The magnetohydrodynamic (MHD) effect is observed in flowing electrolytic fluids and their interactions with magnetic fields. The magnetic field (B0), when perpendicular with the electrolytic fluid flow (μ), causes the shift of the charged particles in the fluid to shift across the length of the vessel (L) normal to the plane of B0 and flow, creating a voltage (VMHD) observable through voltage potential measurements across the flow (Eqn. 1)[1]. 
VMHD=0Lu×B0·dL
(1)
In the medical field, this phenomenon is commonly encountered inside of a human body inside of an MRI machine (Fig. 1).

The effect appears most prominently inside the aortic arch due to orientation and size, and is a large contributing factor to noise observed in intra-MRI ECGs [2, 3]. Traditionally, this MHD induced voltage (VMHD) was filtered out to obtain clean intra-MRI ECGs, but recent studies have shown that the VMHD induced in a vessel is related to the blood flow through it (stroke volume in the case of the aortic arch) [4]. Further proof of this relationship can be shown from the increase in VMHD measured from periphery blood vessels during periods of elevated heart rate from exercise stress, when compared to baseline state [5]. Previously, a portable device was built to utilize induced VMHD as an indicator of flow [6]. The device was capable of showing change in blood flow, utilizing a blood flow metric obtained from VMHD, however a quantitative relationship between VMHD and blood flow has yet to be established.

This study aims to define the relationship between induced VMHD and magnetic field strength in a controlled setting. Through modulating the distance between a pair of magnets around a flow channel, we hope to better realize the relationship between magnetic field strength and induced VMHD with constant flow and electrolytic solution concentration.

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