David P. Markel

Bubble-driven inertial micropump

The fundamental action of the bubble-driven inertial micropump is investigated. The pump has no moving parts and consists of a thermal resistor placed asymmetrically within a straight channel connecting two reservoirs. Using numerical simulations, the net flow is studied as a function of channel geometry, resistor location, vapor bubble strength, fluid viscosity, and surface tension. Two major regimes of behavior are identified: axial and non-axial. In the axial regime, the drive bubble either remains inside the channel, or continues to grow axially when it reaches the reservoir. In the non-axial regime, the bubble grows out of the channel and in all three dimensions while inside the reservoir. The net flow in the axial regime is parabolic with respect to the hydraulic diameter of the channel cross-section, but in the non-axial regime it is not. From numerical modeling, it is determined that the net flow is maximal when the axial regime crosses over to the non-axial regime. To elucidate the basic physical principles of the pump, a phenomenological one-dimensional model is developed and solved. A linear array of micropumps has been built using silicon-SU8 fabrication technology that is used to manufacture thermal inkjet printheads. Semi-continuous pumping across a 2 mm-wide channel has been demonstrated experimentally. Measured net flow with respect to viscosity variation is in excellent agreement with simulation results.

One-dimensional model of inertial pumping.

A one-dimensional model of inertial pumping is introduced and solved. The pump is driven by a high-pressure vapor bubble generated by a microheater positioned asymmetrically in a microchannel. The bubble is approximated as a short-term impulse delivered to the two fluidic columns inside the channel. Fluid dynamics is described by a Newton-like equation with a variable mass, but without the mass derivative term. Because of smaller inertia, the short column refills the channel faster and accumulates a larger mechanical momentum. After bubble collapse the total fluid momentum is nonzero, resulting in a net flow. Two different versions of the model are analyzed in detail, analytically and numerically. In the symmetrical model, the pressure at the channel-reservoir connection plane is assumed constant, whereas in the asymmetrical model it is reduced by a Bernoulli term. For low and intermediate vapor bubble pressures, both models predict the existence of an optimal microheater location. The predicted net flow in the asymmetrical model is smaller by a factor of about 2. For unphysically large vapor pressures, the asymmetrical model predicts saturation of the effect, while in the symmetrical model net flow increases indefinitely. Pumping is reduced by nonzero viscosity, but to a different degree depending on the microheater location.