of the solenoid. The generation of high magnetic fields from the solenoid needed a large current. This created an increase in temperature causing the resistance to go up reducing the magnetic field.

References

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3) P. Kuzhir, M. T. López-López, and G. Bossis, “Abrupt contraction flow of magnetorheological fluids,” Physics of Fluids (1994-present) 21, 053101 (2009); doi: 10.1063/1.3125947

4) E. B. Bagley, “End corrections in the capillary flow of polyethylene,” J. Appl. Phys. 28, 624 (1957).

5) A. Mongruel and M. Cloitre, “Extensional flow of semidilute suspensions of rod-like particles through an orifice,” Phys. Fluids 7, 2546 (1995).

6) H. L. Weissberg, “End correction for slow viscous flow through long tubes,” Phys. Fluids 5, 1033 (1962).