One-dimensional model of inertial pumping

TL;DR

This paper introduces and analyzes a one-dimensional model of inertial pumping driven by a vapor bubble in a microchannel, revealing optimal heater placement and effects of viscosity on flow.

Contribution

The paper presents a novel simplified one-dimensional model for inertial pumping, including analytical and numerical analysis of symmetric and asymmetric configurations.

Findings

Optimal microheater location exists at low and intermediate vapor pressures.

Asymmetrical model predicts about half the net flow of the symmetrical model.

Viscosity reduces pumping efficiency, with effects depending on heater placement.

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.