## Abstract

Two-phase parallel microflows, i.e., stratified flow and core-annular flow, have many applications in lab-on-chip devices. These include transport and reaction processes, such as liquid-liquid extraction and phase transfer catalysis. The phase holdup (fraction of the microchannel volume occupied by a specified phase) is a key parameter of these flow systems. In this work, mathematical models based on fundamental principles are used to predict the phase holdup in stratified flow and core-annular flow. For stratified flow, a two-dimensional model of flow in a rectangular channel of arbitrary aspect ratio is considered. A simpler one-dimensional model of stratified flow between infinite parallel plates is also analyzed. In the case of core-annular flow, axisymmetry is assumed in the model. The results of the models agree well with published experimental results. The dependence of phase holdup on the flow-rate fraction (the primary operating variable which can be controlled experimentally) is studied in detail. The nature of this relationship varies with the ratio of fluid viscosities and the channel's aspect ratio (in the case of stratified flow). In the literature, the holdup is sometimes erroneously assumed to be identical to the flow-rate fraction. It is shown that this is not possible in the case of core-annular flow, while in stratified flow it is true only for a unique critical flow-rate. This critical flow-rate is viscosity dependent. The aspect ratio of the channel is found to have a considerable influence on the holdup in stratified flow when the fluids have different viscosities. However, even in such cases, there exists a point of geometric invariance at which the holdup is independent of the aspect ratio. At this point, the simple one-dimensional model of stratified flow can predict the holdup with complete accuracy.

Original language | English |
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Pages (from-to) | 1057-1067 |

Number of pages | 11 |

Journal | Microfluidics and Nanofluidics |

Volume | 16 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 2014 |

Externally published | Yes |

## Keywords

- Core-annular flow
- Flow-rate fraction
- Holdup
- Microflows
- Stratified flow