Wednesday, October 31, 2012

1210.7905 (P. E. Kornilovitch et al.)

One-dimensional model of inertial pumping    [PDF]

P. E. Kornilovitch, A. N. Govyadinov, D. P. Markel, E. D. Torniainen
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 non-zero 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 two. 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 a non-zero viscosity but to a different degree depending on the microheater location.
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