Deriving an Analytical Model for Hydro-Magnetic Micro Flow Controller

Fluid control, namely pumping and valving, is a critical factor in the performance of micro-fluidic systems. In recent years a variety of micro-fluidic systems are developed for the purpose of miniaturizing fluid handling, and chemical analysis to develop Lab On a Chip (LOC) technology. The mentioned facts resulted in design and fabrication of a novel hydro-magnetic flow controller. The idea behind this device is that magnetic particles, mixed and dispersed in a carrier liquid, can be accumulated in the form of a piston. Depending upon dragging speed of these pistons, which itself is a function of switching time, this device can be used to either increase (pumping) or decrease (valving) the flow rate. The valving characteristic of the setup, which occurs at higher switching times, was concurrent with regular forming of pistons in micro-tube. Experimental results in this part show a meaningful trend for the flow rate changes versus effective parameters of the flow. Considering this fact, lead us to propose a mathematical (analytical) model, which is a function of concerning parameters. Pressure head difference, concentration, material of particles, switching time, working fluid and, switching mode, depending on their complexity, have been introduced into the mathematical model, completely theoretically or semi-experimentally. The equations were derived based on the recognition of the leakage flow through the formed pistons and the pumped flow after each switching. The model was validated by the experimental results for nickel particles of less than 10μ in diameter and 0.5 gNi/100ccH₂O concentration in water for a defined pressure head in a pressure driven flow setup.