One-dimensional model of inertial pumping

Abstract

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.

Single-pulse dynamics and flow rates of inertial micropumps

“…Advancing a previous study [17], we report here first successful imaging of single-pulse inertial flow captured with a 4 µs resolution. Consistent with theoretical predictions [17,18], we observe a characteristic N-shape flow in the long arm of the channel. The measured flow rate is used to calibrate the full threedimensional (3D) CFD model [17] and an effective onedimensional (1D) model [18] of inertial pumping to extract the unknown bubble strength.…”

“…Some of them utilize asymmetric nozzle-diffuser geometries [6,7] while others use multiple heaters to create asymmetric heating [8,9] or a traveling vapor plug [10,11,12,13,14]. A more recent development is the inertial pump that relies on dynamic asymmetry of the bubble's expansion-collapse cycle when a microheater is located close to one end of a channel [15,16,17,18,19,20]. Such pumps have characteristic sizes from several microns to hundreds of microns.…”

Microfluidic switchboards with integrated inertial pumps

“…Variations in the channels' width and height, inlet-outlet geometry, and active resistor area can result in device-to-device variations of fluidic resistances on the order of several percent. The inertial pump is a highly nonlinear device [10], which amplifies variations of displaced volume to tens of percent. Secondly, flow rates are very dependent on the physical properties of the fluid under test, primarily temperature, which affects the strength of vapour bubbles, and viscosity.…”

Interactions between two oscillating bubbles in a rigid tube

“…Ory [8] developed the calculation using incompressible viscous N-S equation, finding that a net flow developed when the bubble was not located at the midpoint of the tube. Lately, this pumping effect was studied by Yin [9], Torniainen [10] and Kornilovitch [11], focusing on the development of a one-dimensional model to predict the net flow rate. Besides the pumping effect, researchers were also interested in the bubble deformation and the jet produced by the collapse.…”